AP Physics 1 2.1: Systems and Center of Mass

Define a physical system, decide which interactions matter, and use a system-level model to describe properties such as center-of-mass motion.

[Maximum number: 3]

(12 points, suggested time 25 minutes)

(a)

The students calculate the value of $g_{\text {exp }}$ to be significantly lower than the accepted value of $9.8 \mathrm{~m} / \mathrm{s}^{2}$ .

[ 3 ]

(i)

What is a physical reason, other than friction or air resistance, that could lead to a significant difference in the experimentally determined value of $g_{\text {exp }}$ ?

[ 1 ]

(ii)

Briefly explain how the physical reason you identified in part (c)(i) would lead to the decrease in the experimentally determined value of $g_{\text {exp }}$ .

Figure for Question (ii) — AP Physics 1: Algebra-Based

The students want to confirm that the acceleration is the same whether the cart rolls up or down the ramp. The students start the cart at the bottom and give the cart a quick push so that it rolls up the ramp and momentarily comes to rest. The x-axis is still defined to be parallel to the ramp with the origin at the top.

[ 2 ]

For correctly indicating the functional dependence between the reason listed in part (c)(i) and $g_{\text {exp }}$

Accept one of the following:

- Correctly indicating the functional dependence between the physical factor in the materials used and $g_{\text {exp }}$ (e.g., if the rotational inertia of the rotating wheels is nonnegligible, the cart will have a smaller acceleration and $g_{\text {exp }}$ will be smaller.)

- Correctly indicating the functional dependence between the physical factor in the environment and $g_{\text {exp }}$ (e.g., if the experiment was performed at a high elevation, the acceleration will be smaller and $g_{\text {exp }}$ will be smaller.)

- Correctly indicating the functional dependence between the physical error in the measurement collection and $g_{\text {exp }}$ (e.g., if the angle of the ramp is smaller than the measured value, the cart will have a smaller acceleration and $g_{\text {exp }}$ will be smaller.)

Example Response

The expression I derived for the value for $g_{\text {exp }}$ did not take into consideration that the wheels had any rotational inertia. If the wheels have rotational inertia and are rotating, the acceleration of the cart would be less than $g \sin \theta$ , so the value of $g_{\text {exp }}$ would be less than $9.8 \frac{\mathrm{~m}}{\mathrm{~s}^{2}}$ .

Total for part (c) 2 points

[Maximum number: 1]

Two identical objects, 1 and 2, are initially at rest. Object 1 remains at rest while Object 2 begins to accelerate in the +x-direction. Which of the following claims regard ing the location of the center of mass of the two-object system is correct?

A

The location of the center of mass does not change.

B

The location of the center of mass moves in the +x direction at a constant speed.

C

The location of the center of mass accelerates in the +x-direction and is located between the two ob jects.

D

The location of the center of mass accelerates in the +x-direction and is located at the same location as Object 2.

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AP Physics 1 2.1: Systems and Center of Mass

Exam points

Covered syllabus points

Covered syllabus points

2.1 Systems and Center of Mass question 1

Question (a)

Question (i)

Question (ii)

2.1 Systems and Center of Mass question 2