Physics Archive: Questions from 2024-06-2

Block A has a mass of 72 kg and rests on block B, which has a mass of 36 kg, as shown in (Figure 1). Part A If the coefficients of static and kinetic friction are indicated in the figure, determine the largest horizontal force P which can be applied to block B so that block A does not slip on block B while block B slides. Express your answer to three significant figures and include the appropriate units. P = Value Units Submit Request Answer Figure 1 of 1

Evaluate the magnitude of the net magnetic force on a current loop of l1 = 2, 1R, l2 = 6R, and r = 2, 1R in an external magnetic field B→ = 3, 2Boj in terms of BoRI. Express your answer using two decimal places.

A ladder 10 feet long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 2 ft/s, how fast is the ladder falling down the wall when the bottom of the ladder is 8 feet from the wall?

(9a) A fireworks rocket is moving at a speed of v0 = 41.7 m/s. The rocket suddenly breaks into two pieces of equal mass, which fly off at different velocities as shown in the drawing. What is the magnitude of v1? (9b) What is the magnitude of v2?

Part A - Distance mass B moves The system is released from rest and mass A moves downward a distance of 3.6 ft, and mass B moves a distance x. What is the value of x ? Express your answer to two significant figures and include the appropriate units. View Available Hint(s) Submit Part B - Find the speed of mass B for a given speed of mass A The system is released from rest and mass A moves downward at a constant speed of 9.6 ft/s. What is the magnitude of the upward speed of mass B ? Express your answer to two significant figures and include the appropriate units. View Available Hint(s) Submit Part C - Find the acceleration of mass B for a given acceleration of mass A The system is released from rest and mass A moves downward with an acceleration of 2.0 ft/s2. What is the magnitude of the upward acceleration of mass B ? Express your answer to two significant figures and include the appropriate units. View Available Hint(s) aB = Value Units

A top view of a 3-way "tug of war" is shown. The three forces are given by F1 is 19.0 N at a direction of 12.5 degrees E of N;F2 is 11.5 N due West; and F3 is 17.5 N due South. There is a 3.50 kg mass is at the origin that is subjected to all forces. Prompts (1) The vector angle of F1? (2) The magnitude of the net force on the object at the origin. (3) The magnitude of the acceleration of the object. (4) The direction of motion of the object. (5) The distance the object travels in a straight line if the forces are maintained for 3.25 s. Answers Select match

The roller-coaster car shown below ( h1 = 41 m, h3 = 28 m, h4 = 11 m), is dragged up to point 1 where it is released from rest. Assuming no friction, calculate the speed at points 2, 3, and 4. State appropriate mks units with your answers. point 2 point 3 point 4 If 115,256 J of thermal energy was generated going from point 1 to point 3 , how fast would a 949 kg roller coaster be going at point 3 ? State the appropriate mks units with your answer.

One particle has a mass of 3.32×10−3 kg and a charge of +8.35 μC. A second particle has a mass of 6.89×10−3 kg and the same charge. The two particles are initially held in place and then released. The particles fly apart, and when the separation between them is 0.109 m, the speed of the 3.32×10−3 kg-particle is 157 m/s. Find the initial separation between the particles. Number Units

The figure shows the distance traveled versus time curve for a toy car. What was the toy car's average speed during the time interval from t = 2 s to t = 8 s?

A block (m = 15 kg) is pushed across the floor a distance of 1.5 m. A force of 53 N is applied at a 30∘ angle above the horizontal as shown in the diagram above. How much work (in joules) was done by the person pushing the block? Report your answer as a positive number.

A safety mechanism of a lift is simplified by the figure below. A 300 kg block is to slide over an inclined surface. The coefficient of friction between the block rollers and the inclined surface is μ = 0.3. If the system is in equilibrium, work out the following: (a) Free body diagram of the complete system. (b) Find the normal force N on the block and the maximum friction force Fmax. (c) Find the mass of the lift mo required to satisfy the equilibrium and prevents the block moving downward, (d) Find tension force in the cable (e) If the mass of the lift is 150 kg, μ = 0.3, and surface angle is increased to 30∘ will the block move upward? Explain the answer.

A 30 kg mass is held against a spring of stiffness 600 N/m on a smooth horizontal surface compressing it by an amount d. When the mass is released from rest (from point A ), the spring accelerates it until it reaches its relaxed length, after which the mass moves away from the spring. It then encounters a rough horizontal patch of length 3.25 m (beginning at point B), with a coefficient of kinetic friction of 1/9. After leaving the rough patch (at point C) the mass continues to move horizontally until it reaches x = 0, after which it moves along the smooth vertical surface described by: y(x) = x3 9 (with x and y in m, for x > 0 ). When the mass reaches x = +2.0 m along the cubic curve (labelled point D on the diagram), its speed is measured to be 2.50 m/s. Ignore air resistance throughout this problem, and take g = 10 m/s2 (in −y direction). a) [5] What initial compression d in the spring was required so the mass arrives at point D moving at 2.50 m/s? b) [5] At point D, what is the instantaneous i) magnitude of the normal force the curve exerts on the mass and ii) the mass' rate of change of speed? (Note: Since you've been given the speed at D, parts a and b are completely independent of each other.)

In the figure the four particles are fixed in place and have charges q1 = q2 = 4 e, q3 = 3 e, and q4 = −12 e. Distance d = 3.99 μm. What is the magnitude of the net electric field at point P due to the particles? Number Units

A block of mass m = 1.10 kg is dropped from height h = 38.0 cm onto a spring of spring constant k = 640 N/m (see the figure). Find the maximum distance the spring is compressed.

A particle of mass m = 3.0 kg is released from rest in position A and then slides down the smooth vertical-plane track. Determine its angular momentum (positive if counterclockwise, negative if clockwise) about both points A and D(a) as it passes position B and (b) as it passes position C. Answers: (a) As it passes B, HA = kg⋅m2/s, HD = kg⋅m2/s (b) As it passes C, HA = kg⋅m2 /s, HD = kg⋅m2/s

A 300-N uniform plank leans against a frictionless wall as shown. The length of the plank is L, and the exact length is not needed to be known to solve this problem. There is friction between the floor and the ladder. Find the minimum coefficient of static friction between the ladder and the floor needed to prevent the ladder from slipping.

The 75 kg student in (Figure 1) balances a 1200 kg elephant on a hydraulic lift. Figure 1 of 1 Part A What is the diameter of the piston the student is standing on? Express your answer with the appropriate units. View Available Hint(s) d = Part B When a second student joins the first, the height difference between the liquid levels in the right and left pistons is 35 cm. What is the second student's mass? Express your answer with the appropriate units. View Available Hint(s) m =

Consider the 58.0 kg mountain climber in the figure. (a) Find the tension in the rope (in N) and the force that the mountain climber must exert with her feet (in N) on the vertical rock face to remain stationary. Assume that the force is exerted parallel to her legs. Also, assume negligible force exerted by her arms. tension in rope N force on feet N (b) What is the minimum coefficient of friction between her shoes and the cliff?

A 28.0 kg block is connected to an empty 2.00 kg bucket by a cord running over a frictionless pulley. The coefficient of static friction between the table and the block is 0.45 and the coefficient of kinetic friction between the table and the block is 0.34 . Sand is gradually added to the bucket until the system just begins to move (Figure 1). Figure 1 of 1 Part A Calculate the mass of sand added to the bucket. Express your answer using two significant figures. msand = kg Submit Request Answer Part B Calculate the acceleration of the system. Express your answer using two significant figures. a = m/s2 Submit Request Answer

(a) A girl is sitting in an old automobile tire which is suspended as shown in figure 3. If the girl and the tire together have a mass of 60 Kg, determine the tension in the ropes CA and CB

Two blocks are connected over a mass-less pulley (see figure below). The mass of block A is 10 kg and the coefficient of kinetic friction is 0.20. Block A slides down the incline at constant speed. (a) What is the mass of block b? (b) If block A is released from rest at a high of 10 m, find the energy of the block when it reach the bottom of the incline.

Total Work By Multiple Forces You pull a 19.0 kg block a distance of 4.50 m by applying a force of Fa = 43.0 N at an angle of θ = 25.0∘, as shown in Figure 2. The frictional force is 18.0 N. Question 3 (1 point) Retake question (b) What is the work done by the frictional force? Your Answer: Answer units Question 4 (1 point) Retake question (c) What is the total work done by all forces acting on the object? Your Answer: Answer units Question 5 (1 point) Retake question (d) If the block starts from rest, what is its speed after travelling the 4.50 m? Your Answer: Answer units Question 6 (1 point) Retake question (e) Determine the speed of the block if there was no friction, but the same force was applied. Your Answer:

Consider the following. (a) Red blood cells often become charged and can be treated as point charges. Healthy red blood cells are negatively charged, but unhealthy cells (due to the presence of a bacteria, for example) can become positively charged. In the figure, three red blood cells are oriented such that they are located on the corners of an equilateral triangle. The red blood cell charges are A = 1.70 pC, B = 7.40 pC, and C = −4.50 pC. Given these charges, what would the magnitude and direction of the electric field be at cell A? magnitude N/C direction counterclockwise from the +x axis (b) If the charge of cell A were doubled, how would the electric field at cell A change? The magnitude of the field would be halved. The field would be unchanged. The magnitude of the field would be quadrupled. The magnitude of the field would be doubled.

Three blocks, A, B, and C, of masses 1, 2, and 3 kg, respectively, are initially at rest on a frictionless surface as indicated in the figure above. What force F has to be applied on block C to accelerate the three blocks at 2 m/s2? F = N

The 1.6−kg block slides along a smooth plane and strikes a nonlinear spring with a speed of v = 5 m/s. The spring is termed "nonlinear" because it has a resistance of Fs = ks2, where k = 600 N/m2. and Part A Determine the speed of the block after it has compressed the spring s = 0.2 m. Express your answer to three significant figures and include the appropriate units. Submit Request Answer

A 15.0 kg rocket is to be launched vertically from the surface of a planet with mass 6.50×1023 kg, a radius of 3.50×106 m, and no atmosphere. With what initial kinetic energy (J) should the rocket be launched for it to reach a maximum height of 7.50×106 m? 4.87×108 8.33×108 9.91×107 2.27×108 1.28×108 4.04×108 5.15×108 2.89×108 3.12×108 3.76×108

The coefficient of kinetic friction between the 2.0 kg block show in the figure and the table is 0.30. What is the acceleration of the 2.0 kg block?

