Physics AP Practice
A student swings a ball on a light rod at a constant speed in a vertical circle, as shown in the figure. Which of the following correctly ranks the magnitudes of the forces exerted by the rod on the ball F1, F2, F3, and F4 when the ball is at locations 1, 2, 3, and 4, respectively?
(F2=F3) > F4 > F1
Two astronauts are connected by a taut cable and are initially at rest with respect to a nearby space station. Astronaut X throws a large container to Astronaut Y. Figure 1 above shows the astronauts immediately after the container is thrown by Astronaut X, and Figure 2 shows the astronauts immediately after the container is caught by Astronaut Y. Which of the following describes the motion of Astronaut Y in Figures 1 and 2 ?
(Figure 1): moves to the left (Figure 2): does not move
Three identical rocks are launched with identical speeds from the top of a platform of height 0 h . The rocks are launched in the directions indicated above. Which of the following correctly relates the magnitude vy of the vertical component of the velocity of each rock immediately before it hits the ground?
(vy1 = vy2) > vy3
Three spheres, with masses indicated above, are initially far away from each other, and the gravitational potential energy of the three-sphere system is zero. The spheres are then brought together until each sphere is a distance r from the other two, as shown above. What is the new gravitational potential energy of the three-sphere system?
- 5Gm^2/r
A meterstick with a uniformly distributed mass of 0.5 kg is supported by a pivot placed at the 0.25 m mark from the left, as shown. At the left end, a small object of mass 1.0 kg is placed at the zero mark, and a second small object of mass 0.5 kg is placed at the 0.5 m mark. The meterstick is supported so that it remains horizontal, and then it is released from rest. One second after it is released, what is the change in the angular momentum of the meterstick?
0
Rock 1, of mass m, reaches a maximum height hmax after being launched. During the time between the instant rock 1 is launched from height h0 and the instant it returns to height h0, the work done on the rock by the gravitational force is
0
Two carts of masses 1kg and 2kg travel together, as shown in Figure 1. At time t=2 s, a compressed spring inside the 2kg cart expands, and the carts separate. Figure 2 shows a graph of the carts' velocities as a function of time. What is the magnitude of the change in linear momentum, if any, of the two-cart system between t=0 s and t= 4s ?
0 kg * m/s
A small block slides without friction along a track toward a circular loop. The block has more than enough speed to remain firmly in contact with the track as it goes around the loop. The magnitude of the block's acceleration at the top of the loop is
Greater than g
In a classroom at time t = 0 , a sphere is thrown upward at a 45° angle to the horizontal. At time t1, while the sphere is still rising, it bounces off the ceiling elastically and with no friction. Which of the following pairs of graphs could represent the sphere's horizontal velocity and vertical velocity as functions of time t?
Horizontal Velocity: horizontal line above x-axis Vertical Velocity: decreasing positive linear line from 0-t1, and then decreasing negative line from t1-t2
A sphere with the same mass and radius as the original cylinder, but a smaller rotational inertia, is released from rest from the top of the ramp. Ks and Kc are the sphere's and the cylinder's total kinetic energy at the bottom of the ramp, respectively. How do Ks and Kc compare, and why?
Ks = Kc, because the gravitational force does equal work on each object as it rolls down the ramp.
An object is subject to multiple forces that result in the object having horizontal and vertical velocity components vx and vy, respectively as a function of time, as shown. Which of the following free-body diagrams could represent the forces exerted on the object?
Long line southwest, shorter line directly north, small line directly east
The graph above shows the speed of a truck as it moves along a straight, level road. Which of the following describe a method to determine the distance d the truck travels during the 10 s time interval shown? Select two answers.
Multiply the average speed of 18 m/s by the 10 s travel time. Calculate the area under the line in the graph.
A student is asked to move a box from ground level to the top of a loading dock platform, as shown in the figures above. In Figure 1, the student pushes the box up an incline with negligible friction. In Figure 2, the student lifts the box straight up from ground level to the loading dock platform. In which case does the student do more work on the box, and why?
