Two blocks placed one above the other are connected through a cable AB as shown in the figure. The coefficient of static friction between all the surfaces is 0.4 and the kinetic friction is 0.3. The system is initially at rest. Find: (a) the minimum force P to start the motion. (b) the minimum force required to maintain constant speed once the motion starts. (c) the minimum force to start the motion if the cable is disconnected right at the beginning.
A plum is located at coordinates (−5.80 m, 0, 8.39 m). In unit-vector notation, what is the torque about the origin on the plum if that torque is due to a force F→ whose only component is (a) Fx = 9.72 N, (b) Fx = −9.72 N, (c) Fz = 9.72 N, and (d) Fz = −9.72 N? (a) Number i^ j^ k^ Units (b) Number i^ j^ k^ Units (c) Number i^ j^ k^ Units (d) Number i^ j^ k^ Units
The 2225−N block shown is in contact with 45∘ incline. The coefficient of static friction is 0.25. Compute the value of the horizontal force P necessary to (a) just start the block up the incline or (b) just prevent motion down the incline.
The device pictured in the figure entertains infants while keeping them from wandering. The child bounces in a harness, with a spring constant k, and is suspended off of the ground. Part (a) If the spring stretches x1 = 0.245 m from equilibrium while supporting an 7.15−kg child, what is its spring constant, in newtons per meter? Part (b) What is the time, in seconds, for one complete bounce of this child about the point x1? Part (c) What is the child's maximum velocity, in meters per second, if the amplitude of her bounce, relative to x1, is 0.19 m? v =
Determine the height h in feet at which the bullet can strike the disk and cause it to roll without slipping at A. No slipping means friction at point A is zero. The disk weighs 20 lbs and has a radius of 1 ft.
In the figure shown, a mass m1 = 2 kg slides up a frictionless track until it collides with and stick to m2 = 4 kg, which is sitting at rest at height h = 2 m on a ramp of angle θ = 30∘, as shown in the figure. After the collision the two blocks moved together to point B a distance L = 0.05 m where the coefficient of kinetic friction is 0.4. If ml has a speed of 8 m/s at point A, find: a) The impulse delivered to m2 as a result of the collision. b) Use energy concepts to determine the speed of m2 and m1 at point B.
Two blocks are connected by a negligible mass string passing over a frictionless pulley of radius R = 0.1 m and moment of inertia I = 0.02 kgm2. A 64.8 N horizontal force acts on the 8.00−kg object. The 8 kg block moves to the right with a constant linear acceleration a. The coefficient of kinetic friction between the horizontal surface and the 8 kg block μk is 0.5. Determine (a) the linear acceleration a of the system, (b) T1 and T2 the tensions in the two parts of the string.
A box of mass m = 9.00 kg is located at the top of a ramp of height h = 7.00 m, as shown in the figure. The coefficient of kinetic friction between the ramp and the box is μk = 0.6. You give the box a push so that it starts sliding down with an initial speed of 2.50 m/s. The box continues its motion on a rough horizontal surface for 15.00 m until it hits a spring of spring constant k = 300. N/m and fully compresses it by 50.0 cm before coming to rest. What is the coefficient of kinetic friction between the horizontal surface and the box?
The coefficient of static friction between the m = 3.70−kg crate and the 35.0∘ incline of the figure below is 0.260. What minimum force F→ must be applied to the crate perpendicular to the incline to prevent the crate from sliding down the incline? N
An initially stationary block of mass m = 5.0 kg is attached to a relaxed spring with a spring constant K = 16 N/m on a rough plane inclined at an angle θ (with cosθ = 0.8 and sinθ = 0.6). The coefficient of kinetic friction between the block and the plane is μk = 0.40. A vertically downward uniform force F = 240 N acts on the block as it moves from A to B a distance d = 2.5 m down the plane. During this descent from A to B , calculate the amount of work done on the block by: a) the normal force, b) the gravitational force, c) the spring force, d) the force F , and e ) the force of kinetic friction. f) Deduce the kinetic energy and the speed of m as it passes through point B.