An astronaut of 100 kg at 100 meters from his spaceship finds himself hopelessly drifting away at a speed of 6.06 m/s, he decides to throw a heavy wrench (10 kg) to rescue himself. With what speed (relative to himself) does he need to throw the wrench in order to slow down by 20% of the initial drifting speed (albeit still drifting away)? Note: world record of baseball pitch is over fifty meter per second. Before mA = 100 kg mW = 10 kg

M1 Two packages at UPS start sliding down the 20∘ ramp shown in FIGURE P7.33. Package A has a mass of 5.0 kg and a coefficient of friction of 0.20. Package B has a mass of 10 kg and a coefficient of friction of 0.15 . How long does it take package A to reach the bottom? FIGURE P7.33

Two rail trucks of masses 6000 kg and 2000 kg collide head-on at equal speeds v. Immediately after the collision, the 6000 kg truck stops relative to the ground and the 2000 kg truck moves off with a speed of 6.0 ms−1. a. Determine the initial speed v of the trucks. b. Show that the collision is elastic.

Pulley and Two Blocks Two blocks m1 = 2 kg, m2 = 1 kg are hanging from a pulley as shown in the figure below. The moment of inertia through the axis of rotation passing through the center of the pulley is I = 1.70 kgm2. The ropes are attached at two different distances from the center of the pulley. R1 = 50 cm and R2 = 20 cm. Find the tensions T1 and T2. Pick the correct answer T1 = 21 N, T2 = 17 N T1 = 29 N, T2 = 16 N T1 = 20 N, T2 = 19 N T1 = 24.5 N, T2 = 17.64 N I don't know how to do this problem

Bob is pulling a box of his toys of mass 15.0 kg along a rough horizontal surface for a distance of 6.00 m. The tension force in the rope is 58.0 N and the angle is 30∘ with respect to the horizontal. The frictional force on the box is 18.0 N. How much work is done on the box by the friction force, in Joule? Use g = 10.0 m/s2. Your answer needs to have 3 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.

A 65.0−kg file cabinet of is sliding down a rough ramp for a distance of 5.00 m as shown. The friction force on the box is 75.0 N. Match the answers with questions. (Hint: Clearly draw the force vector and displacement vector for all cases. ) Your answer needs to have 3 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement. What is the angle between the weight force vector and the A. 75∘ displacement vector? B. none of the given What is the angle between the normal force vector and the displacement vector? C. 195∘ What is the angle between the friction force vector and the D. 0∘ displacement vector? E. 180∘ F. 15∘ G. 345∘ H. 90∘

A 65.0-kg file cabinet of is sliding down a rough ramp for a distance of 5.00 m as shown. The friction force on the box is 75.0 N. During this proces5, what is the work done on the cabinet by its own weight, in Joule? Use g = 10.0 m/s2. Your answer noods to have 3 significant figures, inciuding the negative sign in your answer If needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.

A woman at an airport is towing her 20.0 kg suitcase at constant speed by pulling on a strap at an angle of 30∘ above the horizontal. The friction coefficient between the wheels of the suitcase and the floor is 0.5 and the woman pulls on the strap with a 35.0 N force. (a) Draw a free-body diagram of the suitcase (b) What is the magnitude of the normal force that the ground exerts on the suitcase? Hint: Use Newton's Second Law and decompose forces. (c) What is the friction force acting on the suitcase?

Three point objects with masses m1 = 3.0 kg, m2 = 1.2 kg, and m3 = 2.7 kg are arranged in the configuration shown in the figure. The distance to mass m1 is d1 = 24 cm and the distance to mass m3 is d3 = 43 cm. The distances are measured from the axis O. What is the combined moment of inertia I for the three point objects about the axis O? I =

Two boxes, X (mass = 12 kg ) and Y (mass = 8.0 kg ), are connected by a light rope as shown, and can slide along a horizontal rough surface. The force of friction on box X is 24 N and the force of friction on box Y is 16 N. A force is applied that gives the boxes an acceleration of 2.0 m/s2 [east]. Calculate the force the CENTER rope applies on box X. Select one: a. 32 N [W] b. 16 N [E] c. 24 N [W] d. 32 N [E]

In the figure, a uniform sphere of mass m = 0.801 kg and radius r = 0.151 m is held in place by a massless rope attached to a frictionless wall a distance L = 3.00 m above the center of the sphere. Find (a) the tension in the rope and (b) the force on the sphere from the wall. (a) Number Units (b) Number Units

A 2000−kg truck is being used to lift a 400−kg boulder B that is on a 50−kg pallet A. The acceleration of the rear-wheel drive truck is 1 m/s2. Determine the reaction at each of the front wheels. (You must provide an answer before moving on to the next part.) The reaction at each of the front wheel is N↑.

The figure gives the acceleration of a 7.00 kg particle as it moves along an x axis from x = 0 to x = 8.0 m. (Notice the word "acceleration:") At x = 8.0 m, it has a kinetic energy of 42 J. What was its speed (m/s) at x = 0? a(m/s2)

The 1.0 kg block in (Figure 1) is tied to the wall with a rope, It sits on top of the 2.0 kg block. The lower block is pulled to the right with a tension force of 20 N. The coefficient of kinetic friction at both the lower and upper surfaces of the 2.0 kg block is μk = 0.42. For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of Car on rolling board. Figure 1 of 1 What is the tension in the rope holding the 1.0 kg block to the wall? Express your answer with the appropriate units. Part B What is the acceleration of the 2.0 kg block? Express your answer with the appropriate units.

A special pendulum consists of a disk (mass M = 1.0 kg, radius R = 0.2 m, placed vertically so that it is free to rotate around its axis) and a small and dense cylinder of mass m = 0.24 kg attached to the edge of the disk, as shown below. Initially, the system is in the position shown in the figure (the line uniting the disk and cylinder center is horizontal) and released so that it starts to rotate around the disk axis. Determine the maximum velocity of the cylinder. Neglect friction and consider g = 9.80 m/s2. Select one: a. 0.61 m/s b. 0.92 m/s c. 1.08 m/s d. 1.13 m/s

A radio controlled car, with a mass of 3.0 kg, travels counterclockwise around the curved path shown (viewed from above, gravity is directed into the paper). The radius of curvature of the path is 2.0 m. When at the top of the curve (shown) the speed of the car is 2 m/s and it is slowing down with aT = −2.1 m/s2. The car is not slipping. a. What is the frictional force vector that the ground is applying to the car at the point shown? (Express the force in terms of i and j unit vectors.) b. What is the force that the ground is applying to the car in the z-direction (out of the paper)? c. What is the magnitude of the total force that the ground is applying to the car? d. What is the minimum static coefficient of friction such that the car would not slip at the time shown?

A machine part consists of a thin, uniform 4.00−kg bar that is 1.50 m long, hinged perpendicular to a similar vertical bar of mass m_rod = 3.33 kg and length 1.80 m. The longer bar has a small but dense m_ball = 1.88−kg ball at one end (see figure). By what distance will the center of mass of this part move if the vertical bar is pivoted counterclockwise through 90∘ to make the entire part horizontal? HINT: it may be easier to first calculate how much the center of mass moves horizontally and vertically, separately.

In the figure an electric dipole swings from an initial orientation i(θi = 22.4∘) to a final orientation f(θf = 22.4∘) in a uniform external electric field E→. The electric dipole moment is 2.72×10−27 C⋅m; the field magnitude is 3.43×106 N/C. What is the change in the dipole's potential energy? Number Units

In the figure an electric dipole swings from an initial orientation i(θi = 22.3∘) to a final orientation f(θf = 22.3∘) in a uniform external electric field E→. The electric dipole moment is 1.89×10−27 C⋅m; the field magnitude is 3.34×106 N/C. What is the change in the dipole's potential energy? Number Units

Three blocks are connected on the table as shown below. The coefficient of kinetic friction between the block of mass m2 and the table is 0.305 . The objects have masses of m1 = 3.75 kg, m2 = 1.30 kg, and m3 = 1.90 kg, and the pulleys are frictionless. (a) Draw free-body diagrams for each of the objects. This answer has not been graded yet. (b) Determine the acceleration of each object, including its direction. m1: magnitude direction m2: magnitude m/s2 direction m3 : magnitude m/s2 direction (c) Determine the tensions in the two cords. left cord N right cord N (d) If the tabletop were smooth, would the tensions increase, decrease, or remain the same? The tension in the left cord will increase while the tension in the right cord will decrease. The tension in the left cord will decrease while the tension in the right cord will increase. The tensions in the both cords will remain the same.

In the figure, a small block of mass m = 0.015 kg can slide along the frictionless loop-the-loop, with loop radius R = 17 cm. The block is released from rest at point P, at height h = 7R above the bottom of the loop. How much work does the gravitational force do on the block as the block travels from point P to (a) point Q and (b) the top of the loop? If the gravitational potential energy of the block-Earth system is taken to be zero at the bottom of the loop, what is that potential energy when the block is (c) at point P, (d) at point Q, and (e) at the top of the loop? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units

Beginning from rest when θ = 20∘, a 35 kg child slides with negligible friction down the slide which is in the shape of a 2.5 m circular arc as shown below. Determine the tangential acceleration and the speed of the child, and the normal force exerted on her when θ = 30∘.

The spring is placed between the wall and the 10 kg block. If the block is subjected to a force of F = 500 N, determine its velocity when s = 0.5 m. When s = 0, the block is at rest and the spring is uncompressed. The contact surface is smooth.

Consider an inelastic collision between a 1 Kg cart moving to the right at 2 m/s and a 2 Kg cart moving to the left at 4 m/s. What is the speed and direction of the 2 carts after they have stuck together? A mass m1 traveling to the right with a speed v1 makes a glancing collision with a mass m2 initially at rest. After the collision the masses have speeds v1, and v2, and move in directions θ1 and θ2, as shown below. Determine the velocity of m2 after collision (i. e. find v2′)

The spool has a mass of 150 kg and a radius of gyration kG = 0.3 m. If the coefficients of static and kinetic friction at A are μs = 0.2 and μk = 0.15, respectively, determine the angular acceleration of the spool if P = 620 N

A long uniform rod of length 2.00 m and mass 6.00 kg is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest in a vertical position as shown in Figure P10.61. Figure P10.61 (a) What is the angular speed of the rod at the instant it is horizontal? (b) What is the magnitude of the angular acceleration of the rod at the instant it is horizontal? (c) Find the components of the acceleration of the rod's center of mass. ax = ay = (d) Find the components of the reaction force at the pivot. Rx = Ry =

A child of 40 kg slides down a rough slide inclined at 38 degrees. The coefficient of kinetic friction between the child and the slide is μk = 0.31. If the child starts from rest at the top of the slide, a height of 4.8 m above the bottom, how fast is she traveling when she reaches the bottom in m/s?

The figure shows a container of mass m1 = 3.1 kg connected to a block of mass m2 by a cord looped around a frictionless pulley. The cord and pulley have negligible mass. When the container is released from rest, it accelerates at 1.7 m/s2 across the horizontal frictionless surface. What are (a) the tension in the cord and (b) mass m2?

