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AP Physics C: Mechanics 3.2 Work Questions

Analyse energy transfer by work using force components, path integrals, force-position graphs, the work-energy theorem, dissipative forces, and experimental data.

Syllabus
Effective Fall 2024
Course
AP Physics C: Mechanics

Exam points

  • calculate constant-force work from the force component along a displacement
  • integrate variable force or use force-position graph area to determine signed work
  • apply net work to changes in kinetic energy and compare motion at different speeds
  • separate work by conservative forces from energy dissipated by friction or drag
  • derive work for nonlinear springs, changing tension, or other position-dependent interactions

Covered syllabus points

3.2.A—Describe the work done on an object or system by a given force or collection of forces

Question 1

[Maximum number: 6]

A box is connected to one end of a rigid rod. Both the box and the rod have negligible mass. The other end of the rod is connected to a pivot. The box is open on one side, and a block is placed inside the box.

The center of mass of the block is displaced a vertical distance h, as shown in Figure 1. The block-box system is then released from rest and swings downward. There is negligible friction about the pivot. When the system is at the lowest point of its swing, the rod collides with a rigid stopper, as shown in Figure 2. The box comes to rest, and the block is launched horizontally out of the box. The block moves across a horizontal surface toward a motion sensor that measures the speed of the block. All frictional forces are negligible.

Figure 1

Figure 1

Figure 2

Figure 2

Question (a)

(a)

The experiment is repeated, but the horizontal surface on which the block slides is replaced with a new rough surface, as shown in Figure 3. The coefficient of kinetic friction between the block and the new surface is μ\mu.

Figure 3

Figure 3

The block-box system is pulled aside so that the center of mass of the block is displaced various vertical distances h and then released from rest. For each vertical distance, students measure the position x=xmax x=x_{\text {max }} at which the block comes to rest.

The students' measurements of h and xmax x_{\text {max }} are shown in Table 1.

Table 1

Table 1

[ 4 ]

Question (i)

(i)

Indicate two quantities, either measured quantities from Table 1 or additional calculated quantities, that could be graphed to produce a straight line that could be used to determine μ\mu.

Vertical axis:

Horizontal axis:

[ 1 ]

Question (ii)

(ii)

On the grid provided, create a graph of the quantities indicated in part C (i).

- Use Table 2 to record the measured or calculated quantities that you will plot.

- Clearly label the axes, including units as appropriate.

- Plot the points you recorded in Table 2.

Figure for Question (ii) — AP Physics C: Mechanics
[ 2 ]

Question (iii)

(iii)

Draw a best-fit line to the data graphed in part C (ii).

[ 1 ]

Question (b)

(b)

Using the best-fit line that you drew in part C (iii), calculate an experimental value for μ\mu.

[ 2 ]
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