AP Physics Study Guide

An object of mass m attached to a spring with constant k oscillates with amplitude A. Assuming air resistance and the mass of the spring to be negligible, which of the following changes alone would cause the period of this oscillation to increase? I. Increasing m II. Increasing A III. Using a spring with greater k

I only

Block X of mass M is attached to block Y of mass 2M by a light string that passes over a pulley of negligible friction and mass, as shown above. In which direction will the center of mass (COM) of the two-block system move after it is released from rest, and what is the magnitude of the acceleration a of block X ?

(COM) | a Down and to the right | 2g/3

A thin rod of length d on a frictionless surface is pivoted about one end, as shown above, and can rotate freely. The rod is at rest when it is struck by a sphere with linear momentum of magnitude pi perpendicular to the rod. The sphere rebounds along its original line of motion with momentum of magnitude pf. What is the magnitude of the angular momentum of the rod immediately after the collision?

(pf + pi )d

The pendulum illustrated above has a length of 2 m and a bob of mass 0.04 kg. It is held at an angle Ѳ, as shown, where cosѲ = 0.9. The frequency of oscillation is most nearly

(√5/2π) Hz

A person applies an impulse of 5.0 kg∙m/s to a box in order to set it in motion. If the person is in contact with the box for 0.25 s, what is the average force exerted by the person on the box?

20.0 N

An object moves up and down the y-axis with an acceleration given as a function of time t by the expression a = A sin ωt, where A and ω are constants. What is the period of this motion?

2π/ω

A ball is dropped and bounces off the floor. Its speed is the same immediately before and immediately after the collision. Which of the following is true about the collision between the ball and the floor?

The ball's momentum changes direction but not magnitude.

A graph of the angular velocity ω as a function of time t is shown for an object that rotates about an axis. Three time intervals, 1-3, are shown. Which of the following correctly compares the angular displacement Δθ of the object during each time interval?

Δθ2>Δθ1=Δθ3

The figure above shows the net force exerted on an object as a function of the position of the object. The object starts from rest at position x = 0 m and acquires a speed of 3.0 m / s after traveling a distance of 0.090 m. What is the mass of the object?

0.030 kg

A 1.0 kg lump of clay is sliding to the right on a frictionless surface with speed 2 m/s . It collides head-on and sticks to a 0.5 kg metal sphere that is sliding to the left with speed 4 m/s . What is the kinetic energy of the combined objects after the collision?

0J

A block of mass M is sliding with an initial speed vi along a horizontal surface with negligible friction. A constant force of magnitude FA is exerted on the object at an upward angle of 60∘ from the horizontal, causing the object to speed up. If the block remains in contact with the floor, what is the change in the block's kinetic energy as it moves a horizontal distance Δx ?

1/2FAΔx

A force F is exerted on a 5 kg block to move it across a rough surface, as shown above. The magnitude of the force is initially 5 N, and the block moves at a constant velocity. While the block is moving, the force is instantaneously increased to 12 N. How much kinetic energy does the block now gain as it moves a distance of 2 m?

14 J

A simple pendulum is used to determine the acceleration due to gravity at the surface of a planet. The pendulum has a length of 2 m and its period is measured to be 2 s. The value of g obtained in this investigation is most nearly

20 m/s2

A 100 kg cart goes around the inside of a vertical loop of a roller coaster. The radius of the loop is 3 m and the cart moves at a speed of 6 m/s at the top. The force exerted by the track on the cart at the top of the loop is

200 N

A block that is connected to a horizontal spring is allowed to oscillate, and a graph of its velocity as a function of time is shown in the figure. At t=7s, the block detaches from the spring. All frictional forces are considered to be negligible. What distance will the block travel from t=7s to t=10s?

3.0m

A block of mass 2 kg slides along a horizontal tabletop. A horizontal applied force of 12 N and a vertical applied force of 15 N act on the block, as shown above. If the coefficient of kinetic friction between the block and the table is 0.2, the frictional force exerted on the block is most nearly

7N

An object weighing 120 N is set on a rigid beam of negligible mass at a distance of 3 m from a pivot, as shown above. A vertical force is to be applied to the other end of the beam a distance of 4 m from the pivot to keep the beam at rest and horizontal. What is the magnitude F of the force required?

90 N

Two blocks are connected to identical ideal springs and are oscillating on a horizontal frictionless surface. Block A has mass m, and its motion is represented by the graph of position as a function of time shown above on the left. Block B's motion is represented above on the right. Which of the following statements comparing block B to block A is correct?

Because block B has more mass, its acceleration is smaller than that of block A at any given displacement from the equilibrium position.

A force of constant magnitude F and fixed direction acts on an object of mass m that is initially at rest. If the force acts for a time interval ∆t over a displacement ∆x , what is the magnitude of the resultant change in the linear momentum of the object?

F ∆t

An object is moving in the positive x-direction while a net force directed along the x-axis is exerted on the object. The figure above shows the force as a function of position. What is the net work done on the object over the distance shown?