Spheres A (0.020 kg)B(0.030 kg) and C (0.050 kg) are approaching the origin as they slide on a frictionless air table (see figure). The initial velocities of A and B are given in the figure. All three spheres arrive at the origin at the same time and stick together. All three then travel at a speed of 0.50 m/s in the +x direction. (a) Find the magnitude and direction (in terms an angle CCW from +x) of the initial velocity of C. (b) Find the change in the kinetic energy of the system in the collision? Answer: (a) 1.77 m/s, +8.44∘; (b) ΔK = −0.092 J

Problem 14.39 The 9 kg cylinder A and 1 kg cylinder B are released from rest. (Figure 1) Figure 1 of 1 Part A Determine the speed of A after it has moved 2 m starting from rest. Neglect the mass of the cord and pulleys. Express your answer to three significant figures and include the appropriate units. vA =

An object of mass m = 1.00 kg is observed to have an acceleration of a→ with a magnitude of 18.0 m/s2 in a direction θ = 61.5∘ east of north. The figure below shows a view of the object from above. The force F→2 acting on the object has a magnitude of 8.59 N and is directed north. Determine the magnitude and direction of the force F→1 acting on the object. magnitude N direction

A 4.00−kg mass and a 3.00−kg mass are attached to opposite ends of a very light 42.0 - cm-long horizontal rod (Fig.). The system is rotating at angular speed ω = 5.60 rad/s about a vertical axle at the center of the rod. Determine (a) the kinetic energy KE of the system, and (b) the net force on each mass.

Calculate the power required of a 1400 kg car when (a) the car climbs a 10∘ hill at a steady 80 km/hr (b) the car accelerates along a level road from 90 to 110 km/hr in 6 sec to pass another car. Assume the retarding force on the car is Fr = 700 N (Ans: 6.8×104 watt, 6.12×104 watt)

A contestant in a winter games event pulls a 30.0 kg block of ice across a frozen lake with a rope over his shoulder as shown in Figure 4.29 (b). The coefficient of static friction is 0.1 and the coefficient of kinetic friction is 0.03. (a) (b) Figure 4.29 (a) Calculate the minimum force F he must exert to get the block moving. (b) What is its acceleration once it starts to move, if that force is maintained? m/s2

The 100−lb wheel has a radius of gyration of kG = 0.75 ft. If the upper wire is subjected to a tension of T = 50 lb, determine the velocity of the center of the wheel in 3 s, starting from rest. The coefficient of kinetic friction between the wheel and the surface is μk = 0.1.

A 1.6-kg table is supported on four springs. A 0.8−kg chunk of modeling clay is held above the table and dropped so that it hits the table with a speed of 1.65 m/s (Fig. below). The clay makes an inelastic collision up and down. After a long time the table comes to rest 6.0 cm below its original position. (a) What is the effective spring constant of all four springs taken together? (b) With what maximum amplitude does the platform oscillate?

A gymnast with mass 50.0 kg stands on the end of a uniform balance beam as shown in the figure. The beam is 5.10 m long and has a mass of 270 kg (excluding the mass of the two supports). Each support is 0.590 m from its end of the beam. In unit-vector notation, what are the forces on the beam due to (a) support 1 and (b) support 2? (a) Number Units (b) Number Units

Only two forces act on an object (mass = 6.19 kg), as in the drawing. Find the (a) magnitude and (b) direction (relative to the x axis) of the acceleration of the object. (a) Number Units (b) Number Units

A counterweight of mass m = 4.50 kg is attached to a light cord that is wound around a pulley as shown in the figure below. The pulley is a thin hoop of radius R = 6.00 cm and mass M = 2.50 kg. The spokes have negligible mass. (a) What is the net torque on the system about the axle of the pulley? (b) When the counterweight has a speed v, the pulley has an angular speed ω = v/R. Determine the magnitude of the total angular momentum of the system about the axle of the pulley. (c) Using your result from (b) and τ→ = L→/dt, calculate the acceleration of the counterweight. (Enter the magnitude of the acceleration.)

A 50-kg student pulls on a rope attached to a 2-kg box, which moves at constant speed along a smooth surface, as shown. Which of the following corresponds to a force pair? The friction between the box and the surface, and the horizontal component of the push on the box. The normal force on the box and the weight of the box. The push on the box by the student and the push on the student by the box. The vertical component of the push applied by the student and the weight of the box. The weight of the box and the weight of the student. There are no force pairs because the acceleration of the box is zero.

Two blocks, one with a mass of 6 kg and one with a mass of 9 kg, are connected by a rope and are sitting on a frictionless surface. You attach a second rope to the 6 kg block and start pulling with a force of 30 N. What is the tension in the rope between the blocks? 18 N 24 N 36 N 6 N 12 N

In the figure, block A (mass 1.6 kg) slides into block B (mass 2.4 kg), along a frictionless surface. The directions of velocities before and after the collision are indicated; the corresponding speeds are vAi = 5.4 m/s, vBi = 2.0 m/s, and vBf = 4.5 m/s. What is velocity vAf (including sign, where positive denotes motion to the right)? Number Units the tolerance is +/−1 in the 2 nd significant digit

An electric field is constant at every point on a square surface that is 0.80 m on a side. This field has a magnitude of 6.1 N/C and is oriented at an angle of 35∘ with respect to the surface, as the drawing shows. Calculate the electric flux ΦE passing through the surface. ΦE =

A 2.5 -kg block rests on top of a 2-kg block supported by, but not attached to, a spring of constant 40 N/m. The upper block is suddenly removed. Determine the maximum speed reached by the 2 -kg block. The maximum speed reached by the 2−kg block is m/s. Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.

The crates A and B of mass mA = 50 kg and mB = 90 kg, respectively, are connected by a pulley system. The system is released from rest on the inclined surfaces for which θ = 30∘. Friction between A and the inclined surface on which it slides is insufficient to prevent slipping, and friction between B and the incline on which it slides is negligible. The cables in the pulley system are inextensible, and the coefficient of kinetic friction between crate A and the horizontal surface is μk. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Determine the required value of μk so that the speed of B is 7 m/s after it slides 5 m down the incline. (Round the final answer to four decimal places.) Required information

A thin rod with a mass of 3.49 kg and a length of 45.2 cm is free to rotate in the x−y plane and about the z axis, which passes through its center. Initially at rest, a constant torque, τ→ = (34.5 mN⋅m) k^, is applied through 5.48 s. thin rod, perpendicular to rotation axis through center I = 1 12 ML2

In figure, two blocks: m = 10 kg (iron) and M = 5 kg (aluminum) are connected by a rope via a frictionless pulley. The coefficient of Kinetic friction between mass M and the inclined plane is 0.1, θ = 30 degree. Find (a) Acceleration of the hanging mass (b) Tension on the rope

Two blocks, A and B (with mass 55 kg and 130 kg, respectively), are connected by a string, as shown in the figure below. The pulley is frictionless and of negligible mass. The coefficient of kinetic friction between block A and the incline is μk = 0.30. Determine the change in the kinetic energy of block A as it moves from (C) to (D), a distance of 17 m up the incline (and block B drops downward a distance of 17 m) if the system starts from rest. J

The figure shows a plot of the force on a 6.0 kg particle versus the position of the particle along an x axis. The particle moves rightward along the axis. At x = 0, the particle has a kinetic energy of 14 J. What is the particle's speed (m/s) at x = 12 m? 17 2.4 16 2.8 5.0 4.0 3.5 9.0 8.8 4.6

A block of mass m = 1.62 kg slides down a frictionless incline (see the figure). The block is released a height h = 3.91 m above the bottom of the loop. At what speed does the block leave the track?

A 35.0 kg child is standing on a 7.0 kg skateboard holding a 4.2 kg ball. The child throws the ball at a speed of 3.5 m/s relative to the ground. What is the speed of the child and skateboard immediately after they release the ball? Give your answer in m/s to 3 decimal places.

The electric field in a region is given by E = a b+cx x^, where a = 200 Nm/C, b = 2.0 m, and c = 2.0. What is the net charge enclosed by the shaded volume shown below?

part 1 of 2 A block of mass 1 kg and one of mass 7 kg are connected by a massless string over a pulley that is in the shape of a disk having a radius of 0.39 m, and a mass of 9 kg. In addition, the blocks are allowed to move on a fixed block-wedge of angle 31∘, as shown. The coefficient of kinetic friction is 0.25 for both blocks. What is the acceleration of the two blocks? The acceleration of gravity is 9.8 m/s2. Assume the positive direction is to the right. Answer in units of m/s2. part 2 of 2 Find the tension in the horizontal part of the string. Answer in units of N.

A parallelepiped is in an electric field which, to the left of the dashed line, has the value E→left = ⟨−71.42, 0, 0⟩ N/C, and E→right = ⟨71.42, 0, 0⟩N/C to the right of the dashed line. The top and bottom of the parellelepiped are rectangles lying in the x−z plane, and measure l1 by l2, as shown. The left and right faces are rectangles inclined by an angle θ = 75.64∘ from the x axis, and measure l2 by l3. The values of l1, l2, and l3 are 23.62 cm, 10.82 cm, and 31.12 cm, respectively. What charge is contained inside the parallelepiped?

In the figure an electric field is directed out of the page within a circular region of radius R = 4.00 cm. The magnitude of the electric field is given by E = (0.500 V/m⋅s)(1 − r/R)t, where radial distance r ≤ R and t is in seconds. What is the magnitude of the magnetic field that is induced at radial distances (a)3.00 cm and (b) 7.00 cm ? (a) Number Units (b) Number Units

The figure shows a horizontal beam of mass M = 51.3 kg and length L = 6.7 m supported at its left end by a frictionless pin and at the other end by an ideal cable attached to wall h = 8 m above the beam. A mass m = 23.6 kg is suspended from the beam a distance d = 2.2 m from the wall. Find the tension in the cable.

(a) Three point charges are located on the circumference of a circle of radius r, at the angles shown in the figure. What is the electric field at the center of the circle due to these point charges? (Express your answer in vector form. Use the following as necessary: ke, q, and r. ) E→ = (b) What If? What is the minimum electric field magnitude that could be obtained at the center of the circle by moving one or more of the charges along the circle, with a minimum separation of 6.50∘ between each of the charges? Express your result as the ratio of this new electric field magnitude to the magnitude of the electric field found in part (a). Eminimum Epart (a) =

A mass of m = 4 kg is attached to a massless spring of spring constant k = 500 N/m compressed by d = 0.3 m as shown in the figure at right. This spring-mass system is on a table such that the potential energy of the spring is equal to the gravitational potential energy of the mass measured relative to the Ug = 0 reference level shown in the figure. The y coordinate (h) of the mass is: A). 0.3 m B). 0.6 m C). 1.2 m D). 0.9 m

part 1 of 2 A beaker of mass 1.1 kg containing 2.9 kg of water rests on a scale. A 3.2 kg block of a metallic alloy of density 5300 kg/m3 is suspended from a spring scale and is submerged in the water of density 1000 kg/m3 as shown in the figure. What does the hanging scale read? The acceleration of gravity is 9.8 m/s2. Answer in units of N. part 2 of 2 What does the lower scale read?

