Translational Kinetic Energy & Potential Energy (College Board AP® Physics 1: Algebra-Based): Exam Questions

Figure 1

A long track, inclined at an angle to the horizontal, has small speed bumps on it. The bumps are evenly spaced a distance apart, as shown in Figure 1. The track is actually much longer than shown, with over 100 bumps. A cart of mass is released from rest at the top of the track. A student notices that after reaching the 40th bump the cart's average speed between successive bumps no longer increases, reaching a maximum value . This means the time interval taken to move from one bump to the next bump becomes constant.

The student then increases the angle of incline of the ramp but everything else stays the same.

Indicate whether the maximum speed of the cart is greater than, less than or equal to that of the original ramp .

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

Use ideas about energy to justify your answer.

Figure 1

A physics class is asked to design a low-friction slide that will launch a block horizontally from the top of a lab table. Teams 1 and 2 assemble the slides as shown in Figure 1 and use identical blocks 1 and 2, respectively. Both slides start at the same height above the tabletop. However, Team 2's table is lower than Team 1's table. To compensate for the lower table, Team 2 constructs the right end of the slide to rise above the table top so that the block leaves the slide horizontally at the same height above the floor as does Team 1's block.

Both blocks are released from rest at the top of their respective slides. Block 1 lands a horizontal distance , and Block 2 lands a horizontal distance from their respective tables.

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

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

Justify your answer using qualitative reasoning beyond referencing equations.

Derive an expression for the time taken by Block 1 to hit the floor after leaving the slide in terms of , , and physical constants as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference book.

In another experiment, teams 1 and 2 use tables and low friction slides with the same height. However, the two slides have different shapes, as shown in Figure 2.

Figure 2

Both blocks 1 and 2 are released from rest at the top of their respective slides at the same time.

Does Block 1 hit the floor in more time, less time, or the same time as Block 2? Use the equation derived in part b) to justify your answer.

Figure 1

Two blocks are connected by a string that passes over a pulley, as shown in Figure 1. Block 1 is on a horizontal surface and is attached to a spring that is at its unstretched length. Frictional forces are negligible in the pulley's axle and between the block and surface. Block 2 is released from rest and moves downward before momentarily coming to rest.

The spring constant of the spring is , the mass of block 1 is and the mass of block 2 is . Block 2 starts from rest and speeds up, then it slows down and momentarily comes to rest at a position below its initial position. is the distance moved by block 2 before momentarily coming to rest.

The system includes the spring, Earth, both blocks, and the string, but not the surface. The initial state is taken to be when the blocks are at rest just before they start moving, and the final state is taken to be when the blocks first come momentarily to rest.

Diagram A shows the initial and final states for the system when the surface has negligible friction. Diagram B shows the initial and final states for the system when the surface has nonnegligible friction.

The shaded bars in the energy bar charts represent the potential energy of the spring and the gravitational potential energy of the blocks-Earth system, and respectively, in the initial and final states. Draw shaded rectangles to complete the energy bar chart for the final state when the surface has nonnegligible friction.

• Positive energy values are above the zero-energy line (“0”), and

  negative energy values are below the zero-energy line.

• Shaded regions should start at the dashed line representing zero energy.

• Represent any energy that is equal to zero with a distinct line on the

  zero-energy line.

• The relative height of each shaded region should reflect the magnitude

  of the respective energy consistent with the scale shown.

Figure 2

Figure 1

A group of students have a wheel mounted on a horizontal axle and a small block of known mass attached to one end of a light string. The other end of the string is attached to the wheel's rim and wrapped around it several times, as shown in Figure 1. When the block is released from rest and begins to fall, the wheel begins to rotate with negligible friction.

The students want to test whether the decrease in the gravitational potential energy of the block-Earth system is equal to the increase in the block's translational kinetic energy from when the block starts moving to immediately before it reaches the floor.

Describe an experimental procedure that the students could use to test their idea. Provide enough detail so that students could replicate the experiment, including any steps necessary to reduce experimental uncertainty.

Describe how the data collected in part a) could be plotted to create a linear graph and how that graph would be analyzed to determine whether the increase in the block's translational kinetic energy is equal to the decrease in the gravitational potential energy of the block-Earth system as the block falls.

Figure 1

A group of students are given a projectile launcher which consists of a spring with an attached plate, as shown in Figure 1. When the spring is compressed, the plate can be held in place by a pin at any of three positions A, B, or C.

Figure 2

Figure 2 shows a steel sphere placed against the plate, which is held in place by a pin at position C. The sphere is launched upon release of the pin. The students have access to the projectile launcher and equipment usually found in a school laboratory.

The students are asked to take measurements to create a graph that could be used to determine the spring constant of the spring.

Describe an experimental procedure the students could use to collect the data needed to determine the spring constant of the spring. Include any steps necessary to reduce experimental uncertainty. If needed, you may include a simple diagram of the setup with your procedure.

Describe how the data collected in part a) could be plotted to create a linear graph, and how that graph would be analyzed to determine the spring constant of the spring.