Two identical blocks are arranged differently as shown in the figure (a and b) on a rough surface. A horizontal force F is applied to the blocks and the blocks slide in both arrangements. Which arrangement has a greater kinetic friction "a" has a greater friction "b" has a greater friction Both have the same friction Not enough information to tell
A moving particle encounters an external electric field that decreases its kinetic energy from 9320 eV to 7590 eV as the particle moves from position A to position B. The electric potential at A is −41.0 V, and that at B is +23.0 V. Determine the charge of the particle. Include the algebraic sign (+ or -) with your answer. Number Units
A moving particle encounters an external electric field that decreases its kinetic energy from 9790 eV to 5340 eV as the particle moves from position A to position B. The electric potential at A is −65.0 V, and that at B is +34.0 V. Determine the charge of the particle Include the algebraic sign (+ or -) with your answer. Number Units
Problem #3. A mass of 1238.4 kg is released from a rest at position A on a semicircular track of radius r1 = 1.7 m that is connected to a circular looped track of radius r2 = 1.2 m as shown in the figure below (not drawn to scale, arrows indicate the direction that the mass travels). The track is frictionless except for a segment between B and C that is 1.0 m long, where it has a coefficient of static friction of 0.2 and a coefficient of kinetic friction of 0.3. A. Determine the speed (in m/s) of the mass at position A. B. Determine the speed (in m/s) of the mass at position C. C. If the mass is to remain on the track at all times (including at position D), determine the minimum speed (in m/s) that the mass must have at position C."
In the figure, a block of mass m = 17 kg is released from rest on a frictionless incline of angle θ = 33∘. Below the block is a spring that can be compressed 3.8 cm by a force of 160 N. The block momentarily stops when it compresses the spring by 6.7 cm. (a) How far does the block move down the incline from its rest position to this stopping point? (b) What is the speed of the block just as it touches the spring?
A block slides down a ramp, which is on a table, as shown. The ramp makes an angle θ with the horizontal. It takes it t1 seconds to slide down the ramp of length L, starting from rest. What is the speed of the block at t1? L t1 2 Lt1 sin(θ) 2L t1 cos(θ) 2L t1 gsin(θ) t1 not enough information
A force of F→ = 66.6 x^ N acts on a block m1 = 12.5 kg which is in contact with a block m2 = 23.6 kg. Both blocks lie on a flat, frictionless surface. What is the magnitude of the acceleration of the pair of blocks? This is a positive number. Give your answer in units of m/s2.
A 15 kg crate slides a distance r = 5.7 m down a 57∘ slope. The coefficient of kinetic friction between the crate and the slope is ∖mu_k = 0.666. If it starts from rest, what is its speed at the bottom of the slope? This is a positive number. Give your answer in units of m/s.
A block of mass m1 = 24.8 kg lies on a rough table. The coefficient of static friction between the block and the table is μs = 0.477. The block is connected to a mass m2 by means of a pulley as shown. What is the maximum mass m2 such that block m1 is stationary? Give your answer in units of kg.
The crate shown is held against wedge B by a spring. The spring is 94% of its original uncompressed length l = 3 m and the spring constant is given as k = 1550 N/m. The coefficient of static friction at all contacting surface is μs = 0.1. The mass of the crate is m = 30 kg and the angle is θ = 15∘. Neglect the mass of the wedge. Assume the crate only moves in the y direction and that wedge A cannot move. Determine (1) The normal force exerted by the crate on the wedge (2) The smallest horizontal force P to move the crate upward
Figure 1 shows Block A having mass mA = 3 kg and is attached to a spring with stiffness k = 100 kN/m and upstretched length l0 = 0.5 m. Another Block B with mass mB = 5 kg is pressed against Block A so that the spring deforms a distance 0.2 m. The surface plane is not a smooth surface, having the coefficient of kinetic friction between the plane and the block is given as μk = 0.3. Answer the following Q1 to Q4. Figure 1 Q1. Based on the figure, what are the force components that are acting on Block A? a. Spring force, weight, 2 normal forces, friction force, applied force b. Spring force, weight, normal force, friction force c. Spring force, weight, 2 normal forces, friction force d. Spring force, weight, normal force, friction force, applied force Q2. Draw kinetic diagram for Block A. Q3. Draw kinetic diagram for Block B. Q4. Given aA = aB = a (as block A and block B are moving together), determine the acceleration of the block, a.