As in the figure, a small block with mass 0.029 kg can slide without friction on the ramp with a loop at the bottom. The loop radius is R = 10 cm. The mass is released at a point at height h which is 5.7 R above the lowest point. What is the change in gravitational potential energy for the block in going from the starting point to the top of the loop? Ignore the size of the block for this problem. ΔUg = J In the absence of friction, what would the kinetic energy of the block be at point Q (after starting at height h and sliding down the track to that point)? Ignore the size of the block for this problem. K = J In the absence of friction, what would the instantaneous velocity of the block be at point Q (after starting from rest at height h and sliding down the track to that point)? Ignore the size of the block for this problem. v = m/s

Suppose the coefficient of static friction between box A and the floor is 0.4, as shown at right. The coefficient of static friction between box B and a different floor is 0.6, as shown below right. mA = mB = 10 kg. A horizontal 30 N force is applied to each box, and both boxes remain at rest. Is the magnitude of the friction force exerted on box A greater than, less than, or equal to that exerted on box B? The magnitude of friction force on A is greater than the magnitude of friction force on B. The magnitude of friction force on A is less than the magnitude of friction force on B. The magnitude of friction force on A is equal to the magnitude of friction force on B. There is not enough information to answer the question.

A 5.00−kg block is placed on top of a 10.0−kg block (Fig. P5.36). A horizontal force of 45.0 N is applied to the 10−kg block, and the 5.00−kg block is tied to the wall. The coefficient of kinetic friction between all moving surfaces is 0.200. (a) Draw a free-body diagram for each block and identify the action-reaction forces between the blocks. (b) Determine the tension in the string and the magnitude of the acceleration of the 10.0−kg block. Figure P5.36

15-93. Disks A and B have a mass of 15 kg and 10 kg, respectively. If they are sliding on a smooth horizontal plane with the velocities shown, determine their speeds just after impact. The coefficient of restitution between them is e = 0.8.

During a collision, a 1,147 kg vehicle, moving at 17.6 m/s, strikes a parked 1,985 kg vehicle with a force of 394 kN (1 kN = 1000 N). What is the magnitude (in kN) of the force that the parked car exerts on the moving car? F = kN

A father pulls his young daughter on a sled with a constant velocity on a level surface a distance of 10 m, as illustrated in (Figure 1). Figure 1 of 1 If the total mass of the sled and the girl is 31 kg and the coefficient of kinetic friction between the sled runners and the snow is 0.25, how much work does the father do? Express your answer using two significant figures. W = J Submit Previous Answers Request Answer

A person pushing a uniformly-loaded 53.7 kg wheelbarrow of length L with pushing force P→ is attempting to get it over a step. The maximum horizontal force that the person can apply is Px = 265 N. What is the maximum height h of the step, expressed as a fraction n of the wheel's radius R, that the person can get the wheelbarrow over? The gravitational acceleration is g = 9.81 m/s2. h = R

After a mishap, a 77.2 kg circus performer clings to a trapeze, which is being pulled to the side by another circus artist, as shown here. Calculate the tension (in N) in the first rope, T→1, if the person is momentarily motionless. (Enter the magnitude.) N Calculate the tension (in N) in the second rope, T→2, if the person is momentarily motionless. (Enter the magnitude.) N Include a free-body diagram in your solution. (Submit a file with a maximum size of 1 MB.) Choose File no file selected This answer has not been graded yet.

A 2 kg disk rotates at 10 rev/s. Two 1 kg masses are tied to the disk with light string, and are rotating with it at 10 rev/s. At the point of time illustrated, both strings break. The masses move away in straight lines. After the strings break and the masses depart, what is the angular speed of the disk in rad/s?

The two blocks A and B have a mass of 5 kg and 10 kg, respectively. If the pulley can be treated as a disk of mass 3 kg and radius 0.15 m, determine the acceleration of block A. Neglect the mass of the cord and any slipping on the pulley

In the figure, two blocks are connected over a pulley. The mass of block A is 14.0 kg and the coefficient of kinetic friction between A and the incline is 0.260. Angle θ of the incline is 39.0∘. Block A slides down the incline at constant speed. What is the mass of block B? Number Units

Two blocks A and B, of mass 4 kg and 5 kg, respectively, are connected by a cord which passes over pulleys as shown. A 4 kg collar C is placed on block A and the system is released from rest. After the blocks have moved 0.9 m, collar C is removed and blocks A and B continue to move. Determine the speed of block A just before it strikes the ground. (Round the final answer to three decimal places.) The speed of block A just before it strikes the ground is m/s.

During a hammer thrower's practice swings, the 7.1−kg head A of the hammer revolves at a constant speed v in a horizontal circle as shown. If ρ = 0.93 m and θ = 60∘, determine (a) the tension in wire BC, (b) the speed of the hammer's head. TBC = 80.4 N and vA = 2.3 m/s TBC = 40.2 N and vA = 1.15 m/s TBC = 20.4 N and vA = 3.3 m/s TBC = 50.6 N and vA = 4.3 m/s

During a hammer thrower's practice swings, the 7.1 kg head A of the hammer revolves at a constant speed v in the horizontal circle shown. The radius of curvature is .93 m and theta = 60 degrees a) Determine the tension in the wire BC. b) Determine the speed of the head. c) How Far from the thrower will the hammer land assuming that it slips out of his hand is 3 feet above ground and traveling horizontally? Assume no air friction.

In the figure, a 116 kg uniform log hangs by two steel wires, A and B, both of radius 1.20 mm. Initially, wire A was 2.50 m long and 1.75 mm shorter than wire B. The log is now horizontal. Young's modulus for steel is 2.00×1011 N/m2. What are the magnitudes of the forces on it from (a) wire A and (b) wire B? (c) What is the ratio dA/dB?

The figure shows a 2,248-kg plane towing a 161-kg glider. Ignoring drag and friction, calculate the tension in the cable between them if their acceleration is 3.24 m/s2. tension = N

The cart and package have a mass of 25 kg and 12 kg. respectively. If the cart is initially at rest, and the package lands on it as shown, determine the final common velocity of the cart and the package after impact? 0.75 m/s 0.52 m/s 0.84 m/s 1.6 m/s

II. Practice applying the strategy A. A 125 kg gorilla is holding on to a 300 kg branch at a distance of 2/3 from the bottom of the branch (as shown). The angle between the vine and the branch is 30∘. Find the force in the vine and the force at the bottom of the branch ( x and y components, and total). Step 1: Draw all the forces acting on the branch. Identify which forces are known and which are unknown (on diagram). Important: For the contact between the branch and the tree, represent the x and y components of the force the tree exerts on the branch Ftree , x, and Ftree , y. Which direction do they have to go based on the other forces? Step 2: Based on the knowns and unknowns, choose a point of rotation for which to write τnet = 0 which will eliminate all but one unknown. Write that equation and solve for the unknown. Step 3: Use Fnet, x = 0 and Fnet, y = 0 to solve for any other unknowns. Note: this has nothing to do with torques! It's just sum of forces.

A woman at an airport is towing her 20.0 kg suitcase at constant speed by pulling on a strap at an angle θ above the horizontal (Fig. 4.76). She pulls on the strap with a 35.0 -N force, and the friction force on the suitcase is 20.0 N. Figure P4.76 a. Draw a free-body diagram of the suitcase. b. What angle does the strap make with the horizontal? c. What is the magnitude of the normal force that the ground exerts on the suitcase?

Assume the three blocks ( m1 = 1.0 kg, m2 = 2.0 kg, and m3 = 2.5 kg) portrayed in the figure below move on a frictionless surface and a force F = 46 N acts as shown on the 2.5 kg block. (a) Determine the acceleration given this system (in m/s2 to the right). m/s2 (to the right) (b) Determine the tension in the cord connecting the 2.5 kg and the 1.0 kg blocks (in N ). N (c) Determine the force exerted by the 1.0 kg block on the 2.0 kg block (in N ). N (d) What If? How would your answers to parts (a) and (b) of this problem change if the 2.0 kg block was now stacked on top of the 1.0 kg block? Assume that the 2.0 kg block sticks to and does not slide on the 1.0 kg block when the system is accelerated. (Enter the acceleration in m/s2 to the right and the tension in N.) acceleration m/s2 (to the right) tension N

Two blocks A and B with masses mA = 10 kg and mB = 4 kg are connected by an inextensible cable and released from rest shown in Figure 1 (where block A is placed in position C ). The coefficients of kinetic friction between two blocks and the 30∘ inclined plane are μA = 0.1 and mB = 0.3. The cable is in tension in the entire motion and the sizes of blocks are negligible. (Take gravitational acceleration as 10 m/s2) (a) Draw separate free body diagrams of blocks A and B. Indicate clearly all the forces, directions of motion and coordinate systems. [4 marks] b) Based on the free body diagrams in part (a), establish the equations of motion for blocks A and B and determine the tension in the cable between two blocks. [12 marks] (c) Determine the time required for block A to move 2.5 m from positions C to D along the incline and the velocity of block A when it reaches position D. [4 marks] Figure 1

A cubical box (equal side lengths) of mass 1.7 kg (outline shown in blue in the figure) is supported at an angle θ = 16 degrees relative to a horizontal surface. The cable supporting the box is at an angle perpendicular to the in-plane diagonal of the box (shown as a dotted line). What is the minimum coefficient of static friction between the box and the horizontal surface such that the box will not slide?

A body of mass 2.0 kg is moving along the x-axis with a speed of 3.0 m/s at the instant represented below. (a) What is the acceleration (in m/s^2) of the body?

The diving board shown in figure has a mass of 28 kg. The acceleration of gravity is 9.81 m/s2. What is the magnitude of the force required to apply at point A such that the board stays horizonal when a 71 kg diver stands at the end of the diving board. Answer in units of kN.

Blocks A and B, each with a mass of 1.0 kg, are hung from the ceiling of an elevator by ropes 1 and 2. What is the force exerted by rope 1 on block A when the elevator is stationary? 22 N. 12 N. 10 N. 20 N. 2 N.

