AP Physics Mid Term Answers

Sphere 1 of mass m and sphere 2 of mass 2m hang from light strings. Sphere 1 is pulled back, as shown above, and released from rest. Sphere 1 has kinetic energy Ki immediately before colliding with sphere 2. The two spheres stick together and move horizontally for an instant after the collision. During the collision, what is the change in the kinetic energy ΔK of the two-sphere system?

-2Ki/3

A box of mass m slides up a ramp with initial velocity +v0. The kinetic friction force on the box has magnitude f. Which of the following is a correct equation that could be used to determine the acceleration a of the box?

-f-mg sin theta= ma

A block is set on a rough horizontal table where frictional forces are not negligible. The block is pushed against a horizontal spring, and it is released at time t=0. The spring pushes the block across the table. At time t=t1, the block leaves the table. The block strikes the ground at time t=t2. Which of the following describes the change in mechanical energy of the block-spring system for times 0<t<t1 and t1<t<t2 ?

0<t<t1: Decreases t1<t<t2: Increases

A toy doll and a toy robot are standing on a frictionless surface facing each other. The doll has a mass of 0.20 kg, and the robot has a mass of 0.30 kg. The robot pushes on the doll with a force of 0.30 N. The magnitude of the acceleration of the robot is

1.0 m/s^2

An amusement park ride consists of a large vertical wheel of radius R that rotates counterclockwise on a horizontal axis through its center, as shown above. The cars on the wheel move at a constant speed v. Points A and D represent the position of a car at the highest and lowest point of the ride, respectively. A person of weight Fg sits upright on a seat in one of the cars. As the seat passes point A, the seat exerts a normal force with magnitude 0.8Fg on the person. While passing point A, the person releases a small rock of mass m, which falls to the ground without hitting anything. What is the normal force exerted on the rider when passing point D?

1.2 Fg

An amusement park ride consists of a large vertical wheel of radius R that rotates counterclockwise on a horizontal axis through its center, as shown above. The cars on the wheel move at a constant speed v. Points A and D represent the position of a car at the highest and lowest point of the ride, respectively. A person of weight Fg sits upright on a seat in one of the cars. As the seat passes point A, the seat exerts a normal force with magnitude 0.8Fg on the person. While passing point A, the person releases a small rock of mass m, which falls to the ground without hitting anything.The kinetic energy of the rock when it is at the same height as point D is most nearly

1/2m(v^2+4gR)

A meteoroid is in a circular orbit 600 km above the surface of a distant planet. The planet has the same mass as Earth but has a radius that is 90 % of Earth's (where Earth's radius is approximately 6370 km). The acceleration of the meteoroid due to the gravitational force exerted by the planet is most nearly

10 m/s^2 toward the center of the planet

On another planet, a ball is in free fall after being released from rest at time t=0. A graph of the height of the ball above the planet's surface as a function of time t is shown. The acceleration due to gravity on the planet is most nearly

16 m/s^2

The graph above shows the potential energy U of a system as one object in the system moves along the x-axis and the rest of the system does not move. Six evenly-spaced points along the x-axis are labeled. At point H, the object is moving in the positive x-direction and the mechanical energy of the system is 5.0 J. As the object moves, no energy enters or leaves the system. What is the kinetic energy of the object at point K?

3 J

At time t=0s, an object is moving to the right with a velocity v that can be modeled by the equation v=(4.2 m/s)-(1.4 m/s^2)t. At what time, if any, does the object change its direction of motion?

3.0 s

The graph shows the acceleration as a function of time for an object that is at rest at time t=0s. The distance traveled by the object between 0 and 2s is most nearly

3m

A 2.0kg disk is able to move on a straight, level track with negligible friction. With the disk initially at rest, a horizontal force is applied to the disk. The force is measured as a function of the disk's displacement, and the data are shown in the graph. When the disk's displacement is 2.0m, the speed of the disk is most nearly

4.0 m/s

An engineer measures the velocity v of a remote-controlled cart on a straight track at regular time intervals. The data are shown in the graph above. During which of the following time intervals did the cart return to its position at time t=0 s ?