A uniform electric field exists everywhere in the x, y plane. This electric field has a magnitude of 4000 N/C and is directed in the positive x direction. A point charge −6.0×10−9 C is placed at the origin. Find the magnitude of the net electric field at (a) x = −0.16 m, (b) x = +0.16 m, and (c)y = +0.16 m. (a) Number Units (b) Number Units (c) Number Units
The drawing shows an electron entering the lower left side of a parallel plate capacitor and exiting at the upper right side. The initial speed of the electron is 3.72×106 m/s. The capacitor is 2.00 cm long, and its plates are separated by 0.150 cm. Assume that the electric field between the plates is uniform everywhere and find its magnitude.
A circular wire loop of radius 13.2 cm carries a current of 3.89 A. It is placed so that the normal to its plane makes an angle of 37.3∘ with a uniform magnetic field of magnitude 15.9 T. (a) Calculate the magnitude of the magnetic dipole moment of the loop in amperes-square meters. (b) What is the magnitude of the torque acting on the loop? (a) Number Units (b) Number Units
Location A is 2.30 m to the right of a point charge q. Location B lies on the same line and is 4.00 m to the right of the charge. The potential difference VB−VA = 50.0 V. What is the magnitude and sign of the charge? Number Units
Determine the ratio of the relativistic kinetic energy to the nonrelativistic kinetic energy (1/2mv2) when a particle has a speed of (a) 1.26×10−3 c. and (b) 0.852c. (a) Number Units (b) Number Units
A moving particle encounters an external electric field that decreases its kinetic energy from 9630 eV to 8340 eV as the particle moves from position A to position B. The electric potential at A is -42.0 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
In the figure R1 = 6.55 Ω, R2 = 19.7 Ω, and the ideal battery has emf E = 12.1 V. (a) What is the magnitude of current i1? (b) How much energy is dissipated by all four resistors in 1.86 min? (a) Number Units (b) Number Units
The figure here shows an overhead view of three horizontal forces acting on a cargo canister that was initially stationary but that now moves across a frictionless floor. The force magnitudes are F1 = 2.90 N, F2 = 3.50 N, and F3 = 10.0 N, and the indicated angles are θ2 = 50.0∘ and θ3 = 32.0∘. What is the net work done on the canister by the three forces during the first 4.20 m of displacement? Number Unit
The drawing shows three point charges fixed in place. The charge at the coordinate origin has a value of q1 = +11.4 μC; the other two have identical magnitudes, but opposite signs: q2 = −3.98 μC and q3 = +3.98 μC. (a) Determine the net force exerted on q1 by the other two charges. (b) If q1 had a mass of 1.50 g and it were free to move, what would be its acceleration?
QA = QB = 1.5 C, and QC = −3.0 C are located as shown in the diagram. a) Calculate the electric field from charges B and C at the location of point A. In other words, you may want to start by redrawing the diagram with charge A replaced by point P. Draw the electric field contributions from B and C at that point. b) What is the net electric force on QA?
A bowling ball encounters a 0.760−m vertical rise on the way back to the ball rack, as the drawing illustrates. Ignore frictional losses and assume that the mass of the ball is distributed uniformly. The translational speed of the ball is 7.15 m/s at the bottom of the rise. Find the translational speed at the top.
Consider the baby being weighed in the figure. (a) What is the mass of the child and basket (in kg ) if a scale reading of 80 N is observed? kg (b) What is the tension T1 (in N) in the cord attaching the baby to the scale? N (c) What is the tension T2 (in N) in the cord attaching the scale to the ceiling, if the scale has a mass of 0.480 kg? N (d) Draw a sketch of the situation indicating the system of interest used to solve each part. The masses of the cords are negligible. (Submit a file with a maximum size of 1 MB.) Choose File no file selected This answer has not been graded yet.
The coefficient of static friction between the 200−kg crate and the flat bed of the truck is μs = 0.3. i. CONSTRUCT the Free Body Diagram and the kinematic diagram. ii. FORMULATE the shortest time for the truck to reach a speed of 60 km/h, starting from rest with constant acceleration, so that the crate does not slip. Figure 2(b)
The 10−lb block has a speed of 4 ft/s when the force of F = (8t2) lb is applied. Determine the velocity of the block when it moves s = 30 ft. The coefficient of kinetic friction at the surface is μs = 0.2.