Three blocks of masses m1 = 1 kg, m2 = 2 kg, and m3 = 4 kg, are connected by massless strings, one of which passes over a frictionless pulley of negligible mass, as shown in the Figure below. Calculate each of the following. (a) a, the acceleration of the system. Answer: 1.4 m/sec2. (b) T1, the tension in the string connected to m1. Answer: 11.2 N. (c) T2, the tension in the string connected to m3. Answer: 33.6 N.

A pulley is massless and frictionless. 3 kg, 2 kg, and 7 kg masses are suspended as in the figure. What is the tension T1 in the string between the two blocks on the left-hand side of the pulley? The acceleration of gravity is 9.8 m/s2. T1 = (13 4 kg) (9.8 m/s2)T1 = (21 4 kg) (9.8 m/s2)T1 = (19 4 kg) (9.8 m/s2)T1 = (5 kg) (9.8 m/s2)T1 = (7 2 kg) (9.8 m/s2)T1 = (17 4 kg) (9.8 m/s2)

4 particles with masses, 1 kg, 2 kg, 3 kg, and 4 kg are located in the coordinate at time 0 shown below. The velocities are 2i m/s, (3i − 3j) m/s, −1.5j m/s, and −4i m/s respectively. What is the total angular momentum of the 4-particle-system about the coordinate's origin.

Problem: A budding gymnast of mass M = 50.0 kg balances herself on a uniform rigid beam of mass m = 12.0 kg as shown. The beam is supported by one support at each end. The supports are a distance L = 2.20 m apart. The gymnast is at a distance d = 0.44 m from the left support. Magnitude of acceleration due to gravity g = 10 m/s2 What is the magnitude of the vertical upward force exerted on the beam by each support? 26. A FL = 500 N, FR = 120 N B FL = 310 N, FR = 310 N C FL = 460 N, FR = 160 N D FL = 160 N, FR = 460 N E FL = 100 N, FR = 60 N

Arlene is to walk across a "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is 10.0∘, as shown below. If her mass is 50.0 kg, what is the tension in the rope at this point? Arelene's weight is 490 N. What is the net force on Arlene if the tension is 1500 N? Is the direction of the net force up or down?

A sled is tied to a tree on a frictionless, snow-covered hill, as shown in the figure. The maximum tension the string can sustain is 40.0 N. If the sled weighs 77.0 N, (a) find the magnitude of the tension force FT→ exerted by the string on the sled, and (b) find the magnitude of the normal force n→ exerted by the hill on the sled. (c) Will the string snap?

The figure above represents the free body diagram for a object of mass 4.4 kg. The magnitudes of the force vectors in the figure are: F1 = 9.8 N F2 = 2.5 N F3 = 6.1 N F4 = 3.1 N And the angle of the plane is θ = 34 degrees In the absence of friction, calculate the x component of the object's acceleration (in m/s^2). Note that the length of the vectors in the picture may not reflect the actual magnitudes of the Forces. Provide your answer as a positive or negative number ONLY, with 1 decimal place (e. g. 1.2 or -1.2). Do not write the units (e. g. s or m or m/s etc.) in the answer box. Do not use scientific notation.

When two objects of unequal mass are hung vertically over a frictionless pulley of negligible mass as in figure (a), the arrangement is called an Atwood machine. The device is sometimes used in the laboratory to determine the value of g. Determine the magnitude of the acceleration of the two objects and the tension in the lightweight string. The Atwood machine. (a) Two objects connected by a massless inextensible (b) The free-body diagrams for string over a frictionless pulley. the two objects. a b

Forces stick-block. In the figure below, a 40 kg block is pushed across a frictionless floor by means of a 3.8 kg stick. The block moves from rest through distance d = 71 cm in 1.5 s at constant acceleration. (a) Identify all horizontal third-law force pairs. (b) What is the magnitude of the force on the stick from the hand? (c) What is the magnitude of the force on the block from the stick? (d) What is the magnitude of the net force on the stick? F→SB = −F→BS (stick and block) (a) F→HS = −F→SH (hand and stick) F→HB = −F→BH (hand and block) (b) Number Units (c) Number Units (d) Number Units

Integrated Concepts - Simple Harmonic Motion, Collision (stick together) As in Figure (a), a 3.91 kg block is attached to a spring with a force constant of 700.00 N/m. The green vertical dashed line indicates the equilibrium position (x = 0). A bullet of 0.075 kg moves toward the block at a speed of v0 = 470.00 m/s. The bullet is embedded in the block after the collision as in figure (b). (i) Find the common speed v of the Block + Bullet after the collision. Hint: What physics law is used for collisions? m/s (ii) The Block+Bullet moves on a frictionless horizontal surface and compresses the spring. What is the x in Figure (c) when the Block+Bullet reaches a momentary rest? Report x as NEGATIVE. m (iii) How much time does it take the Block+Bullet to move from figure (b) to figure (c)? (iv) What is the speed of the Block+Bullet when it reaches x2 = −0.46 m? m/s

The 19-cm-diameter disk in (Figure 1) can rotate on an axle through its center. You may want to review (Pages 304 - 307). For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of Nutcracker. Figure 1 of 1 Part A What is the net torque about the axle? Express your answer to two significant figures and include the appropriate units. Submit Request Answer Provide Feedback

Consider a billiard ball of radius r and mass m struck horizontally by the cue stick at height h with a force P, as depicted in the figure below. The moment of inertia of the ball is IG = 2 5 mr2. Assume the force from the cue stick is much larger than the friction force. a. Given h = 3.5 cm, the ball rolls without slipping, and the ball's angular velocity is ω = 8 rad/s after the impact, determine the radius of the ball and the linear velocity of the ball after the impact.

As shown, three blocks are stacked on top of each other inside a stationary elevator. Answer the following question with reference to the six forces defined as follows: the force of the 3−kg block on the 2−kg block, F3 on 2, the force of the 2−kg block on the 3−kg block, F2 on 3 , the force of the 2−kg block on the 1−kg block, F2 on 1, the force of the 1−kg block on the 2−kg block, F1 on 2 , the force of the 1−kg block on the floor, F1 on floor, and the force of the floor on the 1−kg block, Ffloor on 1. Rank the magnitude of the forces. Rank from largest to smallest. To rank items as equivalent, overlap them. View Available Hint(s) Largest Smallest

Two disks are initially at rest, each of mass M = 4 kg, connected by a string between their centers, as shown in the figure. The disks slide on low-friction ice as the center of the string is pulled by a string with a constant force F = 15 N through a distance d = 2.7 m. The disks collide and stick together, having moved a distance b = 2.0 m horizontally. (a) What is the final speed of the stuck-together disks? vf = m/s (b) When the disks collide and stick together, their temperature rises. Calculate the increase in internal energy of the disks, assuming that the process is so fast that there is insufficient time for there to be much transfer of energy to the ice due to a temperature difference. (Also ignore the small amount of energy radiated away as sound produced in the collisions between the disks.) ΔEinternal = J

A block of mass 8 kg is pushed against a wall by a stick that is oriented at and angle 66∘ with the horizontal direction and is being pulled by a vertical string at the same time. The block is moving along the wall with a constant downward velocity. There is kinetic friction between the block and the wall. Given that the normal force exerted by the stick on the block is 43 N and the tension on the block is 37 N. find the coefficient of kinetic friction between the wall and the block, μk, that allows the block to slide with constant velocity. Use g = 9.8 m/s2 and retain your answer to two decimal places. You are encouraged to draw a free-body diagram in your solution, which will provide you with partial credit if you submit your self-grading later.

Consider two blocks M1 on top of M2 on a level table. There is no friction between block M2 and the table, but there is friction between block M1 and block M2. Denote the coefficients of static and kinetic friction between the blocks as μs and μk, respectively. The applied force F is applied to block M1 at an angle θ below the horizontal. The blocks start from rest. First, we will consider the situation where F is small enough that the two blocks stick together. (a) Draw free-body diagrams for the two masses. Be sure to label all forces and the direction of the accelerations. Also be sure to define an appropriate coordinate system for each free-body diagram. (b) Write down the Newton's second law equations for each block and each dimension (x and y). (c) Write down an inequality relating the force of friction and the normal force. (d) Identify the two Newton's third law pairs - i. e. the pairs of forces between the two blocks that are equal and opposite. (e) Find the acceleration of the blocks as a function of F, θ, M1, M2, g, μs, and μk. (You don't have to use all of these, but you will use at most these. ) (f) Find a condition on F such that the blocks stick together. i. e. Write an inequality in the form F ≤ Fmax for the blocks to stick together where Fmax is in terms of θ, M1, M2, g, μs, and μk.

A block of mass 5 kg is pushed against a wall by a stick that is oriented at and angle 45∘ with the horizontal direction and is being pulled by a vertical string at the same time. The block is moving along the wall with a constant upward velocity. There is kinetic friction between the block and the wall. Given that the normal force exerted by the stick on the block is 69 N and the tension on the block is 24 N, find the coefficient of kinetic friction between the wall and the block, μk, that allows the block to slide with constant velocity. Use g = 9.8 m/s2 and retain your answer to two decimal places. You are encouraged to draw a free-body diagram in your solution, which will provide you with partial credit if you submit your self-grading later.

A uniform rod of weight 5 N is pivoted at point O and two forces of magnitudes 10 N and 20 N are applied on it as shown. Calculate the initial angular acceleration of the bar. (g = 10 m/s2), (Imad = 1/12 MR2 around its center )

1D vertical spring A vertical spring with force constant 180 N/m is compressed by an attached 15 Kg block at rest. At 2.5 m above the 15 Kg block, a 10 Kg block is released from rest. The 10 Kg block falls 2.5 meters and collides with the 15 Kg block, and the collision is completed inelastic (the blocks stick together). The combined 25 Kg will move, compressing the spring more. Calculate how far down the 15 Kg block goes (the maximum magnitude of the downward displacement of the 15 Kg block from the initial position). Type your answer.

A CD has been rotating with angular speed of 2 rad/s and it starts to speed up with angular acceleration of 0.5 rad/s2. A coin stands on the cd 5 cm far from the center as shown. At t = 0, the coin has angular position shown in the figure. At t = 4 s, calculate (a) instantaneous angular velocity, (b) angular position, (c) number of revolutions, (d) speed of the coin, (c) net linear acceleration of the coin, (f) total kinetic energy of the system. (Icd = 1/2MR2, Md = 20 g, mcoin = 10 g, radius of the CD:R = 6 cm)

A large block of mass M is at rest on a frictionless surface and is connected to a spring with force constant k. The spring is initially in its relaxed, equilibrium position. A second block with mass m approaches the first with a speed v0. After they collide, the blocks stick together (due to magnets embedded in the blocks) and move to the right, compressing the spring. Between the initial situation shown above, and the final position when the spring is at maximum compression, which of the following quantities are conserved? Explain your reasoning. Momentum only Energy only Both energy and momentum Neither energy nor momentum B. (10 points) What is the maximum compression of the spring?