7s<t<10s

At time t=0, a cart is at x=10 m and has a velocity of 3 m/s in the −x- direction. The cart has a constant acceleration in the +x-direction with magnitude 3 m/s2<a<6 m/s2 . Which of the following gives the possible range of the position of the cart at t=1 s ?

8.5m<x<10 m

Blocks 1 and 2 are connected by a light string that passes over a pulley with negligible mass and friction, as shown in the figure. Block 1 is on a table covered with two different materials, A and B. The two-block system is released from rest, and the speed of block 1 begins to increase. When block 1 reaches material B, its speed increases at a greater rate. Which of the following correctly compares the coefficient of kinetic friction U between block 1 and the two materials and describes the change in the magnitude of the net force on block 2 as block 1 slides from material A to material B?

Coefficients: UA>UB Net Force: Increases

A block is attached to the end of a string and initially moves at a constant speed in a horizontal circle of constant radius, as shown. The radius is then increased slowly while the speed remains the same. Which of the following graphs best represents the force exerted on the block by the string as a function of the radius?

Downward exponential line

Three blocks, A, B, and C, are pushed by a constant force Fthat is applied on block A as shown. There is negligible friction between the blocks and the surface. When a small object is attached to the top of block B, the normal force between blocks A and B is FAB and the normal force between blocks B and C is FBC. How will the values of FAB and FBC change if the small object is moved to the top of block C and the experiment is repeated?

FAB: Stays the same FBC: Increases

Three blocks are pushed along a rough surface by a force with magnitude P, as shown above. Fc is the magnitude of the contact force between blocks 2 and 3, and Ff, Fn, and Fg are the magnitudes of the friction, normal, and gravitational forces on block 3, respectively. Which of the following is a correct free-body diagram for block 3?

Fn pointing straight up, Fg pointing straight down, Ff pointing shortly to the left, Fc pointing (longer than Ff) to the right.

A block is set on a table, where there is negligible friction between the block and the table. The block is connected to an identical hanging block by a lightweight string that passes over an ideal pulley as shown. When the blocks are released from rest, the two-block system gains kinetic energy because work is done on the system. Which type of force or forces make a nonzero contribution to the net work done on the two-block system?

Gravitational force only

A box of mass m is released from rest and accelerates down a ramp that is at an angle (theta) to the horizontal, as shown. The coefficient of kinetic friction between the box and the ramp is U. As the box is sliding down the ramp, how are the magnitudes of the horizontal and vertical components of the box's velocity changing, if at all?

Horizontal Component: Increases Vertical Component: Increases

At time t=0, a projectile is launched from the top of a cliff at an angle of 30 degrees below the horizontal. Which of the following pairs of graphs best represents the horizontal displacement Δx and the vertical velocity component Vvert of the projectile as a function of time t?

Horizontal displacement: Going up from point O Vertical Velocity Component: Going down starting below point O

The graph above shows the potential energy U of a system as one object in the system moves along the x-axis and the rest of the system does not move. Six evenly-spaced points along the x-axis are labeled. At point H, the object is moving in the positive x-direction and the mechanical energy of the system is 5.0 J. As the object moves, no energy enters or leaves the system. In which segment does the net force exerted on the object have the greatest magnitude?

LM

A vertical spring has unstretched length L0, as shown in Figure 1. A block is attached to the top of the spring and slowly lowered until it is at rest and the spring has length Leq, as shown in Figure 2. The block is then pushed down until the spring is compressed to length Lcomp, as shown in Figure 3, and then released. After release, at what height will the kinetic energy of the block be maximum?

Leq

A simple pendulum consists of a sphere tied to the end of a string of negligible mass. The sphere is pulled back until the string is horizontal and then released from rest. Assume gravitational potential energy is zero when the sphere is at its lowest point. What angle will the string make with the horizontal when the kinetic energy and the potential energy of the sphere-Earth system are equal?

Less than 45

A satellite in a circular orbit around Earth is initially not rotating with respect to its center of mass. Two identical thrusters on opposite sides of the satellite fire in opposite directions over the same 10-minute time interval, as shown above, and then turn off. How does the firing of the thrusters affect the mechanical energy of the satellite-Earth system and the shape of the satellite's orbit, if at all?

