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.

In experiment 2, the student increases the angle of incline of the ramp, but everything else stays the same.

Indicate whether the maximum speed of the cart in experiment 2 is greater than, less than, or equal to that in experiment 1 by writing one of the following:

Use ideas about energy to justify your answer. In your justification, include qualitative reasoning beyond mathematical derivations or expressions.

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 hypothesize that 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, and want to collect data to test this hypothesis.

i) Indicate quantities that could be measured by the students that would allow them to determine the decrease in gravitational potential energy of the block-Earth system and the increase in the translational kinetic energy of the block as it falls.

ii) Briefly describe a method to reduce experimental uncertainty for the measured quantities.

i) Indicate what quantities the students could graph on the horizontal and vertical axes to create a linear graph that can be used to determine whether the decrease in gravitational potential energy is equal to the increase in translational kinetic energy.

ii) Briefly describe how the graph will be analyzed to determine whether the decrease in gravitational potential energy is equal to the increase in translational kinetic energy.

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 of known mass 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.

i) Indicate the measurements the students could make that would allow them to determine the spring constant of the spring.

ii) Briefly describe a method to reduce experimental uncertainty for the measured quantities.

i) Indicate what quantities the students could graph on the horizontal and vertical axes to create a linear graph that could be used to determine the spring constant of the spring.

ii) Briefly describe the relationship between the spring constant and a feature of the graph from part b)i).

The students perform another experiment using the projectile launcher, where they measure the range of spheres of different masses and their time of flight. The spring constant of the spring is . Table 1 shows the horizontal range of each sphere and its time of flight .

Table 1

The students create a graph with plotted on the vertical axis.

i) Label the horizontal axis of Figure 3 with a measured or calculated quantity. Include units, as appropriate. The graphed quantities should yield a linear graph that can be used to determine an experimental value for the mass of the sphere.

ii) On the grid in Figure 3, create a graph of the quantities indicated in part c)i).

• Clearly label the horizontal axis with a numerical scale

• Plot the corresponding data points on the grid

• Any columns added to Table 1 for scratch work will not be scored

Figure 3

iii) Draw a best-fit line to the data graphed in part c)ii).

Calculate an experimental value for the mass of the sphere using the best-fit line that you drew in part c)iii).