Two bullets with masses m1 and m2 are fired to a ballistic pendulum of mass 800 g as shown. The bullets stick in the pendulum and the block begins to rise. What is the maximum height that the block reach? (g = 10 m/s2.)

A 450−g block is pushed against a horizontal spring of negligible mass until the spring is compressed a distance x. The spring constant of the spring is 280 N/m. When it is released, the block travels along a frictionless, horizontal surface to point B, the bottom of a vertical circular track of radius R = 1.00 m, and continues to move up the track. The speed of the block at the bottom of the track is 12.0 m/s. a. What is x? (3 - Appl) b. What is the speed of the block at the top, point T, of the track? (3 - Appl)

Frederik Andersen, a goalie for the Toronto Maple Leafs hockey team is standing on the ice (assumed to be frictionless). Brad Marchand, a hockey player from the despised Boston Bruins, fires a puck ( m = 0.17 kg) at Andersen with a velocity of 65 m/s [east]. a. If Andersen catches the puck, bringing it to a stop with his glove in a time of 5.0×10−3 s, what is the average force (magnitude and direction) exerted on the goalie by the puck? b. Instead of catching the puck, Andersen slaps it with his stick and returns the puck straight back to Marchand with a velocity of 65 m/s [west]. The puck and stick are in contact for a time of 5.0×10−3 s. Now what is the average force exerted on Andersen by the puck?

A 12.0−g wad of sticky clay is hurled horizontally at a 100−g wooden block initially at rest on a horizontal surface. The clay sticks to the block. After impact, the block slides 7.50 m before coming to rest. If the coefficient of kinetic friction between the block and the surface is 0.650 , what was the speed of the clay immediately before impact? (5 - Appl) A curling stone A (mA = 25 kg) is moving at 3.0 m/s [E] down the centre line of the ice toward an opponent's stone B (mB = 15 kg), initially at rest. Immediately after this collision, stone A continues moving with a velocity of 1.8 m/s [E22∘N]. What is the velocity of stone B after the collision? ( 5−Appl)

There are only two forces exerted on the simple meter stick shown in the figure (imagine it is floating in space, for example). The stick is otherwise free to move. The forces are exerted at = 30∘ measured from the meter stick. When measured with respect to an axis through the center of the meter stick, the net torque resulting from the forces exerted on the meter stick is (take clockwise to be positive and counter clockwise to be negative) equation sheet Select one: a. 25 Nm b. 12.5 Nm c. 0 Nm d. 21.7 Nm e. 6.25 Nm

A meter stick is placed on a frictionless horizontal surface and is pinned, so that it is free to rotate about an axis through its 0−cm position, as shown in Figure 14.2. Two forces, F1 and F2, are applied to the meter stick as shown. If the magnitude of F1 = 250 N, F2 = 85 N, r1 = 35 cm, θ1 = 40∘, and θ2 = 60∘, what is the value of r2, such that the meter stick does not rotate? 66.4 cm 76.4 cm 85.0 cm 40.0 cm 79.2 cm

A cable attached to a block holds the block at rest on a frictionless ramp (angle α < 90∘). The ramp exerts a normal force on the car. How does the magnitude of the normal force n and the magnitude of the cable tension T compare to the weight w of the car? n < w, T > w n = w, T < w n = w, T = w n < w, T < w n = w, T > w

A block of mass 22 kg is pushed by a stick that is oriented at and angle 41∘ with the horizontal direction and is being pulled by a horizontal string at the same time. The block is moving along the floor with a constant velocity to the right. There is kinetic friction between the block and the floor. Given that the normal force exerted by the stick on the block is 101 N and the tension on the block is 11 N, find the coefficient of kinetic friction between the floor and the block, μk, that allows the block to slide with constant velocity. Use g = 9.8 m/s2 and retain your answer to two decimal places. You are encouraged to draw a free-body diagram in your solution, which will provide you with partial credit if you submit your self-grading later.

A block is moving to the right across a rough table at a constant speed of 2 m/s. The tables and the blocks are identical in the two cases. In case A, the block is pushed with a stick and in case B, the block is pulled with a string. The angle that the applied force makes with the horizontal is the same in both cases. The magnitude of the force on the block by the stick in case A is greater than the tension on the block by the string in case B. The magnitude of the force on the block by the stick in case A is less than the tension on the block by the string in case B. The magnitude of the force on the block by the stick in case A is equal to the tension on the block by the string in case B.

In this problem we will consider the collision of two cars initially moving at right angles. We assume that after the collision the cars stick together and travel off as a single unit. The collision is therefore completely inelastic. As shown below, two cars collide. Car one has an initial mass and velocity of m1 = 1,140 kg, and v1 = 15.2 m/s. Car two has a mass of m2 = 1,570 kg and an initial velocity of v2 = 22.4 m/s. Find the magnitude and direction of the final two car system's momentum. Figure 2. Two cars collide at a right angle, car one is moving to the left, and car two is moving upward.

Two identical carts A and B roll down a hill and collide as shown in the figure below. i) A starts from rest. It rolls down and collides head-on with B which is initially at rest on the ground. The two carts stick together. ii) A and B are at rest on opposite sides of the hill. They roll down, collide head-on and stick together. Which statement is true about the two-cart system just after the carts collide in the two cases? Select all that are True. The momentum of the system is the same in both cases (but no zero). The momentum of the system is greater in case (i) than in case (ii). The momentum of the system is zero in case (ii). The momentum of the system is greater in case (ii) than in case (i).

A block is being pressed against a vertical wall with external force F→ and sliding down (as shown in the figure). When it slides down for a distance of d, what is the expression for the work done by the external force F→ during the process? Pick the correct answer Fdcos⁡(γ) Fdsin⁡(γ) Fdcos⁡(β) Fdsin⁡(α) Fdcos⁡(α) The work done by the external force on the block is: Pick the correct answer Positive Cannot determine Zero Negative

A rectangular coil of wire, 22.0 cm by 35.0 cm and carrying a current of 1.40 A, is oriented with the plane of its loop perpendicular to a uniform 1.50-T magnetic field, as shown in figure. Calculate the net force and torque that the magnetic field exerts on the coil.

Colliding discs Two discs are initially at rest, each of mass M, connected by a string between their centers, as shown in the figure. The discs slide on low-friction ice as the center of the string is pulled by a string with a constant force F through a distance d. The discs collide and stick together, having moved a distance b horizontally. a. What is the final speed of the stuck-together discs? b. When the discs collide and stick together, their temperature rises. Calculate the increase in internal energy of the discs, assuming that the process is so fast that there is insufficient time for there to be much transfer of energy to the ice due to the temperature difference. (Also ignore the small amount of energy radiated away as sound produced in the collisions between the discs.)

The force component acting on an object along the displacement varies with the displacement s as shown in the graph. 1) Determine the work done on the object as it travels from s = 0.0 to 12 m. 2) Calculate the final velocity after the 12 m distance traveled by the car. 3) What is the power generated by the force in the mentioned interval.

The boxes are stacked as shown. The force P is 40−lb. Determine the maximum acceleration of the top block Determine the acceleration of the system if they stick together Determine if the top block slips relative to the bottom block Determine the actual accelerations of each block. Ans: 9.66, 12.88

A puck slides on a frictionless table hitting a block. In which scenario does the puck exert the most force on the block? A B C

Two blocks, with masses m1 = 2.5 kg and m2 = 14 kg, approach each other along a horizontal, frictionless track. The initial velocities of the blocks are v1 = 1.20 m/s to the right and v2 = 0.34 m/s to the left. The two blocks then collide and stick together. Part A Which of the graphs in (Figure 1) could represent the force of block 1 on block 2 during the collision? B C D A

Two disks are initially at rest, each of mass M = 4 kg, connected by a string between their centers, as shown in the figure. The disks slide on low-friction ice as the center of the string is pulled by a string with a constant force F = 11 N through a distance d = 2.6 m. The disks collide and stick together, having moved a distance b = 1.9 m horizontally. (a) What is the final speed of the stuck-together disks? vf = m/s (b) When the disks collide and stick together, their temperature rises. Calculate the increase in internal energy of the disks, assuming that the process is so fast that there is insufficient time for there to be much transfer of energy to the ice due to a temperature difference. (Also ignore the small amount of energy radiated away as sound produced in the collisions between the disks.) ΔEinternal = J

Two pieces of tofu slide across the table towards each other. The first piece ( m = 82.1 g) travels to the right at 10.3 m/s, while the second piece (m = 107.4 g) moves to the left at 11.4 m/s. Upon contact, the two pieces of tofu stick together, as one large, glorious piece of tofu. What is the final speed of the combined tofu after the collision. [Answer in m/s with 3 sig digits, but do not enter the units with your answer] Your Answer:

A 0.17- kg hockey puck is sliding to left with a speed of 15 m/s when it is hit by a hockey stick. If the puck is in contact with the stick for 0.15 s and it rebounds with a speed of 32 m/s, what was the average force exerted by the hockey stick on the puck? Assume the amount of friction or air resistance acting on the puck is negligible. (a) Fav = 2.89 N (b) Fav = 7.99 N (c) Fav = 19.3 N (d) Fav = 53.3 N (e) Fav = 313 N

One end of a M = 0.1 kg meter stick is attached to a wall, and provided with a pivot. A vertical force F is applied to the other end to make the net torque about the pivot point zero. What is the magnitude of F and the direction of the torque produced by F. F = 0.5 N, torque = 0.5 Nm into the page. F = 0.1 N, torque = 0.1 Nm out of page. F = 0.5 N, torque = 0.5 Nm out of page. F = 0.1 N, torque = 0.2 Nm out of page. F = 1 N, torque = 1 Nm upward.

Drawing free body diagrams a) A book is at rest on a table. Draw a free body diagram showing all forces acting on the book. b) A man pushes a box in the direction of the arrow shown. Draw a free body diagram showing all forces acting on the box. c) Block 1 and Block 2 are hung over a frictionless pulley. Assume Block 1 is sitting on a frictionless surface. Block 1 has a mass of 5.0 kg and Block 2 has a mass of 2.0 kg. Draw a free body diagram for both blocks.