Neither method, because the work is the same in both cases, since using the ramp decreases the force by the same factor that it increases the distance
A blue sphere and a red sphere with the same diameter are released from rest at the top of a ramp. The red sphere takes a longer time to reach the bottom of the ramp. The spheres are then rolled off a horizontal table at the same time with the same speed and fall freely to the floor. Which sphere reaches the floor first?
Neither; the spheres reach the floor at the same time.
A soft foam block of mass m slides without friction in the positive x-direction with speed v. At time t = 0 , a student briefly pushes the block with a force probe in the positive x-direction. The graph above shows the force probe's measurements as a function of time during the push. Which of the following statements is true about the block's momentum between t = 0 and t = t1?
The momentum of the block has increased by approximately 1/2 F0t
The motion of an object is shown in the velocity-time graph. Which best describes the motion of the object?
The object travels in the same direction for the entire time.
A box experiences a varying net force that changes its velocity. The graph shows the velocity of the box as a function of time. Which of the following correctly describes the net work, Wnet , done on the box for the given intervals of time?
Between 0 and t1: Wnet = 0 ; Between t1 and t2: Wnet = 0 ; Between t2 and t3: Wnet < 0
Two blocks are on a horizontal, frictionless surface. Block A is moving with an initial velocity of v0 toward block B, which is stationary, as shown above. The two blocks collide, stick together, and move off with a velocity of v0/3 . Which block, if either, has the greater mass?
Block B
Two lab carts have the same mass and are free to move on a horizontal track. The carts' wheels have negligible mass. Cart 1 travels to the right at 1.0 m/s and collides with cart 2, which is initially at rest, as shown at left above. Cart 2 has a compressed spring-loaded plunger with a nonnegligible amount of stored energy. During the collision, the spring-loaded plunger pops out, staying in contact with cart 1 for 0.10 s as the spring decompresses. Negligible mechanical energy dissipates during the collision. Taking rightward as positive, the carts' velocities after the collision could be which of the following? Select two answers.
Cart 1: -0.5m/s ; Cart 2: 1.5 m/s Cart 1: -1.0m/s ; Cart 2: 2.0 m/s
The figures show a cart moving over the top of a hill (Case 1), moving at the bottom of a dip (Case 2), and moving at the top of a vertical loop (Case 3). In each case, the normal force acting on the car is Fn and the weight of the car is Fg. In which case is it always true that Fn>Fg , and in which case is it always true that Fn<Fg?
Case 2: Fn>Fg Always; Case 1:Fn<Fg Always
Two systems are in oscillation: a simple pendulum swinging back and forth through a very small angle and a block oscillating on a spring. The block-spring system takes twice as much time as the pendulum to complete one oscillation. Which of the following changes could make the two systems oscillate with the same period?
Decreasing the mass of both the block and the pendulum bob
A vertical spring launcher is attached to the top of a block and a ball is placed in the launcher, as shown in the figure. While the block slides at constant speed to the right across a horizontal surface with negligible friction between the block and the surface, the ball is launched upward. When the ball reaches its maximum height, what will be the position of the ball relative to the spring launcher?
Directly above the spring launcher
An apple is released from rest 500 m above the ground. Due to the combined forces of air resistance and gravity, it has a speed of 40 m s when it reaches the ground. What percentage of the initial mechanical energy of the apple-Earth system was dissipated due to air resistance? Take the potential energy of the apple-Earth system to be zero when the apple reaches the ground.
84%
A student uses a spring scale to exert a horizontal force on a block, pulling the block over a smooth floor. The student repeats the procedure several times, each time pulling the block from rest through a distance of 1.0 m. For which of the following graphs of force as a function of distance will the block be moving the fastest at the end of the 1.0 m?
staircase graph
A 1.0 kg block is attached to an unstretched spring of spring constant 50 N/m and released from rest from the position shown in Figure 1 above. The block oscillates for a while and eventually stops moving 0.20 m below its starting point, as shown in Figure 2. What is the change in potential energy of the block-spring-Earth system between Figure 1 and Figure 2 ?
−1.0 J
A 0.5 kg pendulum bob is raised to 1.0 m above the floor, as shown in the figure above. The bob is then released from rest. When the bob is 0.8 m above the floor, its speed is most nearly
2 m/s
Four different constant forces are exerted on a 2.0 kg object. The figure represents the magnitude and direction of each force. If the object is initially at rest, how long will it take the object to reach a speed of 2.0 m/s ?