F0d

Two small objects of mass m0 and a rotating platform of radius R and rotational inertia Ip about its center compose a single system. Students use the system to conduct two experiments. The objects are assumed to be point masses. Experiment 1 [picture] Each object of mass m0 is placed a distance r1 away from the center of the platform such that both masses are on opposite sides of the platform. A constant tangential force F0 is applied to the edge of the platform for a time Δt0, as shown in Figure 1. The system is initially at rest. Experiment 2 [picture] Each object of mass m0 is placed a distance r2 away from the center of the platform such that both masses are on opposite sides of the platform. Distance r2<r1 . A constant tangential force F0 is applied to the edge of the platform for a time Δt0 , as shown in Figure 2. The system is initially at rest. Which of the following graphs represents the angular displacement of the system as a function of time for the system in experiment 1?

Graph that is curving up (almost like an exponential function)

Three forces act on an object. If the object is in translational equilibrium, which of the following must be true? I. The vector sum of the three forces must equal zero II. The magnitudes of the three forces must be equal III. All three forces must be parallel.

I only

How does an air mattress protect a stunt person landing on the ground after a stunt?

It reduces the kinetic energy loss of the stunt person.

The diagram above shows a top view of a child of mass M on a circular platform of mass 5M that is rotating counterclockwise. Assume the platform rotates without friction. Which of the following describes an action by the child that will result in an increase in the total angular momentum of the child-platform system?

None of the actions described will change the total angular momentum of the child-platform system.

A kitten sits in a lightweight basket near the edge of a table. A person accidentally knocks the basket off the table. As the kitten and basket fall, the kitten rolls, turns, kicks, and catches the basket in its claws. The basket lands on the floor with the kitten safely inside. If air resistance is negligible, what is the acceleration of the kitten-basket system while the kitten and basket are in midair?

The acceleration is directed downward with magnitude equal to g because the system is a projectile.

A person is running on a track. Which of the following forces propels the runner forward?

The force of friction exerted by the ground on the person

A spaceship is traveling from Earth to the Moon. Which of the following is true of the gravitational force on the ship due to the two objects when the ship is equidistant from Earth and the Moon?

There is a net force because the force exerted by Earth is greater than that exerted by the Moon.

Two identical wheels, wheel 1 and wheel 2, initially at rest begin to rotate with constant angular accelerations α. After rotating through the same angular displacement, Δθ0 , the angular velocity of wheel 1 is ω1 and the angular velocity of wheel 2 is ω2=3ω1 . How does the angular acceleration of wheel 2, α2, compare to the angular acceleration of wheel 1, α1 ?

α2=9α1

The graph above shows velocity v as a function of time t for a 0.50 kg object traveling along a straight line. The graph has three segments labeled 1, 2, and 3. A rope exerts a constant force of magnitude FT on the object along its direction of motion the whole time. During segment 2 only, a frictional force of magnitude Ff is also exerted on the object. For another identical object initially at rest, no frictional force is exerted during segment 2 (between t = 2 s and t = 4 s). A rope exerts the same constant force of magnitude FT as in the previous scenario. What is the change in the object's kinetic energy during segment 2?

12.0 J

A student attaches a block to a vertical spring of unknown spring constant k0 so that the block-spring system will oscillate if the block-spring system is released from rest at a vertical position that is not the system's equilibrium position. The student varies the object's mass and uses a stopwatch to determine the time it takes the object to make one oscillation. The student creates the graph that is shown. The slope of the line of best fit is equal to which of the following quantities?

2π/√k0

In which of the following situations is the kinetic energy of the object decreasing?

A baseball is heading upward after being thrown at an angle.

The figures below indicate forces acting on a rod in different situations. The lengths of the force vectors are proportional to the magnitudes of the forces. In which situation is the rod in both translational and rotational equilibrium?

Shaped like a T

A system consists of a disk rotating on a frictionless axle and a piece of clay moving toward it, as shown in the figure above. The outside edge of the disk is moving at a linear speed v, and the clay is moving at speed v/2. The clay sticks to the outside edge of the disk. How does the angular momentum of the system after the clay sticks compare to the angular momentum of the system before the clay sticks, and what is an explanation for the comparison?

It is the same because there is no external torque acting on the system.

A system consists of two spheres, of mass m and 2m, connected by a rod of negligible mass, as shown above. The system is held at its center of mass with the rod horizontal and released from rest near Earth's surface at time t = 0 . Which of the following best explains why the system does not rotate around its center of mass as it falls?

The Earth exerts a larger gravitational force on the sphere of mass 2m, but that sphere is closer to the center of mass and the torques cancel out.

An object is moving to the right with speed vi when a force of magnitude F is exerted on it. In which of the following situations is the object's direction of motion changing and kinetic energy decreasing at the instant shown?

The one with F pointing up to the top-left

A person holds a book at rest a few feet above a table. The person then lowers the book at a slow constant speed and places it on the table. Which of the following accurately describes the change in the total mechanical energy of the Earth-book system?