The acceleration of these blocks is found to be 5.0 m/s2 when pushed by a 120 N force. Set up the equations for the system and find the normal force on each mass, and the polar form of the force exerted on the 5 kg block by the stick. Answers: n1 = 69.0 N, n2 = 78.0 N. C = (63.2 N, −27.3∘)

A uniform meter-stick of mass M = 10 kg is hanging with the support of a hinge A and a cable at an angle θ = 45∘ as shown in the figure below. If the block of mass m = 8 kg moves beyond x = 0.73 m from hinge A, the cable breaks. Find the maximum tension T the cable can withstand. [5 Pts]With the block placed at x = 0.5 m, what are the horizontal and vertical components of the force on the bar from hinge A ? [10 Pts] Suppose the block of mass m is now at x = 0.74 m and the cable breaks, what is the angular acceleration of the system right after the cable breaks (You can assume that the block is a point mass)? [5 Pts]

A ball moves in the direction of the arrow labeled c in the figure. The ball is struck by a stick which briefly exerts a force on the ball in the direction of the arrow laveled e in the figure. Which arrow best describes the direction of Δ[(p)\vec], the change in the ball's momentum? j zero magnitude b c e g i a f j zero magnitude h d

A small block of mass m rests on the rough, sloping side of a triangular block of block of mass M which itself rests on a horizontal frictionless table (see the figure). The rough incline surface has a coefficient of static friction μs. A) Suppose that you apply a horizontal force F to push the triangular block (see the figure). Explain what will happen to the small block if the applied force F is relatively small. You gradually increase force F, and explain what will eventually happen to the small block as the force is sufficiently large. B) Draw a free body diagram for each of the blocks m and M. What is the direction of acceleration of these two blocks when they stick and move together? How many forces act on each of the blocks m and M? How many Newton's 3rd law force pairs are there in these two free body diagrams? Set up a coordinate system fixed to the table. Is the block M an inertial frame? C) Determine the minimum horizontal force F such that the small block will start moving up the incline. Draw coordinate systems, and write down intermediate steps with equations.

The loaded cab of an elevator has a mass of 4.20×103 kg and moves 220 m up the shaft in 17.0 s at constant speed. At what average rate does the force from the cable do work on the cab? Number Units

A uniform stick of length l and mass m is held horizontally. At t = 0 it is released. At the same time, a sharp upward blow by a force of magnitude F and direction perpendicular to the stick is applied at a distance d from the center for a duration Δt. The stick flies up into the air and falls back under gravity. Determine the distance d such that when the center of the stick falls back to the same height it started with, the stick will have rotated exactly once. Assume that the force F is much larger than the force of gravity during the time the impulse is applied, and that Δt is very small in comparison to the time the stick is in the air. The stick has a moment of inertia about an axis passing through the center of mass given by ICM = 1 12 ml2. Express you answer in terms of some or all of the following: pi for π, g, l, m, F and Deltat for Δt. d =

A thin rod is attached to a pivot point (with negligible friction), which is affixed to a wall. The other end of the rod is attached to a vertical spring as shown in the figure below. (i) The rod's mass is m = 6.50 kg and its length is L = 6.00 m. The spring constant is k = 660 N/m. The rod is initially horizontal and in equilibrium when its end is pulled up by a small angle θ and released. What is the angular frequency (in rad/s) of the rod as it oscillates in simple harmonic motion? rad/s

Rank the following torques applied to a stick of length L, positive torques are greater than negative ones. The force F has twice the magnitude of the force D and the turning point of each system is marked with a star. All forces are perpendicular to the rod. The forces either act at the middle or the end of the rod. Use the sign convention discussed in class. a) = b) > c) a) > b) > c) c) > b) > a) c) > a) > b)

The figure shows three blocks being pushed across a frictionless floor by horizontal force F→ = 24 N. What is the magnitude of the force on the block of 2 kg exerted by the block of 10 kg? 17 N 14 N 10 N 6.4 N 2.8 N

The 13-cm diameter disk in (Figure 1) can rotate on an axle through its center. Figure Part A What is the net torque about the axle? Express your answer in newton-meters to two significant figures. τ = N⋅m

A large block of mass M is at rest on a frictionless surface and is connected to a spring with force constant k. The spring is initially in its relaxed, equilibrium position. A second block with mass m approaches the first with a speed v0. After they collide, the blocks stick together (due to magnets embedded in the blocks) and move to the right, compressing the spring. What is the maximum compression of the spring?

Three dogs are pulling on a stick in different directions as shown in the figure. The first dog pulls with force F1 = 10i −20.4j + 2k N. The second dog pulls with force F2 = −15i − 6.2k N. The third dog pulls with force F3 = 5i + 12.5j N. a) What is the angle between F1 and F2? b) Find the point-normal equation of the plane containing F2 and F3 and the point P(1, 1, 1). c) Find the distance between the point P(1, 2, −3) and the plane in (b).

As shown in the figure below, a block of mass m is compressed into a spring of force constant k and then released. The block then moves along a frictionless surface hitting another block of same mass m located at the entry of a vertical frictionless loop track of radius R. The two blocks stick together and move around the loop. As they exit, they encounter a frictional surface with kinetic friction coefficient μk. a. During the collision is momentum conserved? And is the collision elastic or inelastic? Explain. All your answers to the questions below should be in terms of the given quantities m, k, R, μk, and g. b. Find the minimum spring compression distance s for the blocks to traverse the vertical loop without falling off the track. c. For the spring compression found in part b., calculate the distance L traveled by the pair of blocks before stopping.

As shown in Figure 3(a), a wooden block B with mass mB = 2.4 kg on a rough inclined plane is connected to a massless spring ( k = 160 N/m ) by a massless cord passing over a pulley P of radius R = 0.25 m and mass Mp = 0.60 kg. The angle of the inclined plane is θ = 37∘ and the coefficients of static and kinetic frictions are μs = 0.35 and μk = 0.30 respectively. The frictional force at the axle of the pulley is negligible. The pulley can be regarded as a solid disk. (a) The system is at rest and in this case, block B is on the verge of sliding down. Figure 3(a) i. Indicate (with labeled arrows) the forces acting on the pulley and the block. ii. Calculate the tension in the string and the extension of the spring. (You can assume that the tensions in the cord on either side of the pulley P are the same for this part.) (b) As shown in Figure 3(b), another wooden block A of mass mA = 1.2 kg made of the same material as block B is released from rest. It slides down a distance l down the rough inclined plane and collides with block B. The two blocks stick together and move down the incline with a common velocity v = 0.80 m/s immediately after collision and the pulley rotates. The cord does not stretch and does not slip on the pulley. Figure 3(b) i. Determine the distance l. ii. Determine the acceleration of the two blocks at the moment they move down together and the pulley starts to rotate. iii. Determine how much further down the slope the two blocks move together after they collide before the two blocks come to a momentary rest.

As a torque activity, your Physics TA sets up the arrangement shown below. A uniform rod of mass mr = 173 g and length L = 100.0 cm is attached to the wall with a pin as shown. Cords are attached to the rod at the r1 = 10.0 cm and r2 = 90.0 cm mark, passed over pulleys, and masses of m1 = 266 g and m2 = 167 g are attached. Your TA asks you to determine the following. (a) The position r3 on the rod where you would suspend a mass m3 = 200 g in order to balance the rod and keep it horizontal if released from a horizontal position. In addition, for this case, what force (magnitude and direction) does the pin exert on the rod? Use standard angle notation to determine the direction of the force the pin exerts on the rod. Express the direction of the force the pin exerts on the rod as the angle θF, measured with respect to the positive x-axis (counterclockwise is positive and clockwise is negative). r3 = m Fp = N θF = (b) Let's now remove the mass m3 and determine the new mass m4 you would need to suspend from the rod at the position r4 = 20.0 cm in order to balance the rod and keep it horizontal if released from a horizontal position. In addition, for this case, what force (magnitude and direction) does the pin exert on the rod? Express the direction of the force the pin exerts on the rod as the angle θF, measured with respect to the positive x-axis (counterclockwise is positive and clockwise is negative). m4 = kg Fp = N θF = (c) Let's now remove the mass m4 and determine the mass m5 you would suspend from the rod in order to have a situation such that the pin does not exert a force on the rod and the location r5 from which you would suspend this mass in order to balance the rod and keep it horizontal if released from a horizontal position. m5 = kg r5 = m

A block of mass m = 1 kg is released from rest at the top of a smooth hemispherical bowl of radius R = 2 m. Lying at the bottom of the bowl there is a second block of mass m = 1 kg. Assuming the surface of the bowl is frictionless, find: If the masses stick together after they collide, how high above the bottom of the bowl will the two masses go before starting to slide back down? 1.5 m 2 m 0.1 m 0.5 m 1 m

Starting from rest, a small block of mass m = 0.25 kg slides down an incline from a height h = 1.2 m. As it slides down, the block experiences a force of kinetic friction of constant magnitude fk = 2.1 N only over a distance L = 0.2 m, as shown in the figure. The incline is frictionless everywhere else. After reaching the bottom of the incline, the block strikes a larger block of mass M = 1.8 kg that is attached to a spring of spring constant k = 6.5 N/m. The large block was originally at rest. The blocks stick together upon impact and travel together on the frictionless horizontal surface. Assume that both blocks are subject to the regular force of gravity (g = 9.80665 m/s2). (a) Determine the speed of the small block right before it collides with the larger block. Answer: m/s (b) Determine the speed of the combination of the two blocks immediately after the collision. Answer: m/s (c) Determine the compression of the spring when the combination of the two blocks comes to rest. Answer: m

Stick Guy pulls a 18−kg crate of stuff across a rough floor with a constant applied force, Fapp = 39.6 N, accelerating it from rest to a speed of 3.4 m/s over a distance of 4.6 m. (a) What was the change in the crate's KE, PE, and ME? ΔKE = J ΔPE = J ΔME = J (b) How much work was done on the crate? Wnet = J (c) How much work was done on the crate by non-conservative forces? Wnc = J (d) How much work did Stick Guy do on the crate? Wapp = J (e) What can you conclude about the work done by friction? Wf = J (f) The magnitude of the frictional force acting on the crate is therefore: f = m = N

In the figure, block 2 (mass 1.70 kg ) is at rest on a frictionless surface and touching the end of an unstretched spring of spring constant 294 N/m. The other end of the spring is fixed to a wall. Block 1 (mass 1.10 kg ), traveling at speed v1 = 5.70 m/s, collides with block 2, and the two blocks stick together. When the blocks momentarily stop, by what distance is the spring compressed? Number Units

Three blocks with masses, m1 = 1 kg, m2 = 2 kg, and m3 = 4.0 kg, are pulled to the right across a horizontal frictionless surface by a constant force, F = 48 N, that acts on the large block as shown in the figure. Two of the blocks, m1 and m3, are connected by an ideal rope while the smallest block, m2, is sitting directly in front of m1 as shown. Take right as the positive direction. Version One. (a) Find the acceleration of the system? m/s2 (b) Determine the magnitude of the tension in the rope between m1 and m3. N (c) What is the magnitude of the normal (contact) force between m1 and m2 ? N Version Two. What if block m2 was placed on top of block m1 instead of in front of it? (a) What would be the acceleration of the system and tension in the rope if m2 and m1 stuck together? a = m/s2 T = N (b) What if the blocks were made of ice so that m2 and m1 didn't stick together? At what rate would each block accelerate? a1 = m/s2 a2 = m/s2 a3 = m/s2 a3 = What would be the tension in the rope?