4.0 s
A student sets an object attached to a spring into oscillatory motion and uses a position sensor to record the displacement of the object from equilibrium as a function of time. A portion of the recorded data is shown in the figure above. The frequency of oscillation is most nearly
2.0 Hz
Block A of mass 2.0 kg is released from rest at the top of a 3.6 m long plane inclined at an angle of 30º, as shown in the figure above. After sliding on the horizontal surface, block A hits and sticks to block B, which is at rest and has mass 3.0 kg. Assume friction is negligible. The speed of the blocks after the collision is most nearly
2.4 m/s
The wheel on a vehicle has a rotational inertia of 2.0 kg⋅m2. At the instant the wheel has a counterclockwise angular velocity of 6.0 rad/s, an average counterclockwise torque of 5.0 N⋅m is applied, and continues for 4.0 s. What is the change in angular momentum of the wheel?
20 kg⋅m2/s
A 12 kg box sliding on a horizontal floor has an initial speed of 4.0 m/s. The coefficient of friction between the box and the floor is 0.20. The box moves a distance of 4.0 m in 2.0 s. The magnitude of the change in momentum of the box during this time is most nearly
48 kg m/s
A student sets an object attached to a spring into oscillatory motion and uses a motion detector to record the velocity of the object as a function of time. A portion of the recorded data is shown in the figure above. The total change in the object's speed between 1.0 s and 1.1 s is most nearly
5 cm/s
The graph above shows the force exerted by a spring as a function of the length of the spring. A block on a frictionless table is pushed against the spring that is fastened to a wall. The spring is compressed until its length is 20 cm. The block is then released. Which of the following values is closest to the kinetic energy with which the block leaves the spring?
3 J
During an experiment a student records the net horizontal force exerted on an object moving in a straight line along a horizontal frictionless track. The graph above shows the force as a function of time. Of the following, which is the best approximation of the magnitude of the change in momentum of the object between 0 s and 4 s?
30 kg ⋅ m/s
After the cylinder leaves the table, but before it lands, how do the rotational kinetic energy and translational kinetic energy of the cylinder change, if at all?
Rotational Kinetic energy: Stays the same Translational Kinetic Energy: increases
A vehicle lands on Mars and explores its surface. The average gravitational field on the surface of Mars is 3.7 N kg . The weight of the vehicle is defined as the gravitational force exerted on it. Which of the following statements are true about the vehicle's weight? Select two answers.
1. The vehicle's weight increased while it was descending to the surface of Mars. 2. The vehicle weighs less on the surface of Mars than on the surface of Earth.
A 2.5 g marshmallow is placed in one end of a 40 cm pipe, as shown in the figure above. A person blows into the left end of the pipe to eject the marshmallow from the right end. The average net force exerted on the marshmallow while it is in the pipe is 0.7 N. The speed of the marshmallow as it leaves the pipe is most nearly
15 m/s
A student sets an object attached to a spring into oscillatory motion and uses a position sensor to record the displacement of the object from equilibrium as a function of time. A portion of the recorded data is shown in the figure above. The total distance traveled by the object between 0.35 s and 0.40 s is most nearly
2 cm
Four rods, each of mass M, are pinned at the left end to the horizontal surface of a table and are shown from above in the following figures. Each rod is free to rotate about a pivot at its left end with negligible friction. In each case, forces are exerted on the rod with different magnitudes and in different directions as shown. The rotational inertia of a rod of mass M and length L about the end of the rod is (1/3)ML2. In which cases do the rods experience equal initial angular accelerations? Select two answers.
1. 2L skinny rod, 2F force downwards 2. L thicker rod, 2F 60 degrees downwards
The angular momentum of a rigid body rotating around a fixed point as a function of time is shown in the graph. Which of the following statements are true? Select two answers.
1. The angular acceleration of the object is constant. 2. The net torque applied to the object is constant.
Two model cars, A and B, have the same mass but different bumpers. The acceleration of each car during its collision with a wall is measured, and the data are shown in the graphs above. Which of the following statements about the collisions are correct? Select two answers.
