Qualitative/Quantitative Translation (College Board AP® Physics 1: Algebra-Based): Exam Questions

Figure 1

Block 1 of mass slides to the right along a horizontal surface with speed toward Block 2 of mass , which is initially at rest, as shown in Figure 1. When Block 1 collides with Block 2, the blocks stick together. Friction between the blocks and the surface is negligible.

If Block 2 is much less massive than Block 1 , estimate the approximate speed of the two-block system after the collision in terms of . Justify your estimate using qualitative reasoning beyond referencing equations.

Starting with conservation of momentum, derive an equation for , the speed of the two–block system after the collision, in terms of , , and . Begin your derivation by writing a fundamental physics principle or an equation from the reference book.

If Block 2 is much less massive than Block 1, does the equation you derived in part b) agree with your qualitative reasoning from part a)? Justify why or why not.

Block 1 of mass and Block 2 of mass are sliding along a horizontal frictionless surface when they collide at time . Before the collision, the blocks slide toward each other. After the collision, the blocks slide together.

Indicate whether the kinetic energy of the two-block system after the collision is greater than, equal to, or less than the kinetic energy before the collision. Justify your answer using qualitative reasoning beyond referencing equations.

Figure 1

The graph in Figure 1 shows the velocities of the blocks as a function of time.

Using the graph in Figure 1, derive an expression for the ratio of the mass of Block 2 to the mass of Block 1, . Begin your derivation by writing a fundamental physics principle or an equation from the reference book.

Does the graph in Figure 1 agree with your qualitative reasoning from part a)? Use the expression derived in part b) to justify your answer.

Figure 1

A student conducts an experiment using a clay ball of mass and a rubber ball of the same mass. Each ball is thrown horizontally with speed toward two identical blocks of mass that are at rest at the edge of identical tables, as shown in Figure 1. After each collision, the blocks fall to the floor. Friction between the blocks and the table is negligible.

In Experiment A, the clay ball sticks to Block A. In Experiment B, the rubber ball bounces off of Block B at a speed of . After the collisions, Block A lands a horizontal distance , and Block B lands a horizontal distance from the table's edge.

Indicate whether is greater than, less than, or equal to .

⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽

Justify your answer using qualitative reasoning beyond referencing equations.

Starting with conservation of momentum, derive an equation for the ratio of the speed of Block A after the collision to the speed of Block B after the collision, . Express your answer in terms of , , and . Begin your derivation by writing a fundamental physics principle or an equation from the reference book.

If the balls are much less massive than the blocks , does the equation you derived in part b) agree with your qualitative reasoning from part a)? Justify why or why not.

Figure 1

The left end of a uniform beam of mass and length is attached to a wall by a hinge, as shown in Figure 1. One end of a string with negligible mass is attached to the right end of the beam. The other end of the string is attached to the wall above the hinge at Point 1. The beam remains horizontal. The hinge exerts a force on the beam of magnitude , and the angle between the beam and the string is .

Figure 2

The string is then attached lower on the wall, at Point 2, and the beam remains horizontal, as shown in Figure 2. The angle between the beam and the string is . The dashed line represents the string shown in Figure 1.

The magnitude of the tension in the string shown in Figure 1 is . The magnitude of the tension in the string shown in Figure 2 is .

Indicate whether is greater than, less than, or equal to .

⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽

Briefly justify your answer, using qualitative reasoning beyond referencing equations.

Starting with Newton’s second law in rotational form, derive an expression for the magnitude of the tension in the string. Express your answer in terms of , , and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference book.

Does the equation you derived in part b) agree with your qualitative reasoning from part a)? Justify why or why not.

A small block of mass is attached to a horizontal ideal spring with a spring constant . The block oscillates on a frictionless surface with an amplitude . A student places a second identical block onto the first block at maximum displacement. The new system continues oscillating. Air resistance is negligible.

Indicate whether the frequency of oscillation increases, decreases, or remains constant after the second block is added. Justify your claim using qualitative energy reasoning beyond referencing equations.

A small block of mass is attached to a horizontal ideal spring with a spring constant . The block oscillates on a frictionless surface with an amplitude . A student adds a second identical block onto the first block at maximum displacement. The new system continues oscillating. Air resistance is negligible.

Derive an expression for the new frequency of oscillation after the second block is added. Express your answer in terms of , , and fundamental constants.

The period of the system is when the additional mass is added. The additional mass is then removed, and the spring constant is halved. The period of this system is now .

Indicate whether is greater than, equal to, or less than after the changes to the system. Justify your prediction.

Figure 1

The left end of a rod of length and rotational inertia is attached to a frictionless horizontal surface by a frictionless pivot, as shown in Figure 1. Point marks the center (midpoint) of the rod. The rod is initially at rest but is free to rotate around the pivot. A disk of mass slides towards the rod with velocity perpendicular to the rod. Following the collision, the disk sticks to the rod a distance from the pivot.

If the disk is much less massive than the rod, indicate whether the rod would gain the largest angular speed if the disk were to hit the rod to the left of point , at point , or to the right of point .

⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ To the left of ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ At ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ To the right of

Justify your answer using qualitative reasoning beyond referencing equations.

Starting with conservation of angular momentum, derive an equation for , the angular speed of the rod after the collision, in terms of , , , , and . Begin your derivation by writing a fundamental physics principle or an equation from the reference book.

The experiment is repeated with a second disk. Following the collision, the second disk bounces backward instead of sticking to the rod. The angular speed of the rod after the second collision is .

Indicate whether is greater than, less than, or equal to .

⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽

Justify your reasoning using the equation you derived in part b).