A 11.4 kg block is pushed d = 2.00 m across a rough horizontal surface with a force of F = 11.0 N, at an angle of 14.0 degrees below the horizontal. How much work is done on the block by the force F? [Answer in units of J with 3 sig digits, but do not enter units with your answer] Your Answer:

There are only two forces exerted on the simple meter stick shown in the figure (imagine it is floating in space, for example). The rod is otherwise free to move. When measured with respect to an axis through the center of the meter stick, the net torque resulting from the forces exerted on the meter stick is 38 N∗m 76 N∗m 17 N∗m 0 N∗m IDON'T KNOW YET

A clay block of mass m moving to the right with speed v0 strikes a second block of mass 3 m moving to the left with the speed v0/3. The two clay blocks stick together after the collision. There are no outside forces acting on the blocks. How much kinetic energy was lost in this inelastic collision?

There are only two forces exerted on the 1-meter long stick shown in the figure (imagine it is floating in space, for example). The stick is not uniform, with its center of mass 70 cm from the left end of the stick, as indicated by point A in the figure. When measured with respect to an axis through the center of mass (point A), the magnitude of the net torque resulting from the forces exerted on the stick is 15.2 N∗m 0 N∗m I AM UNSURE 26.6 N∗m 11.4 N∗m IDON'T KNOW YET

Three blocks are in contact on a frictionless, horizontal table top. An external force is applied to block 1 and the three blocks are moving with a constant acceleration of 4.45 m/s2. Determine the contact force between th e blocks m1 and m2. Express your answer in Newtons. Use m1 = 3.40 kg, m2 = 6.25 kg and m3 = 4.60 kg

To keep a door closed, a wooden stick is wedged between the floor and the doorknob. The stick exerts a 265−N force at B directed along line AB. Replace that force with an equivalent force-couple system at C. The magnitude of an equivalent force at C is ( N)i+( N)j+( N)k. The magnitude of an equivalent couple at C is MC = ( N⋅m)i+( N⋅m)j+( N⋅m)k.

Integrated Concepts - Simple Harmonic Motion, Collision (don't stick together) Keep 3 decimal places. The green vertical dashed line in the figures indicates the equilibrium position (x = 0). In Figure (a), a 4.23 kg block is attached to a spring with a force constant of 710.00 N/m and the spring is compressed to x = −A = −0.68 m. The block is then released and moves on a frictionless horizontal surface. (b) What is the speed of the Block when it reaches x1 = −0.204 m in Figure (b)? Enter a number m/s

A block with a mass of m1 = 2.8 kg is pushed to the right with a force of 278 N for a distance of 8.7 m across a horizontal frictionless surface, after which the force is removed. The 2.8−kg block then collides with a second block with a mass m2 = 4.8 kg, which is initially at rest. The two blocks stick together after the collision. 1) Determine the change in the internal energy of the system of blocks during the collision. 2) Submit Now assume that the 4.8-kg block is traveling at 5.3 m/s to the left before the collision. The two blocks will still stick together after the collision. Determine the change in the internal energy of the system of blocks. Submit

Forces of 56 N and 52 N are applied at the ends of a meter stick and a force of 65 N is applied at its center as shown. Determine the magnitude of the torque on the meter stick due to these forces about the point P. 18 Nm 2.7 Nm 62 Nm 80 Nm

A 200 kg block is pulled at a constant speed of 6.9 m/s across a horizontal floor by an applied force of 119 N directed 38∘ above the horizontal. What is the rate at which the force does work on the block? Number Units

A horizontal underwater plastic meter stick, of mass 407 g and volume 3× 10−4 m3, has two additional forces acting on it. There is a downward force of 2 N applied to the left end of the stick and a 6 N force to the right acting on the extreme right end of the stick. [Hint: The buoyant force on a symmetric body of uniform density acts at the geometric center of the body.] Assume g ≈ 10 N/kg. (a) If we want to suspend the stick from a single cable, how far from the left end of the stick must the force be applied? r = m ( ± 0.01 m) (b) What will be the tension in the cable? T = N ( ± 0.02 N) (c) What angle will the cable make with the vertical? θ = ∘( ± 0.1∘)

As shown in the figure below, blocks A and B move on a frictionless horizontal surface and make a completely inelastic collision. Their masses are mA = 1.0 kg and mB = 3.0 kg. Before collision, their x-velocities are vA1x = 5.0 m/s and vB1x = −1.0 m/s. After the completely inelastic collision, both blocks stick together and move with velocity v2x. What is v2x?

A 60.0 kg skier starts from rest at the top of a ski slope 63.0 m high. (a) If friction forces do −10.9 kJ of work on her as she descends, how fast is she going at the bottom of the slope? (b) Now moving horizontally, the skier crosses a patch of soft snow where μk = 0.21. If the patch is 65.0 m wide and the average force of air resistance on the skier is 180 N, how fast is she going after crossing the patch? (c) The skier hits a snowdrift and penetrates 3.0 m into it before coming to a stop. What is the average force exerted on her by the snowdrift as it stops her?

What is the tension in the rope of Figure 4? Ignore the friction between the man's hands and the rope. Consider that the pulley is ideal, and the rope is massless. (To get full marks you must include free-body diagrams)

A conductive rod, 20 cm long and 10 Ω electrical resistance, moves parallel to itself and without friction, with a speed of 5 cm/s, on a U-shaped conductor, of negligible resistance, located in the inside a magnetic field of 0.1 T. Calculate the magnetic force acting on the electrons in the bar and the electric field inside it. Find the electromotive force that appears between the ends of the rod and the intensity of the electric current that runs through the circuit and its direction. What external force must be applied to keep the rod moving? Calculate the power needed to keep the rod moving.

Figure below shows 3 positions of a dipole, composed of two charges (+q) and (-q) separated by distance d, in uniform electric field E→. Which position corresponds to minimum electric potential energy of the dipole? (a) (b) (c) a) Position (a) b) Position (b) c) Position (c) d) None of previous positions

A 40 kg, 5.0-m-long beam is supported by, but not attached to, the two posts A and B in the figure. A 20 kg boy starts walking along the beam and stops 1.2 m from the right end of the besm. The beam does not tip. a) Draw a fully labelled force diagram for the beam b) Calculate the magnitude of the force exerted by the post B on the beam

The figure shows two charged particles fixed in place. How much work (J) must we do to bring in a third charged particle (Q = +9 e) to the point P indicated, starting from an infinite distance? d1 = 2.00 m, d2 = 5.00 m, q1 = +6 e, q2 = −8 e. 4.67×10.28 1.28×10−28 2.90×10−27 5.67×10−27 6.90×1028 8.54×10.28 7.08×1028 9.67×10−28 3.46×10−27 4.22×10.28

Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of 20.0∘ with the horizontal (see below). He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate and on his body to get up the ramp.

A block of mass 0.60 kg is dropped onto a vertical weightless spring. The spring is initially unstretched. The speed of the block just before it makes contact with the spring is 2.0 ms−1. The block instantaneously stops when the spring is compressed through a distance of 5.1 cm. a. Calculate: i. the initial kinetic energy of the block ii. the work done on the block by the gravitational force, since the first contact with the spring until it stops iii. the elastic potential energy stored in the spring at the instant when the block is at rest. b. Hence, calculate the spring constant. c. Determine the acceleration of the block at the instant when the block is at rest.

A 47.1-kg skater is standing at rest in front of a wall. By pushing against the wall she propels herself backward with a velocity of −1.86 m/s. Her hands are in contact with the wall for 0.997 s. Ignore friction and wind resistance. Find the average force she exerts on the wall (which has the same magnitude, but opposite direction, as the force that the wall applies to her). Note that this force has direction, which you should indicate with the sign of your answer. Number Units

Consider the conductive rod connected to a u-shaped loop of wire, shown below in Figure (a). The rod moves with a constant speed of 3.2 m/s in a 0.45 T magnetic field, and the rod has a length of I = 40 cm. If the rod has a resistance of 2.0 Ω (and resistance in the wires is negligible), how much electric energy will be produced in 0.5 seconds? Enter your solution in Joules.

A net force (Fcos⁡θ) acts on an object moving in the positive x-direction along the axis over 4 m, depicted in the graph below. What is the net work done by this force over this displacement? −6 J 0 +12 J +6 J −12 J

How much energy is stored in the electrical fields in the capacitors (in total) shown below? (b) Is this energy equal to the work done by the 400−V source in charging the capacitors? The current through a 12-gauge wire is given as I(t) = (15.00 A)∗sin⁡[2π(120 Hz)t]. What is the current density at time 10.00 ms ?

The figure above represents the free body diagram for a object of mass 4.4 kg. The magnitudes of the force vectors in the figure are: F1 = 9.8 N F2 = 2.5 N F3 = 6.1 N F4 = 3.1 N And the angle of the plane is θ = 34 degrees In the absence of friction, calculate the x component of the object's acceleration (in m/s^2). Note that the length of the vectors in the picture may not reflect the actual magnitudes of the Forces. Provide your answer as a positive or negative number ONLY, with 1 decimal place (e. g. 1.2 or -1.2). Do not write the units (e. g. s or m or m/s etc.) in the answer box. Do not use scientific notation.

Figure 1 Robin is pushing a crate up an inclined plane. Robin pushes with a force of FRC which is parallel to the plane. Robin moves the crate a distance d (measured parallel to the plane). There is ordinary surface friction between the crate and the plane. This question refers to the situation shown in Figure 1, above. Robin pushed the crate with a constant force and the crate moved at constant speed. The crate moved a distance d = 3.37 meters. The crate has a mass of 21.5 kg and the plane is inclined at an angle of 38.5 degrees above horizontal. The coefficient of kinetic friction between the crate and the plane is 0.22 . Assume the only forces acting on the box are the force exerted by Robin, the forces exerted by the inclined plane (this includes friction), and gravity (with g = 9.81 m/s2. Calculate the work done (in units of joules) on the crate by the inclined plane via the friction force (and only via the friction force) as the crate moved a distance d. (The sign of your answer, positive or negative, is important.)

In the depicted scenario, assuming no influence from friction or air resistance, object m slides and ascends to a height of 6.20 meters above the floor. What is the initial velocity of object m? A) 13.7 B) 14.4 C) 20.8 D) 17.4 E) 4.71 m/s