1. The cars experience approximately the same impulse. 2. The change in momentum for car B occurs over a shorter period of time than for car A.
A block of mass m is at rest on a rough incline, as shown in the figure above. Which of the following forces must have a magnitude equal to mg? Select two answers.
1. The total force exerted on the block by the incline 2. The gravitational force exerted on Earth by the block.
The diagram shows the forces exerted on a block that starts from rest and speeds up as it moves down a rough incline near Earth's surface. Which of the following statements are true? Select two answers.
1. The total mechanical energy of the block-Earth system decreases as the block slides down the incline. 2. The momentum of the block increases as the block slides down the incline.
A block of mass 2.0 kg , starting from rest, is pushed with a constant force across a horizontal track. The position of the block as a function of time is recorded, and the data are shown in the table. What is the magnitude of the change in momentum of the block between zero and 4.0 seconds?
1.6 kg*m/s
A student sets an object attached to a spring into oscillatory motion and uses a motion detector to record the velocity of the object as a function of time. A portion of the recorded data is shown in the figure above. The frequency of oscillation is most nearly
1.60 Hz
On Earth, when a box slides across a horizontal board, the board exerts a frictional force of magnitude F0 on the box. The board and the box are moved to a planet with twice the radius but one-third the mass of Earth. When the box slides across the board, the frictional force exerted by the board on the box is now
1/12 F0
An object is moving to the west at a constant speed. Three forces are exerted on the object. One force is 10 N directed due north, and another is 10 N directed due west. What is the magnitude and direction of the third force if the object is to continue moving to the west at a constant speed?
10√2 N , directed southeast
A 2kg box is pushed from rest across a horizontal surface where friction between the box and the surface is negligible. Students record the applied force at several equally spaced positions while pushing the box and create the graph shown. The change in momentum of the box is most nearly
12 kg⋅m/s
A rubber ball with mass 0.20 kg is dropped vertically from a height of 1.5 m above a floor. The ball bounces off of the floor, and during the bounce 0.60 J of energy is dissipated. What is the maximum height of the ball after the bounce?
12 m
Taking rightward as positive, which pair of graphs could represent the acceleration of block 2 and the center-of-mass acceleration of the two-block system?
Acceleration of block 2: upside down parabola Center of Mass Acceleration: zero flat horizontal line
A cart is moving on a level track in the positive x-direction. A force acting parallel to the x-axis is exerted on the cart. The graph above shows the net force exerted on the cart as a function of displacement. As the cart travels from x = 0 m to x = 4 m , what is the net change in the kinetic energy of the cart?
An increase of 10 J
The figure above shows a rod that is fixed to a horizontal surface at pivot P. The rod is initially rotating without friction in the counterclockwise direction. At time t, three forces of equal magnitude are applied to the rod as shown. Which of the following is true about the angular speed and direction of rotation of the rod immediately after time t ?
Angular Speed: Decreasing Direction of Rotation: Counterclockwise
A meterstick is held as shown above and then released from rest. The tabletop has negligible friction. Which figure below best indicates the path of the center of mass of the meterstick as it falls?
Arrow going straight down
A hollow plastic ball is projected into the air. There is significant air resistance opposing the ball's motion, so the magnitude of the ball's acceleration is not equal to g. At time t, the ball is moving up and to the right at an angle of 45° to the horizontal, as shown above. Which of the following best shows the magnitude a and the direction of the ball's acceleration at time t ?
Arrow southwest: a > g
A projectile fired into the air explodes and splits into two halves of equal mass that hit the ground at the same time. If the projectile had not exploded, it would have landed at point X, which is a distance R to the right of the launch point. After the explosion, one of the halves lands at point Y, which is a distance 2R to the right of the launch point. If air resistance is negligible, where did the other half land?
At the launch point
Three identical forces of magnitude F0 are applied to a meterstick that rests on a horizontal table, as shown in the diagram. At what location on the meterstick would a fourth force, also of magnitude F0, need to be applied in order to establish static equilibrium?
B
The figure shows three cases where two spheres are touching and attract each other with the gravitational force. The radii of the spheres in each case are shown. All of the spheres are made of material with the same density. Which of the following correctly ranks these cases based on the gravitational force between the spheres?
