AP Physics C Mechanics - 3.4 Conservation of Energy- Exam Style questions- FRQs

Conservation of Energy AP  Physics C Mechanics FRQ

Unit 3: Work, Energy, and Power

Weightage : 15-25%

AP Physics C Mechanics Exam Style Questions – All Topics

Question

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.
A. Students are asked to experimentally determine the acceleration due to gravity \(g\) using a linear graph. To determine \(g\), the students are permitted to use measurements from only a meterstick and the motion sensor.
Describe an experimental procedure using the described setup to collect data that would allow the students to determine an experimental value of \(g\) using a linear graph. Include any steps necessary to reduce experimental uncertainty.
B. Describe how the data collected in part A could be graphed and how that graph would be analyzed to determine the value of \(g\).
C. 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 \(\mu\).
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 \(x=x_{max}\) at which the block comes to rest. The students’ measurements of \(h\) and \(x_{max}\) are shown in Table 1.

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: _____________

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.
iii. Draw a best-fit line to the data graphed in part C (ii).
D. Using the best-fit line that you drew in part C (iii), calculate an experimental value for \(\mu\).

Most-appropriate topic codes (AP Physics C: Mechanics):

• Topic \(3.4\) — Conservation of Energy (Parts A, B, C, D)
• Topic \(2.7\) — Kinetic and Static Friction (Parts C, D)
• Topic \(3.2\) — Work (Parts C, D)
▶️ Answer/Explanation

(A)
Measure the height \(h\) at which the block-box system is released using the meterstick. Release the system from rest. Measure the speed \(v\) of the block as it slides across the horizontal surface using the motion sensor. Repeat the measurement of the speed multiple times for the same release height \(h\) to reduce experimental uncertainty, and repeat the experiment for various release heights.

(B)
Plot \(v^2\) on the vertical axis and \(2h\) on the horizontal axis.
According to the conservation of energy, the gravitational potential energy transforms into kinetic energy:
\(mgh = \frac{1}{2}mv^2 \Rightarrow v^2 = 2gh\)
The slope of the best-fit line of \(v^2\) vs. \(2h\) will yield a straight line whose slope is directly equal to \(g\).

(C)(i)
Applying the work-energy theorem to the entire path, the initial potential energy is dissipated by the work done by kinetic friction:
\(mgh – \mu mg x_{max} = 0 \Rightarrow h = \mu x_{max}\)
Therefore, to determine \(\mu\), we can graph \(h\) on the vertical axis and \(x_{max}\) on the horizontal axis.

(C)(ii)
The vertical axis should be correctly labeled as \(h\) with units \((\text{m})\) and a linear scale, and the horizontal axis should be correctly labeled as \(x_{max}\) with units \((\text{m})\) and a linear scale. The data points from Table 1 are accurately plotted on the grid according to these axes.

(C)(iii)


A straight best-fit line is drawn that properly approximates the overall linear trend of the plotted data points.

(D)

Based on the relationship \(h = \mu x_{max}\), the equation matches the linear form \(y = mx + b\) with a \(y\)-intercept of \(0\). The slope of the best-fit line is equal to \(\mu\).
Selecting two arbitrary points on the drawn best-fit line to calculate the slope, for example, \((0.70\,\text{m}, 0.30\,\text{m})\) and \((2.4\,\text{m}, 0.95\,\text{m})\):
\(\text{Slope} = \dfrac{\Delta h}{\Delta x_{max}}\)
\(\text{Slope} = \dfrac{0.95 – 0.30}{2.4 – 0.70}\)
\(\text{Slope} = 0.38\)
\(\mu = 0.38\)

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