A charge of 33.3 nC is placed on the inner conducting core of a spherical capacitor which has a radius of a = 555 mm. The inner radius of the outer shell is equal to b = 888 mm. The gap between a and b is filled with a polystyrene dielectric. What is the magnitude of the potential difference between a and b? This is a positive number. Give your answer in units of Volts.
Three charges are arrayed at the vertices of an equilateral triangle, as shown. The side lengths are s = 6.00 m. Charges 1 and 2 are q1 = q2 = +22.2 μC. What is the magnitude of the electrical force on charge q3 = +33.3 μC? Give your answer in units of Newtons.
A 2.00-kg block starts from rest at the top of a 30.0∘ incline and slides a distance of 2.10 m down the incline in 2.00 s. (a) Find the magnitude of the acceleration of the block. m/s2 (b) Find the coefficient of kinetic friction between block and plane. (c) Find the friction force acting on the block. magnitude N direction (d) Find the speed of the block after it has slid 2.10 m. m/s
A block of mass m = 2.00 kg is attached to a spring of force constant k = 535 N/m as shown in the figure below. The block is pulled to a position xi = 4.30 cm to the right of equilibrium and released from rest. (a) Find the speed the block has as it passes through equilibrium if the horizontal surface is frictionless. m/s (b) Find the speed the block has as it passes through equilibrium (for the first time) if the coefficient of friction between block and surface is μk = 0.350. m/s
A 5.20−kg block is set into motion up an inclined plane with an initial speed of vi = 8.20 m/s (see figure below). The block comes to rest after traveling d = 3.00 m along the plane, which is inclined at an angle of θ = 30.0∘ to the horizontal. (a) For this motion, determine the change in the block's kinetic energy. (b) For this motion, determine the change in potential energy of the block-Earth system. (c) Determine the friction force exerted on the block (assumed to be constant). (d) What is the coefficient of kinetic friction?
Shown below are two carts connected by a cord that passes over a small frictionless pulley. Each cart rolls freely with negligible friction. a. Draw a free-body diagram for each cart b. Calculate the magnitude of the acceleration of each cart c. calculate the magnitude of the tension in the cord.
A 32 N force pushes the 10 kg cart. As a result the 10 kg cart, 5 kg cart, and 2 kg block move to the right. Friction prevents the 2 kg block from slipping. Determine the amount of that friction in Newtons. Type your answer with 2 significant digits. Do not type units or commas. (1 Point)
A block of mass M = 8.00 kg is sitting on a table. A smaller block of mass m = 2.00 kg is sitting on the edge of the larger block as shown in figure (a). A horizontal force of magnitude F = 13.0 N is applied to the smaller block, so that it moves across the surface of the larger block as shown in figure (b). Let m = 2.00 kg, M = 8.00 kg, and μk between the two blocks equals 0.350 . Assume F is constant, and the distance the front of the smaller block moves is L = 3.00 m. b (a) How long (in s) does it take for the smaller block to make it to the far edge of the larger block, as shown in figure (b)? Note that when F→ is applied, both blocks are set in motion. s (b) How far (in m ) does the larger block move? m
In the figure R1 = 80.0 Ω, R2 = R3 = 49.0 Ω, R4 = 79.9 Ω, and the ideal battery has emf E = 6.00 V. (a) What is the equivalent resistance? What is i in (b) resistance 1, (c) resistance 2, (d) resistance 3, and (e) resistance 4? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units
The three blocks in the figure below are connected by massless cords and pulleys. Data: m1 = 5 kg, m2 = 3 kg, m3 = 2 kg. Assume that the incline plane is frictionless. i. Show all the forces that act on each block. ii. Calculate the acceleration of m1, m2, m3. iii. Calculate the tensions on the cords. iv. Calculate the normal force acting on m2.