B > C > A
Based on the data presented in the graph, which of the following lists the points in the order in which the blocks are dropped onto the disk?
B, A, C
Block A is set on a rough horizontal table and is connected to a horizontal spring that is fixed to a wall, as shown. Block A is then also connected to hanging block B by a lightweight string that passes over an ideal pulley, as shown. The friction force exerted on block A by the table is not negligible. The blocks are initially held at rest so that the spring is not stretched. When the blocks are released, hanging block B moves downward and block A on the table moves to the right until the system comes again to rest. Let E1 be the mechanical energy of the blocks-spring system, and let E2 be the mechanical energy of the blocks-spring-Earth system. How do these two energies change from when the blocks are held at rest to when the blocks come to rest again?
Block-Spring System increases; Block-Springs-Earth System Decreases
Carts 1 and 2 are initially moving toward each other, as shown in the top figure. The carts collide and afterward are both moving to the right, as shown in the bottom figure. If the positive direction is to the right, which of the following best represents the force exerted on each cart by the other during the collision as a function of time?
Graph A (Cart 2 on top)
An elevator carrying a person of mass m is moving upward and slowing down. How does the magnitude F of the force exerted on the person by the elevator floor compare with the magnitude mg of the gravitational force?
F < mg
A cart of mass m rolls past the circular bottom of a hill (point P). Which of the following statements about the normal force Fn exerted on the cart at point P is correct?
Fn is greater than mg at point P, because the cart is experiencing an upward acceleration.
A regular hexagon of uniform density is initially at rest and free to rotate about an axis at its center. Three forces, FA, FB, and FC, have equal magnitude and are able to be applied in the direction and at the point shown in the figure. Which of these forces, if applied individually and for the same time interval, will produce the greatest increase in the hexagon's angular speed?
Force FA
Blocks X and Y are glued together and released from rest on a ramp with negligible friction, as shown in trial 1. The blocks are then separated and connected by a light spring, as shown in trial 2. The spring is compressed and the blocks are again released from rest on the ramp. Immediately after the blocks are released, is the net force on the two-block system the same or different between trial 1 and trial 2? Immediately after the blocks are released, is the net force on block Y the same or different between trial 1 and trial 2?
Force on System: The same Force on Block Y: Different
A disk with radius of 0.5 m is free to rotate around its center without friction. A string wrapped around the disk is pulled, as shown above, exerting a 2 N force tangent to the edge of the disk for 1 s. If the disk starts from rest, what is its angular speed after 1 s?
It cannot be determined without knowing the rotational inertia of the disk
A force F0 is applied continuously to a box initially at rest on a horizontal surface. The box slides with negligible friction for equal distances d1 and d2, as shown. How does the kinetic energy gained by the block over distance interval d2, ∆K2, compare to the kinetic energy gained over distance interval d1, ∆K1, and why?
K2 = K1
On a straight horizontal track along which blocks can slide with negligible friction, block 1 slides toward block 2, which is initially at rest. Block 1 collides with an electronic force probe attached to block 2, generating a force vs. time graph and causing block 2 to start sliding. What additional measurements must be made to determine the momentum of block 2 after the collision?
None
The position as a function of time for two objects moving along a straight line is shown in the graph. Which statement is true about the distances the two object have traveled at time tf?
Object 1 has traveled a greater distance
A cart of mass m is moving with negligible friction along a track with known speed v1 to the right. It collides with and sticks to a cart of mass 4m moving with known speed v2 to the right. Which of the two principles, conservation of momentum and conservation of mechanical energy, must be applied to determine the final speed of the carts, and why?
Only conservation of momentum, because the momentum lost by one cart is gained by the other and there is only one unknown quantity.
The figure above shows a uniform meterstick that is set on a fulcrum at its center. A force of magnitude F toward the bottom of the page is exerted on the meterstick at the position shown. At which of the labeled positions must an upward force of magnitude 2F be exerted on the meterstick to keep the meterstick in equilibrium?
Point B
At time t = 0 two figure skaters are moving together over ice with negligible friction, as shown above. Skater 1, represented by the large black dot, is twice as massive as skater 2, represented by the gray dot. At t = 2 s the skaters push off of one another. The location of skater 1 is shown at t = 4 s . At t = 4 s , skater 2 is located at which of the labeled points?