Mechanical Energy of Satelite- Earth System: Increases Shape of Orbit: No effect

In Figure 1, cart Y is connected to cart X by a tight string and is also connected to the hanging block of mass m0 by a light string that passes over a pulley. Figure 2 shows a system that is identical except for one change: cart Y and X are connected by a spring at its equilibrium length. Both systems are released from rest. Is the hanging block's acceleration as a function of time the same in both systems, and why or why not?

No, because the tension in the string connected to the block is constant in one system but not in the other.

Two identical spaceships are moving through space both with speed v0. Both spaceships experience a net force of magnitude F0 over the same time interval. For spaceship 1, the net force acts in the same direction as the spaceship is moving; for spaceship 2, the net force is directed opposite to the spaceship's motion, causing spaceship 2 to slow down but not stop. For which spaceship, if either, does the kinetic energy change by a greater magnitude, and why?

Spaceship 1 will have a greater change in kinetic energy because the distance traveled is greater than that of spaceship 2.

Two objects, X and Y, experience external net torques that vary over a period of 5 seconds. Object X has a moment of inertia I0, and Object Y has a moment of inertia 2I0. The average value of the magnitude of the external net torque exerted on Object X from time t=0 to t=5s is TX. Similarly, the average value for Object Y is TY. The magnitudes of the angular momenta L of Objects X and Y versus t are shown in the graph. Which of the following expressions correctly relates TY to TX ?

TY=2TX

Two frictionless lab carts start from rest and are pushed along a level surface by a constant force. Students measure the magnitude and duration of the force on each cart, as shown in the partially completed data table above, and calculate final kinetic energy and momentum. Which cart has a greater kinetic energy at the end of the push?

The 1 kg cart

A block slides down an inclined plane in a classroom. Which of the following pieces of information are needed to determine whether the velocity of the block will be constant? Select two answers.

The angle of the inclined plane and the coefficient of kinetic friction between the block and the inclined plane.

A launcher with mass m1 is suspended from the ceiling by a string, as shown. A block with mass m2<m1 is launched horizontally. At the moment of launch, the block has unknown speed v2 and the launcher has unknown speed v1 in the opposite direction. Which of the following is a true statement about the forces exerted between the launcher and block?

The block and the launcher exert forces of equal magnitude on each other.

The graph shows the force exerted on a ball by the floor as a function of time as the ball bounces off the floor. If the positive direction is upward, which of the following graphs could represent the force exerted on the floor by the ball?

The graph that is the opposite of figure 1, in the negative Y area

A cart travels toward the right on a track where friction between the cart and track is negligible. The momentum of the cart as a function of time is modeled in the graph. Which of the following statements are true for the time recorded? Select two answers.

The impulse delivered to the cart is nearly equal to 0.75kg times m/s, The net external force exerted on the cart is nearly equal to 0.15 N

An object is moving along a straight, flat section of track. The net force acting on the object as a function of position is shown in the graph, where the positive direction is in the direction of motion of the object. Assuming the object moves from position x=0 to x=7d0 without stopping or moving backward, which of the following statements about its motion are correct? Select two answers

The kinetic energy of the object at position d0 is greater than 2F0d0

A test car and its driver, with a combined mass of 600 kg, are moving along a straight, horizontal track when a malfunction causes the tires to stop rotating. The car skids to a halt with constant acceleration, leaving skid marks on the road during the whole time it skids. Which two of the following measurements, taken together, would allow engineers to find the total mechanical energy dissipated during the skid? Select two answers

The length of the skid marks, and the coefficient of kinetic friction between the tires and the track

An object hangs in equilibrium from a spring, as shown above. The object is then displaced to one of the labeled points X, Y, or Z . Which of the following correctly ranks the elastic potential energy U stored in the spring when the object is at each of the three positions?

Uy>Ux>Uz

Two identical blocks slide along a ramp with negligible friction, as shown. The first block has an initial speed v0 up the ramp while the second has the same initial speed v0 down the ramp. The coordinate system shown defines down the ramp to be the positive x direction. While both blocks are sliding on the ramp, the center of mass velocity of the two-block system is

increasing in the +x direction