For the dumbbell in the Figure, let m = 0.02 kg, a = 0.3 m and E = 640 N/C i^. Initially, the dumbbell is at rest and makes an angle of 60∘ with the x-axis. The dumbbell is then released, and when it is momentarily aligned with the electric field, its kinetic energy is 5.3×10−3 J. Determine the magnitude of q . a. 13.8 μC b. O18.4 μC c. 110.4 μC d. 55.21 μC e. 27.6 μC
A force P→ is applied to push a block of mass M across the ceiling of the room. If the coefficient of kinetic friction between the block and the ceiling is 0.50 , what is the magnitude of the block's acceleration if the magnitude of the force P = 2.0Mg and angle θ = arctan(3/4)? Answer: a = 1.5g
As shown in the figure below, a 2.25 kg block is released from rest on a ramp of height h. When the block is released, it slides without friction to the bottom of the ramp, and then continues across a surface that is frictionless except for a rough patch of width 15.0 cm that has a coefficient of kinetic friction μk = 0.550. Find h (in m) such that the block's speed after crossing the rough patch is 2.90 m/s. (Enter a number.) m
Consider the following. (a) The nail puller shown in the figure above is designed such that you exert a force 34.0 cm from the pivot and the nail is 1.95 cm from the pivot on the other side. Determine the mechanical advantage of the nail puller. (b) Determine the minimum force must you exert in order to apply a force of 1400 N to the nail. N (c) If the nail puller has a mass of 2.10 kg, determine the force the nail puller exerts on the supporting surface. magnitude N direction For part c there are 4 forces acting on the nail-puller: The force from the hand, the force of gravity/weight, the force of the nail pushing back on the nail-puller, and the normal force from the ground.
Block A in the figure below has a mass mA = 5.00 kg, and block B has a mass mB = 8.00 kg. The blocks are forced together, compressing a spring S between them; then the system is released from rest on a level, frictionless surface. The spring, which has negligible mass, is not fastened to either block and drops to the surface after it has expanded. Block B acquires a speed of 1.20 m/s (a) What is the final speed of block A? m/s (b) How much potential energy was stored in the compressed spring? J
The magnitude of the x-component of the resultant force (i. e., Rx) is most nearly: 52.6 lb −37.3 lb −52.6 lb 23.8 lb 37.3 lb
You are pulling a sled with 2 children in it (see below). The children and and sled have a combined mass of 40.0 kg. You are pulling with a total force of Pull = 113 N at an angle of θ = 27.0∘. You pull the sled a horizontal distance of 16.5 m. There is a force of friction between the ground and the sled with a value of f = 29.0 N. What is the work done by gravity on the sled?
A mug rests on an inclined surface, as shown in (Figure 1), θ = 13∘. For the steps and strategies involved in solving a similar problem, you may view the following Example 6-3 video: Part A What is the magnitude of the frictional force exerted on the mug? Express your answer using appropriate units. Part B What is the minimum coefficient of static friction required to keep the mug from sliding? Submit Previous Answers Request Answer
Two vertical walls are separated by a distance of 1.50 m, as the figure shows. Wall 1 is smooth, while wall 2 is not smooth. A uniform board is propped between them. The coefficient of static friction between the board and wall 2 is 1.21. What is the length of the longest board that can be propped between the walls? Number Units
Given: A homogeneous quarter-circle block (with a radius of R and a weight of W ) is supported by a rough, horizontal floor, as shown.. A force P is applied to the block at corner B. Find: For this problem: a) Determine the x-location of the normal force acting on the block by the floor. Express your answer in terms of R. b) What is the minimum coefficient of static friction between the block and ground, μs, that is required to prevent motion of the block? c) Is the block in a state of impending slipping or tipping for the value of μs found in b) above? Explain. For this problem, use: P = W.
A small plastic ball of mass 8.40×10−3 kg and charge +0.205 μC is suspended from an insulating thread and hangs between the plates of a capacitor (see the drawing). The ball is in equilibrium, with the thread making an angle of 30.0∘ with respect to the vertical. The area of each plate is 0.01795 m2. What is the magnitude of the charge on each plate? Number Units
A ladder (length L, and uniformly distributed mass, mL), is leaning against a wall at an angle of θ (see figure below). A man (mass mM ) is standing on a rung of the ladder that is a distance of L/3 from the floor measured along the ladder. The vertical wall is frictionless, and the horizontal floor has a non-zero coefficient of friction, μ. a) (3 Points) Draw a free body diagram indicating all forces acting on the ladder as vectors, and label each one. b) (3 Points) Determine the Normal forces (one provided by the floor, and the other provided by the wall) as functions of the available constants (θ, mM, mL, L, μ, and the acceleration due to gravity, g). c) (4 points) What value of μ is needed to keep the ladder from slipping?