Point D
The figure above shows the paths of two stars of equal mass as they orbit their common center of mass. The positions of the stars at four different times are labeled in the figure. At which of the positions do the stars have their greatest speed?
Position 4 only
As the cylinder rolls down the ramp, how do the potential energy of the cylinder-Earth system and the kinetic energy of the cylinder change, if at all?
Potential Energy of the Cylinder-Earth System: decreases Kinetic Energy of the Cylinder: increases
Steel sphere A of mass M is moving along a horizontal surface with constant speed v. Identical steel sphere B is at rest and hangs on a string of length R attached to a support at point P, as shown in the figure above. The spheres collide, and as a result sphere A stops and sphere B swings a vertical height h before coming momentarily to rest. Knowing values for which of the following will allow determination of the angular impulse on sphere B with respect to P due to the collision?
R, M, and v
Two students need to move two identical boxes of mass M0 across a room where friction between the floor and the boxes cannot be neglected. One student moves the first box by pushing with a force of magnitude F0 at an angle θ from the horizontal, as shown in the figure for scenario 1. The other student moves the second box by pulling with a force of magnitude F0 at the same angle θ from the horizontal, as shown in the figure for scenario 2. Which of the following graphs could describe the motion of the two boxes as they are moved across the room?
Scenario 2 positive linear line Scenario 1 horizontal line
The energy bar charts shown in the figure indicate the gravitational potential energy U and total kinetic energy K for a system at two different times, t1 and a later time t2. The tables describe four different situations.
Situation B and Situation D
The figure above shows a truck pulling three crates across a rough road. Which of the following shows the directions of all the horizontal forces acting on crate 2 ?
Square with three lines going left saying rope, crate 3, and friction, and one line going right saying cable
A water-skier with weight Fg = mg moves to the right with acceleration a. A horizontal tension force T is exerted on the skier by the rope, and a horizontal drag force Fd is exerted by the water on the ski. The water also exerts a vertical lift force L on the skier. Which of the following are correct relationships between the forces exerted on the skier-ski system? Select two answers.
T - Fd = ma L - Fg = 0
Two identical blocks A and B are connected by a lightweight rope. Block A is pulled to the right by a constant force F0. The blocks are moving to the right across a rough surface and approach point P, where the rough surface transitions to a surface with negligible friction. How does the tension, T, in the rope connecting the blocks change, if at all, as block A passes point P?
T increases
The position as a function of time for two objects moving along a straight line is shown in the graph. At which of the following times do the two objects have the same velocity?
Tc
The figure above represents a stick of uniform density that is attached to a pivot at the right end and has equally spaced marks along its length. Any one of the four forces shown can be exerted on the stick as indicated. Which force will create the largest rate of change in the stick's angular momentum?
The 60 N force
Two identical spheres are attached to opposite ends of a thin rod of negligible mass, as shown in the figure. The spheres-rod system is thrown straight upward and is rotating counterclockwise as it moves through the air. Which of the following is correct about the angular momentum of the spheres-rod system while it is in the air? What is a valid justification?
The angular momentum remains constant because there is never a net torque acting on the system
An object is initially at rest. A varying force is applied to the object as shown in the graph. Which of the following correctly explains the momentum of the object at time t=7s ?
The final momentum of the object is negative because the magnitude of the area bounded by the graph and the horizontal axis is less from t=0s to t=2s than from t=2s to t=7s
Two objects, A and B, move toward one another. Object A has twice the mass and half the speed of object B. Which of the following describes the forces the objects exert on each other when they collide and provides the best explanation?
The forces exerted by each object on the other are the same, because interacting objects cannot exert forces of different magnitude on each other.
A student sets an object attached to a spring into oscillatory motion and uses a position sensor to record the displacement of the object from equilibrium as a function of time. A portion of the recorded data is shown in the figure above.
The slope of the tangent to a best-fit sinusoidal curve at 0.65 s
A student sets an object attached to a spring into oscillatory motion and uses a motion detector to record the velocity of the object as a function of time. A portion of the recorded data is shown in the figure above. The acceleration of the object at time t = 0.7 s is most nearly equal to which of the following?