An electric field given by E→ = 6.1 i^ − 4.0(y2 + 4.7) j^ pierces the Gaussian cube of edge length 0.760 m and positioned as shown in the figure. (The magnitude E is in newtons per coulomb and the position x is in meters. ) What is the electric flux through the (a) top face, (b) bottom face, (c) left face, and (d) back face? (e) What is the net electric flux through the cube? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units
In the figure the three particles are fixed in place and have charges q1 = q2 = +3 e and q3 = +1 e. Distance a = 3.79 μm. What is the magnitude of the net electric field at point P due to the particles? Number Units
A small ball is projected horizontally as shown and bounces at point A. Determine the range of initial speed v0 for which the ball will ultimately land on the horizontal surface at B. The coefficient of restitution at A is e = 0.8 and the distance d = 4 m. Problem 3/268
In the arrangement of the figure, billiard ball 1 moving at a speed of 2.2 m/s undergoes a glancing collision with identical billiard ball 2 that is at rest. After the collision, ball 2 moves at speed 1.8 m/s, at an angle of θ2 = 37∘. What are (a) the magnitude and (b) the direction (angle θ1) of the velocity of ball 1 after the collision? (a) Number Units (b) Number Units
A tennis player serves the ball horizontally. a) What minimum speed is required for the ball to clear the 0.9 m high net that is 15 m from the server? The server strikes the ball horizontally at a height of 2.5 m. (4 marks) b) How far does the ball travel in the horizontal direction before it hits the ground? Will the ball land "in", i. e. within the 7 m zone after the net? (1 mark) c) How long is the ball in the air? (2 marks) d) What is the maximum speed that the server can hit the ball horizontally and still have the ball land "in", i. e. right at the 7 m line after the net? (3 marks)
You throw a ball towards a wall at speed 18 m/s and at an angle 40.0∘ above the horizontal. The wall is 21.8 m from the release point of the ball. (a) How long does the ball take to reach the wall? s (b) How far above the release point does the ball hit the wall? m (c) What are the horizontal and vertical components of its velocity as it hits the wall? horizontal m/s vertical m/s (d) When it hits, has it passed the highest point on its trajectory? Yes No not enough information to decide
A bowling ball with a circumference of 27 in. weighs 14 lb and has a centroidal radius of gyration of 3.28 in. If the ball is released with a velocity of 20 ft/sec but with no angular velocity as it touches the alley floor, compute the distance traveled by the ball before it begins to roll without slipping. The coefficient of friction between the ball and the floor is 0.20.
A tennis player strikes the tennis ball with her racket when the ball is at the uppermost point of its trajectory as shown. The horizontal velocity of the ball just before impact with the racket is v1 = 15 m/s and just after impact its velocity is v2 = 21 m/s directed at the 15∘ angle as shown. If the 60 g ball is in contact with the racket for 0.02 s, determine the magnitude of the average force R exerted by the racket on the ball. Also determine the angle β made by R with the horizontal.