A force of 3.2 N acts on a 26 kg body initially at rest. Compute the work done by the force in (a) the first, (b) the second, and (c) the third seconds and (d) the instantaneous power due to the force at the end of the third second. (a) Number Units (b) Number Units (c) Number Units (d) Number Units
The figure shows a rectangular, 20-turn coil of wire, of dimensions 8.1 cm by 3.7 cm. It carries a current of 0.15 A and is hinged along one long side. It is mounted in the xy plane, at an angle of 30∘ to the direction of a uniform magnetic field of magnitude 0.64 T. Find the (a) x, (b) y, and (c) z components of the torque acting on the coil about the hinge line. (a) Number Units (b) Number Units (c) Number Units
A 4.9 kg block is on a horizontal surface. A person pushes horizontally on the block. The coefficient of static friction between block and surface is 0.21 and the coefficient of kinetic friction is 0.19. The block is initially at rest when a pushing force of 16.9 N is applied. During the segment of time that this push is applied, the surface below applies a friction force of magnitude N.
A spherically shaped balloon has a radius of 12.0 m and is filled with helium. The skin and structure of the balloon including the helium have a combined mass of 12, 000. kg. What is the maximum mass of cargo that the balloon can support? Assume the cargo has a high density so that the buoyant force acting on it can be neglected compared to the buoyant force acting on the balloon. You may wish to know that the area of a sphere is 4πr2, the volume of a sphere is 43πr3, the density of air is 1.21 kg/m3, and the density of helium is 0.178 kg/m3. Approximation: you can neglect by the size of the cargo in comparison with the size of the balloon.
Now imagine two identical mass pucks colliding on an air hockey table with an elastic collision; both are going the same speed but in opposite directions (arbitrarily chosen as +x and −x). Their collision paths are offset by exactly their radius (see picture). Assume the force they exert on each other only acts in the 45 degree angle with respect to +x as shown in b. They ricochet as shown in c. (red arrows indicate velocity in a. and c.) a. (6) Explain why they ricochet perfectly into the +y and −y directions. b. (6) Explain why their individual initial momentum in the y direction was zero but now they both have momentum in the y direction. (Specifically, why this doesn't violate the conservation of momentum? ) a. Before collision b. During collision c. After collision
In the figure, a block slides down an incline. As it moves from point A to point B, which are 3.6 m apart, force F→ acts on the block, with magnitude 1.8 N and directed down the incline. The magnitude of the frictional force acting on the block is 5.5 N . If the kinetic energy of the block increases by 31 J between A and B, how much work is done on the block by the gravitational force as the block moves from A to B? Number Units
In the figure, a 5.30 kg block is sent sliding up a plane inclined at θ = 37.0∘ while a horizontal force F→ of magnitude 50.0 N acts on it. The coefficient of kinetic friction between block and plane is 0.300. What are the (a) magnitude and (b) direction (up or down the plane) of the block's acceleration? The block's initial speed is 4.20 m/s. (c) How far up the plane does the block go? (d) When it reaches its highest point, does it remain at rest or slide back down the plane? (a) Number Units (b) (c) Number Units
A machine carries a 7.0 kg package from an initial position of d→i = (0.8 m)i^ + (0.77 m)j^ + (0.28 m)k^ at t = 0 to a final position of d→f = (11.5 m)i^ + (12.0 m)j^ + (10.2 m)k^ at t = 12.0 s. The constant force applied by the machine on the package is F→ = (4.0 N)i^ + (7.0 N)j^ + (7.0 N)k^. For that displacement, find (a) the work done on the package by the machine's force and (b) the average power of the machine's force on the package. (a) Number Units (b) Number Units
An object is moving along a straight line, and the uncertainty in its position is 2.80 m. (a) Find the minimum uncertainty in the momentum of the object. Find the minimum uncertainty in the object's velocity, assuming that the object is (b) a golf ball (mass = 0.0450 kg) and (c) an electron. (a) Number Units (b) Number Units (c) Number Units
A 1340 kg car has just passed a diner. The closest the car came to the diner was R = 40.5 m, but the car has driven another x = 36.7 m in the 2.85 s elapsed since then. If the car travels at constant speed, what is the current magnitude L of the angular momentum of the car about the diner? L = kg⋅m2/s