The slope of the tangent to a best-fit sinusoidal curve at 0.7 s
A sled slides down a hill with friction between the sled and hill but negligible air resistance. Which of the following must be correct about the resulting change in energy of the sled-Earth system?
The sum of the kinetic energy and the gravitational potential energy changes by an amount equal to the energy dissipated by friction.
In trial 1 of an experiment, a cart moves with speed v0 on a frictionless, horizontal track and collides elastically with another cart that is initially at rest. In trial 2, the setup is identical except that the carts stick together during the collision. How does the speed of the two-cart system's center of mass change, if at all, during the collision in each trial?
Trial 1: does not change Trial 2: does not change
Two identical blocks are connected by a lightweight string that passes over a lightweight pulley that can rotate about its axle with negligible friction. The two-block system is released from rest and the blocks accelerate. Which of the following correctly relates the potential energy gained by the block 1-Earth system |∆U1| to the potential energy lost by the block 2-Earth system |∆U2| and provides correct evidence?
U1 < U2
The graphs above show the magnitude F of a force exerted on an object as a function of the object's position x for two trials in an experiment. W1 and W2 are the work done on the object by force 1 and force 2, respectively. How do W1 and W2 compare, and why?
W1 < W2 , because the average value of force 1 is smaller than the average value of force 2.
A block slides down an inclined plane whose roughness varies. Only during time interval 1 does the block slide with negligible friction. The coefficient of kinetic friction during time interval 3 is twice the coefficient of kinetic friction during time interval 2. The graph shows the block's velocity as a function of time. The table lists the mechanical energy dissipated due to friction over the different time intervals. Which of the following claims is true?
W3 > W2 > W4
A bicycle wheel of known rotational inertia is free to rotate about its central axis. With the wheel initially at rest, a student wraps a string around the wheel and pulls the string with a spring scale, causing the wheel to rotate. The student records the tension in the string and the time for which the string was pulled. Without measuring the wheel's final angular speed, can the student find the magnitude of the wheel's final angular momentum, and what is a correct explanation?
Yes. The student also needs to measure the wheel's radius to calculate the torque exerted on the wheel.
Which of the following is a correct expression for the acceleration of the box in scenario 2 ?
[F0 cos0 - u(M0g - F0 sin0)] / M0
A block is released from rest and slides down a frictionless ramp inclined at 30° from the horizontal. When the block reaches the bottom, the block-Earth system has mechanical energy E0. The experiment is repeated, but now horizontal and vertical forces of magnitude F are exerted on the block while it slides, as shown above. When the block reaches the bottom, the mechanical energy of the block-Earth system
is greater than E0
Blocks A and B, of masses mA and mB, are at rest on a frictionless surface, as shown above, with block A fixed to the table. Block C of mass mC is suspended by a string that is tied to block B over an ideal pulley. Which of the following gives the magnitude of the force exerted by block A on block B ?
mCg
A box of mass m is initially at rest at the top of a ramp that is at an angle θ with the horizontal. The block is at a height h and length L from the bottom of the ramp. The block is released and slides down the ramp. The coefficient of kinetic friction between the block and the ramp is µ . What is the kinetic energy of the box at the bottom of the ramp?
mgh - µmgL cos θ
Two satellites are in circular orbits around Earth. Satellite A has speed vA. Satellite B has an orbital radius nine times that of satellite A. What is the speed of satellite B?
vA/3
Two identical objects, X and Y, move toward each other at different speeds on a horizontal surface with negligible friction, as shown in the top figure. The objects then collide elastically and move away from each other. The kinetic energy of object X as a function of time is shown in the graph. Which of the following is true of the speed vY of object Y?
vY after the collision is greater than it was before the collision.
The blocks are now dropped in the reverse order and the final angular speed of the disk is ω2. How does ω2 compare to ω1, the final angular speed shown on the graph from the initial experiment?
w2 = w1
Two identical cars, car 1 and car 2, are moving in opposite directions on a straight road. The position of each car as a function of time is represented in the graph. What is the speed of the center of mass of the two-car system?
zero
