AP Physics C Mechanics 3.2 Work Overview

Describe work as energy transferred by a force through displacement, including calculus-based evaluation for position-dependent forces.

[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 2

(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 $\mu$ .

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 $x=x_{\text {max }}$ at which the block comes to rest.

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

Table 1

[ 4 ]

(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 $\mu$ .

Vertical axis:

Horizontal axis:

[ 1 ]

C (i) For indicating appropriate quantities that could be plotted to produce a linear graph that

can be used to determine $\mu$ , such as h vs. $x_{\text {max }}$

Scoring Note: Reponses that include the reciprocal of the preceding example, in

addition to other equivalent graphs, also earn this point.

(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 ]

(iii)

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

[ 1 ]

(b)

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

[ 2 ]

D For correctly relating the slope of the best-fit line to the value of $\mu$

Examples of acceptable responses includes the following:

Graph	Analysis
h vs. $x_{\text {max }}$	slope $=\mu$

For a value of $\mu$ within a range of 0.30 to 0.50

Example Response

$\begin{aligned} & E_{0}+W=E_{f} \\ & m g h-F_{f} x_{\max }=0 \\ & m g h=\mu m g x_{\max } \\ & h=\mu x_{\max } \end{aligned}$ $\begin{aligned} & y=m x+b \\ & h=\mu x_{\max } \\ & \text { slope }=\mu \\ & \text { slope }=\frac{0.95 \mathrm{~m}-0.30 \mathrm{~m}}{2.4 \mathrm{~m}-0.70 \mathrm{~m}} \\ & \text { slope }=0.38 \\ & \mu=\text { slope }=0.38 \end{aligned}$

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Covered syllabus points

3.2 Work question 1

Question (a)

Question (i)

Question (ii)

Question (iii)

Question (b)