AP Physics P.E
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 FnFn and the weight of the car is FgFg. In which case is it always true that Fn>FgFn>Fg, and in which case is it always true that Fn<FgFn<Fg?
(Fn>Fg case 2) (Fn<Fg case 1)
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?
-5Gm2/r
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?
1.2 m
A block of mass 2.0 kg2.0 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 4.04.0 seconds?
1.6 kg⋅m/s
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 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
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, WnetWnet, done on the box for the given intervals of time?
Box1= Wnet=0 Box2=Wnet=0 Box3=Wnet<0
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.
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 F0t1
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 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.
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
A force F0F0 is applied continuously to a box initially at rest on a horizontal surface. The box slides with negligible friction for equal distances d1d1 and d2d2, as shown. How does the kinetic energy gained by the block over distance interval d2d2, ∆K2∆K2, compare to the kinetic energy gained over distance interval d1d1, ∆K1∆K1, and why?
∆K2=∆K1, because the applied force does the same work on the block over intervals d1 and d2.
A solid disk whose plane is parallel to the ground spins with an initial angular speed ω0ω0. Three identical blocks are dropped onto the disk at locations AA, BB, and CC, one at a time, not necessarily in that order. Each block instantaneously sticks to the surface of the disk, slowing the disk's rotation. A graph of the angular speed of the disk as a function of time is shown.
- B, A, C - W2=W1
An object is subject to multiple forces that result in the object having horizontal and vertical velocity components vxvx and vyvy, respectively as a function of time, as shown. Which of the following free-body diagrams could represent the forces exerted on the object?
-Arrow pointing up from center -Arrow point right from center -Arrow pointing down left diagonally
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.
-The angular speed of the object is constant. -The net torque applied to the object is constant.
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 -2 cm -2 hz
A block of mass m is at rest on a rough incline, as shown in figure above. Which of the following forces must have a magnitude equal to mg? Select two answers.
-The total force exerted on the block by the incline -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.
-The total mechanical energy of the block-Earth system decreases as the block slides down the incline. -The momentum of the block increases as the block slides down the incline.
On Earth, when a box slides across a horizontal board, the board exerts a frictional force of magnitude F0F0 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
1/12F0
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
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
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?
3J
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 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
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
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 Cart 2 −0.5 1.5 Cart 1 Cart 2 -1 m/s 2 m/s
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 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
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
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 Graph is straight Vertical Graph is diagonal then goes straight down then diagonal again
Block AA is set on a rough horizontal table and is connected to a horizontal spring that is fixed to a wall, as shown. Block AA is then also connected to hanging block BB 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 BB moves downward and block AA on the table moves to the right until the system comes again to rest. Let E1E1 be the mechanical energy of the blocks-spring system, and let E2E2 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?
Increases Decreases
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?
It looks like a stair case
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.
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
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 identical blocks AA and BB are connected by a lightweight rope. Block AA is pulled to the right by a constant force F0F0. The blocks are moving to the right across a rough surface and approach point PP, where the rough surface transitions to a surface with negligible friction. How does the tension, TT, in the rope connecting the blocks change, if at all, as block AA passes point PP?
T increases.
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=7st=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=2sthan 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.
Four rods, each of mass MM, 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 MM and length LL about the end of the rod is (1/3)ML2(1/3)ML2. In which cases do the rods experience equal initial angular accelerations? Select two answers.
The rod with a 2l and 2f as well as the rod with the L and 2f with an angle
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
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?
cart 2 line is on top and is even to cart 1 on the bottom
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
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||∆U1| to the potential energy lost by the block 2-Earth system |∆U2||∆U2| and provides correct evidence?
|∆U1|<|∆U2|, because the two-block system gains kinetic energy.
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
