2. The graph shows the x position of a small ball hooked onto a spring of spring constant 2000 N/m. a. What is the mass of the ball? x (cm) N 40 30 20 10 5 10 15 20 25 30 time (ms) b. What is the maximum potential energy stored in the spring during the oscillations? Assume U = 0 at equilibrium.

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Chapter1: Units, Trigonometry. And Vectors
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**Problem 2:**
The graph shows the x position of a small ball hooked onto a spring of spring constant 2000 N/m.

a. **What is the mass of the ball?**

b. **What is the maximum potential energy stored in the spring during the oscillations? Assume \( U = 0 \) at equilibrium.**

**Graph Explanation:**

The provided graph plots the position \( x \) (in centimeters) of a small ball against time (in milliseconds). The x-axis represents time ranging from 0 ms to 30 ms, and the y-axis represents the position \( x \) of the ball ranging from 0 cm to 40 cm. The curve depicts oscillatory motion, indicating that the ball follows a periodic back-and-forth movement due to the spring.

**Graph Details:**

- At \( t = 0 \) ms, \( x \approx 27 \) cm.
- At \( t \approx 7.5 \) ms, \( x \) reaches a peak value of \( x \approx 40 \) cm.
- At \( t \approx 15 \) ms, \( x \approx 20 \) cm which is approximately the midpoint.
- At \( t \approx 22.5 \) ms, \( x \) reaches a minimum value of \( x \approx 0 \) cm.
- The motion then continues to repeat following a sinusoidal pattern.

This periodic motion is characteristic of simple harmonic motion, a type of oscillatory motion. The spring constant provided (2000 N/m) along with this data will allow us to calculate the required physical properties such as the mass of the ball and the maximum potential energy stored in the spring.
Transcribed Image Text:**Problem 2:** The graph shows the x position of a small ball hooked onto a spring of spring constant 2000 N/m. a. **What is the mass of the ball?** b. **What is the maximum potential energy stored in the spring during the oscillations? Assume \( U = 0 \) at equilibrium.** **Graph Explanation:** The provided graph plots the position \( x \) (in centimeters) of a small ball against time (in milliseconds). The x-axis represents time ranging from 0 ms to 30 ms, and the y-axis represents the position \( x \) of the ball ranging from 0 cm to 40 cm. The curve depicts oscillatory motion, indicating that the ball follows a periodic back-and-forth movement due to the spring. **Graph Details:** - At \( t = 0 \) ms, \( x \approx 27 \) cm. - At \( t \approx 7.5 \) ms, \( x \) reaches a peak value of \( x \approx 40 \) cm. - At \( t \approx 15 \) ms, \( x \approx 20 \) cm which is approximately the midpoint. - At \( t \approx 22.5 \) ms, \( x \) reaches a minimum value of \( x \approx 0 \) cm. - The motion then continues to repeat following a sinusoidal pattern. This periodic motion is characteristic of simple harmonic motion, a type of oscillatory motion. The spring constant provided (2000 N/m) along with this data will allow us to calculate the required physical properties such as the mass of the ball and the maximum potential energy stored in the spring.
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