2(a) Peter who is on a moving trolley throws a ball to John (who is stationary) as shown in Fig. Q2 a. The trolley is moving at a constant speed of 3.4 m/s to the right. If the ball leaves the boy with a velocity of 5.4 m/s with the angle, Fig. Q2(a) (i) If John is to catch the ball, find the time taken for the ball to reach John. (5 marks) (ii) Find the distance, X m, between Peter and John at the start of the motion, when the ball leaves Peter. (5 marks) (iii) Find the position of Peter from John when the ball reach John. (5 marks)
Two charges are located on the x axis: q1 = +4.7 μC at x1 = +3.3 cm, and q2 = +4.7 μC at x2 = −3.3 cm. Two other charges are located on the y axis: q3 = +4.4 μC at y3 = +5.5 cm, and q4 = −7.8 μC at y4 = +6.4 cm. Find (a) the magnitude and (b) the direction of the net electric field at the origin. (a) Number Units (b) The net electric field points
A soccer ball is kicked from the ground with an initial speed of 19.4 m/s at an upward angle of 42.1∘. A player 50.8 m away in the direction of the kick starts running to meet the ball at that instant. What must be his average speed if he is to meet the ball just before it hits the ground? Neglect air resistance. Use g = 9.81 m/s2. Number Unit
Figure 3.1 shows four identical pool balls having the same mass m. At the instant shown, ball number 2 and ball number 5 moving with the same velocity of vo = 4 m/s towards ball number 10 and number 12 in which are at rest. If the coefficient of restitution for each ball is e = 0.5, determine the velocity of each ball after the first three collisions occur. (12 marks) Figure 3.1 Movement of the pool ball
A small 1.45 g plastic ball that has a charge q = 1.35 C is suspended by a string that has a length L = 1.00 m in a uniform electric field, as shown in the figure. If the ball is in equilibrium when the string makes a θ = 9.80∘ angle with the vertical, what is the electric field strength E? E = N/C
A small ball of mass m is aligned above a larger ball of mass M = 0.78 kg (with a slight separation, as with the baseball and basketball of Figure (a)), and the two are dropped simultaneously from height h = 3.5 m. (Assume the radius of each ball is negligible compared to h.) (a) If the larger ball rebounds elastically from the floor and then the small ball rebounds elastically from the larger ball, what value of m results in the larger ball stopping when it collides with the small ball? (b) What height does the small ball then reach (see Figure (b))? (a) Number Units (b) Number Units
Consider the following experiment where the ball encounters no resistance from the surface it is running along. For figure 1, the ball in this experiment will run down one side of the curve and then up the other. How would you explain the results and the physics involved? Do you expect the ball to reach the same height? Can predict what will happen in Figure 2? FIGURE 1 FIGURE 2
A ball of mass m1 = 4.00 kg is tied to another ball of mass m2 = 3.00 kg by a string of length 0.500 m. The two balls are swung in a vertical circle by a second string of length 0.500 m connected to m2. As the balls rotate, the strings remain parallel. At the top if the circle, m2 is moving at 4.00 m/s. (a) Draw a free-body diagram for each mass at this instant. (3 marks) (b) What is the tension in the string connecting the two balls at this instant? (4 marks) (c) What is the tension in the string connecting m2 to the centre of the circle at this instant? (3 marks)
In the image are three point charges, Q1 = 15.4 μC, Q2 = −33.6 μC, and Q3 = 87.3 μC, arranged according to the figure. A fourth point charge is located at point A with a charge of QA = 13.5 μC. The charges form a square with height y of 60.1 cm and width x of 60.1 cm. Calculate the magnitude F of the net force on the charge at point A. F = N
Charges of +2.30 nC and −1.00 nC are located at opposite corners, A and C, respectively, of a square which is p = 7.10 m on a side. What is the electric potential at a third corner, B, of the square (where there is no charge)? V
A tennis ball is released at rest vertically from an initial height of h0 on the rigid ground. The maximum height that the tennis ball can reach after its third rebound from the ground is h3, determine the h0/h3 ratio if the coefficient of restitution between the tennis ball and the rigid ground is e = 0,76 (g = 10 m/s2). Note: Please answer with 2 digits after the comma! h0/h3 = ?
A child is swinging in a tyre swing which is supported by two ropes from a horizontal branch as shown. The combined mass of the child and the tyre is 65 kg. Calculate the tension (TA, TB, TC) in each rope. (g = 9.81)
A 26 kg child is on a swing that hangs from 3.0 m long chains as shown in the figure below. What is her maximum speed if she swings out to a 45∘ angle? HINT: Remember that you want to use conservation of energy for this problem. What is special about maximum height? (Remember it's a turnaround point. ) There is a bit of geometry to do. You know how long the chains of the swing are, so how high above the lowest point is the seat of the swing when it is at its maximum height? Make sure to draw a picture and figure out the different lengths. What is the child's maximum speed? m/s
A father fashions a swing for his children out of a long rope that he fastens to the limb of a tall tree. As one of the children with a mass of 50 kg swings from this rope that is 4.4 m long, his tangential speed at the bottom of the swing is 3.7 m/s. What is the centripetal force of the child at the bottom of the swing?