The total mechanical energy decreases, because the person does negative work on the book by exerting a force on the book in the direction opposite to its displacement.

A group of students must study the oscillatory motion of a pendulum. One end of a light string is attached to the ceiling, and the other end of the string is attached to a mass hanger so that small disks of various masses may be stacked on the hanger, as shown in the figure. The students want to determine how the length of the pendulum affects the period of the pendulum. Which of the following procedures should the students use to conduct the experiment?

Measure the length of the string with a meterstick. Place two disks on the hanger. Raise the hanger-disk system to a vertical position above its lowest point. Release the system from rest. Use a stopwatch to determine how long it takes the system to make ten oscillations. Repeat the experiment for different string lengths.

The diagram above shows a top view of a child of mass M on a circular platform of mass 2M that is rotating counterclockwise. Assume the platform rotates without friction. Which of the following describes an action by the child that will increase the angular speed of the platform-child system and gives the correct reason why?

The child moves toward the center of the platform, decreasing the rotational inertia of the system.

For which of the following motions of an object must the acceleration always be zero? I. Any motion in a straight line II. Simple harmonic motion III. Any motion in a circle

None of these motions guarantees zero acceleration.

A uniform disk spins about an axis that passes through the center of the disk and is perpendicular to the plane of the disk, as shown in Figure 1. The disk has an initial angular velocity of ωd and uniformly accelerates to rest over time. The angular velocity of the disk as a function of time is shown in Figure 2. A student must determine the angular displacement of a point on the edge of the disk from t=0 to the instant in time the disk comes to rest if the point's initial velocity is changed to 2ωd but its angular acceleration is the same as shown in Figure 2. How can the graph in Figure 2 be changed before the student can determine the angular displacement? Justify your selection.

Recreate the graph with a vertical intercept that is twice the value of the intercept shown in Figure 2, because the angular velocity is increased from ωd to 2ωd. The slope of the line should be the same in both graphs, because the angular acceleration is the same in both graphs.

A disk is initially rotating counterclockwise around a fixed axis with angular speed w0. At time t = 0, the two forces shown in the figure above are exerted on the disk. If counterclockwise is positive, which of the following could show the angular velocity of the disk as a function of time?

The graph that has a negative slope (downwards)

An object of mass m is initially at rest and free to move without friction in any direction in the xy-plane. A constant net force of magnitude F directed in the +x direction acts on the object for 1 s. Immediately thereafter a constant net force of the same magnitude F directed in the +y direction acts on the object for 1 s. After this, no forces act on the object. Which of the following vectors could represent the velocity of the object at the end of 3 s, assuming the scales on the x and y axes are equal?

The middle one (Looks to have a slope of 1)

A box is given a sudden push up a ramp. Friction between the box and the ramp is not negligible. Which of the following diagrams best represents the directions of the actual forces acting on the box as it moves upward after the push?

The one that has three arrows: one is pointed straight down, another is perpendicular to the left side and the last one is perpendicular to the top side of the box.

A simple pendulum and a mass hanging on a spring both have a period of 1 s when set into small oscillatory motion on Earth. They are taken to Planet X, which has the same diameter as Earth but twice the mass. Which of the following statements is true about the periods of the two objects on Planet X compared to their periods on Earth?

The period of the pendulum is shorter; that of the mass on the spring is the same.

A cart is constrained to move along a straight line. A varying net force along the direction of motion is exerted on the cart. The cart's velocity v as a function of time t is shown in the graph above. The five labeled points divide the graph into four sections. During some part of the motion, the work done on the cart is negative. What feature of the motion indicates this?

The speed is decreasing.

A student predicts that a block sliding down a ramp inclined at 45 degrees should have an acceleration of approximately 7 m/s2. The block is released from rest, and the student measures the distance the block travels and the time it takes to travel that distance. The student determines that the block's acceleration is only 5.5 m/s2. Which of the following is the most likely reason for the difference between the predicted and calculated accelerations?

The student's model used to make the prediction did not account for all of the forces that are exerted on the block.

One end of a string is attached to the ceiling, and the other end of the string is attached to a cradle that has a meterstick that runs through it. The meterstick can slide through the cradle so that the horizontal position of a point on the meterstick can be changed in the horizontal direction. Students may hang objects of various masses from the meterstick, as shown in the figure. The students notice that when the meterstick-cradle-object-object system is not balanced, the meterstick will rotate. Consider the situation shown above in which the center of the meterstick is aligned with the center of the cradle, which is at a position of x=0m. The system is released from rest. Which of the following claims is correct about the motion of the system containing the meterstick, cradle, and two objects if the system is free to rotate?

The system will rotate in the clockwise direction with an increasing angular speed.

A massless rigid rod of length 3d is pivoted at a fixed point W, and two forces each of magnitude F are applied vertically upward as shown above. A third vertical force of magnitude F may be applied, either upward or downward, at one of the labeled points. With the proper choice of direction at each point, the rod can be in equilibrium if the third force of magnitude F is applied at point

V or X only