AP Physics 1 3.1: Translational Kinetic Energy

Relate translational kinetic energy to mass and speed, and recognize that the measured kinetic energy can depend on the observer’s reference frame.

[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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3.1.A—Describe the translational kinetic energy of an object in terms of the object’s mass and velocity question 1