A car with a mass of 1200 kg rounds the top of the hill at a speed of 20 m/s. The friction between the wheels and the road is negligible and the radius of curvature for the hill is 55 m. A. Draw the force diagram and write down a Newton's 2 nd law equation for the car when it is at the top of the hill. B. Find the magnitude of the normal force on the car when it rounds the hill at this speed. C. What is the maximum speed at which the car could round this hill without losing contact with the road?
Two different charges are seperated by a distance of 1.00 m as shown in the figure below. It is given that q1 = −1.80 μC and q2 = 9.80 μC. Determine the value of x (other than infinity) at which the electric field at the indicated point is zero.
A "swing" ride at a carnival consists of chairs that are swung in a circle by 11.3 m cables attached to a vertical rotating pole, as the drawing shows. Suppose the total mass of a chair and its occupant is 182 kg. (a) Determine the tension in the cable attached to the chair. (b) Find the speed of the chair.
An adult exerts a horizontal force on a swing that is suspended by a rope of length L, holding it at an angle θ with the vertical. The child in the swing has a weight W and dimensions that are negligible compared to L. The weights of the rope and of the seat are negligible. In terms of W and θ, determine a. the tension in the rope; b. the horizontal force exerted by the adult. The adult releases the swing from rest. In terms of W and θ determine c. the tension in the rope just after the release (the swing is instantaneously at rest); d. the tension in the rope as the swing passes through its lowest point.
A child with a mass of 38.0 kg is swinging on a rope tire swing with a length L = 2.70 m (see picture below). The tire has a mass of 19.0 kg. When the swing is at its lowest point it has a speed of 4.00 m/s. What is the tension in the rope when the swing and child are at the lowest point? Give your answer rounded to the nearest Newton. Do NOT include units in your answer.
In the figure particles with charges q1 = +8e and q2 = −17e are fixed in place with a separation of d = 25.0 cm. With V = 0 at infinity, what are the finite (a) positive and (b) negative values of x at which the net electric potential on the x axis is zero? (a) Number Units (b) Number Units
Question: In Figure A below, a bullet is fired into a block of wood and the bullet and block of wood swing up to a maximum height. This device is called a ballistic pendulum. Agree or Disagree with the following statement: "The mass of the bullet can be determined if you know the velocity of the bullet, mass of the block of wood, and the maximum height after the collision." Discuss why or why not this is possible. Figure A
A child of mass m is sitting at rest on a swing of length L. Their parent pulls them back making an angle of θ with the vertical as shown in the diagram. The parent uses a force that is perfectly horizontal. a) Find an expression for the force required to pull the child back as a function of the angle made by the swing. θ, m, L, and any fundamental can be in your answer. b) (Calculus version) i. Set up but do not solve an integral that could be used to calculate the work done on the child. ii. Now execute the integral showing that the work done will equal the resulting increase in potential energy. c) (Non calculus version) i. Find an expression for the height of the child above their lowest position as a function of θ and L. ii. Find an expression for the potential energy of the child in terms of m, θ, L, and any fundamental constants. d) The child is released and swings down to the lowest position. i. What is the tension in the cable the instant they are released? (Hint: their velocity the instant they are released is zero, but the net force is unbalanced. ) ii. What is the acceleration of the child the instant the parent releases them? iii. What is the speed of the child at the bottom of their swing? iv. What is the tension in the cable at the bottom of their swing?
A father fashions a swing for his children out of a long rope that he fastens to the limb of a tall tree. As one of the children swings from this rope that is 5.80 m long, his tangential speed at the bottom of the swing is 8.00 m/s. (a) What is the centripetal acceleration, in m/s2, of the child at the bottom of the swing? m/s2 (b) What provides the centripetal force that keeps the child moving in an arc? the weight of the child gravitational acceleration the tension in the rope the height of the tree
Consider the door pictured below looking down from the top. The door is hinged on the left. Three forces, F1, F2, and F3, are applied separately to the door. Each of the forces are of equal magnitude, 15 N, but are applied at different points and at different angles as shown. For which force or forces will the door open the quickest? Force 1 Force 2 Force 3 Forces 1 and 2 Forces 1 and 3 Forces 2 and 3 All are equal
The figure shows a thin rod, of length L = 1.30 m and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball of mass m = 8.60 kg is attached to the other end. The rod is pulled aside to angle θ0 = 17.0∘ and released with initial velocity v→0 = 0 . As the ball descends to its lowest point, (a) how much work does the gravitational force do on it and (b) what is the change in the gravitational potential energy of the ball-Earth system? (c) If the gravitational potential energy is taken to be zero at the lowest point, what is its value just as the ball is released?
