AP Physics 1: Algebra-Based 3.1 Translational Kinetic Energy Questions

Relate translational kinetic energy to mass and speed, calculate changes from motion data, and use its scalar nature to compare physical situations.

Exam points

calculate or rearrange the kinetic-energy relationship using mass and initial or final speed
compare kinetic energies as mass or speed changes, including the squared speed relationship
infer increasing, decreasing or constant kinetic energy from velocity or motion data
determine kinetic energy experimentally from measured mass, distance, time or speed
explain why direction reversal at unchanged speed does not change scalar kinetic energy

Covered syllabus points

3.1.A—Describe the translational kinetic energy of an object in terms of the object’s mass and velocity

[Maximum number: 3]

(12 points, suggested time 25 minutes)
A student hangs a spring of unknown spring constant k vertically by attaching one end to a stand, as shown in Figure 1. The other end of the spring has a small loop from which small cylinders can be hung. In addition to the spring, the student has access only to a variety of cylinders of unknown masses, a stopwatch, and a digital scale.

Using the data in the velocity-time graph, calculate the change in kinetic energy of the cart from $t=0.5 \mathrm{~s}$ to $t=2.0 \mathrm{~s}$ . Show your steps and substitutions.

(i)
For using the kinetic energy equation $K=\frac{1}{2} m v^{2}$ 1 point
For substituting one of the following: 1 point

- 0.25 kg as the mass

- $0.3 \mathrm{~m} / \mathrm{s}$ as the initial velocity

For an answer that approximates the change in kinetic energy to be $\Delta K \approx-0.0113 \mathrm{~J}$ 1 point

Scoring Note: A correct response with no supporting work earns this point only.
Scoring Note: The unit and the negative sign are not required to earn this point.
Example Response

\begin{aligned} & \Delta K=K_{f}-K_{i} \\ & \Delta K=\frac{1}{2} m v_{f}^{2}-\frac{1}{2} m v_{i}^{2} \\ & \Delta K=\frac{1}{2} 0.25(0)^{2}-\frac{1}{2} 0.25(0.3)^{2} \\ & \Delta K=-0.0113 \mathrm{~J} \end{aligned}

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Covered syllabus points

Question 1