A heavy sled is being pulled by two people as shown in the figure. The coefficient of static friction between the sled and the ground is μs = 0.635, the coefficient of kinetic friction is μk = 0.405, and the combined mass of the sled and its load is m = 276 kg. The ropes are separated by an angle ϕ = 29∘, and they make an angle θ with the horizontal. Assuming both ropes pull equally hard, what is the minimum rope tension Tmin required to get the sled moving? Tmin =
Consider blocks m1 and m2, with m1 held at rest on a horizontal table (where the coefficient of kinetic friction between m1 and the table is μk ), and m2 held in place by a movable, massless, frictionless pulley to which it is attached via a massless cable. As shown in Figure 7, the rope attaching m1 is run across a massless, frictionless pulley affixed to the table, which is then threaded through the movable pulley to then attach to the ceiling. The system is released, and the blocks are observed to move out of rest. Consider analyzing the problem from the point at which the system is released from rest up to the point when m1 has displaced by an amount ℓ. Figure 7: Block 1 is held in place on a horizontal table (with friction) with an attached, massless rope running from it to an affixed pulley, and then threading through a movable pulley to then attach to the ceiling. The movable pulley is attached to a hanging Block 2 via a massless cable. The system is released and is seen to displace, with work considerations to be investigated up to the point when Block 1 displaces by an amount ℓ. (a) Determine the work done by each individual force acting on each individual block for the considered displacement. (b) Determine the speed of each block for the considered displacement.
A long solenoid with N2 windings and diameter D2 surrounds a coaxial, narrower solenoid with N1 windings and diameter D1. The current I flows through both solenoids in the same value, as shown in the diagram. Assume the length of both the inner and outer coils is l. (a) What is the magnetic flux through each tum of the inner coil, taking leftward as the positive direction? (5%) (b) What is the magnetic flux through each tum of the outer coil? (5%) (c) What is the inductance as seen by the two leads? (5%) (d) What would be the inductance if the sense of the inner coil were reversed? (5%) (e) In the original configuration, what would be the inductance? (5%) (l = 15.0 cm, D1 = 3.0 cm, D2 = 5.0 cm, N1 = 500, N2 = 750)
A golf ball is launched with the initial conditions shown in the figure. Determine the radius of curvature of the trajectory and the time rate of change of the speed of the ball (a) just after launch and (b) at apex. Neglect aerodynamic drag.
(a) Just after launch, determine the speed v of the ball, the total acceleration a of the ball, the normal component of acceleration an and the tangential component of acceleration at. Answers: V = ft/sec a = ft/sec2 an = ft/sec2 at = ft/sec2
The 3.00-kg object in Figure is released from rest at a height of 5.00 m on a curved frictionless ramp. At the foot of the ramp is a spring of force constant 400 N/m. The object slides down the ramp and into the spring, compressing it a distance x before coming momentarily to rest. (a) Find x. (b) Describe the motion of the object (if any) after the block momentarily comes to rest?
3-) F = 220 N Cart has a mass of 30 kg. Block A has a mass of 20 kg. No friction between the cart and the ground. Friction coefficients between the cart and block are: μs = 0.35 and μk = 0.30. a-) Determine whether the block will slide or not. b-) If the block slides, then calculate the time required for the block to displace on the cart for 1.5 m.
The car A has a forward speed of 16 km/h and is accelerating at 3.1 m/s2. Determine the velocity and acceleration of the car relative to observer B, who rides in a nonrotating chair on the Ferris wheel. The angular rate Ω = 3.4 rev/min of the Ferris wheel is constant. Answers: vA/B = ( i + j) m/s aA/B = ( i + j) m/s2