Physics 211-Module 4 Hands On Activities Packet Part 2 c. What is the speed of the block when the displacement from equilibrium is 5 cm? Hint: use conservation of mechanical energy. Student Add Name Here d. What is the maximum speed during these oscillations? Hint: use conservation of energy and think about what the potential energy is when the speed is maximum. e. The experiment is repeated with the same mass and spring, but the amplitude is doubled. What happens to each of the following quantities: unchanged doubles

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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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plz just do part c, d e.

### Physics 211 - Module 4 Hands-On Activities Packet Part 2

**Student Add Name Here**

#### Questions

**c. What is the speed of the block when the displacement from equilibrium is 5 cm?**
*Hint: use conservation of mechanical energy.*

**d. What is the maximum speed during these oscillations?**
*Hint: use conservation of energy and think about what the potential energy is when the speed is maximum.*

**e. The experiment is repeated with the same mass and spring, but the amplitude is doubled. What happens to each of the following quantities:**

- **Maximum potential energy:**
  - decreases
  - unchanged
  - doubles
  - quadruples

- **Oscillation frequency:**
  - decreases
  - unchanged
  - doubles
  - quadruples

- **Maximum kinetic energy:**
  - decreases
  - unchanged
  - doubles
  - quadruples

- **Maximum speed:**
  - decreases
  - unchanged
  - doubles
  - quadruples

### Explanation of Diagram:

*(The diagram content is unclear and might be better depicted if visible. Provide a description if necessary once visible.)*

---

Make sure to carefully read each question and refer to the key concepts discussed in your lectures regarding the conservation of mechanical energy. Use the hints provided to guide your answers, particularly focusing on how energy transforms between potential and kinetic forms within oscillatory systems. When completing part (e), reflect on the relationships between amplitude, potential energy, kinetic energy, and frequency to accurately determine the changes in each quantity.

Happy studying!
Transcribed Image Text:### Physics 211 - Module 4 Hands-On Activities Packet Part 2 **Student Add Name Here** #### Questions **c. What is the speed of the block when the displacement from equilibrium is 5 cm?** *Hint: use conservation of mechanical energy.* **d. What is the maximum speed during these oscillations?** *Hint: use conservation of energy and think about what the potential energy is when the speed is maximum.* **e. The experiment is repeated with the same mass and spring, but the amplitude is doubled. What happens to each of the following quantities:** - **Maximum potential energy:** - decreases - unchanged - doubles - quadruples - **Oscillation frequency:** - decreases - unchanged - doubles - quadruples - **Maximum kinetic energy:** - decreases - unchanged - doubles - quadruples - **Maximum speed:** - decreases - unchanged - doubles - quadruples ### Explanation of Diagram: *(The diagram content is unclear and might be better depicted if visible. Provide a description if necessary once visible.)* --- Make sure to carefully read each question and refer to the key concepts discussed in your lectures regarding the conservation of mechanical energy. Use the hints provided to guide your answers, particularly focusing on how energy transforms between potential and kinetic forms within oscillatory systems. When completing part (e), reflect on the relationships between amplitude, potential energy, kinetic energy, and frequency to accurately determine the changes in each quantity. Happy studying!
### Simple Harmonic Motion of a Spring-Ball System

#### Problem Statement:
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 Description:
The graph on the right presents the displacement (x) versus time for the small ball attached to a spring. Key features to note in the graph include:

- **Y-Axis (Displacement x in cm):** This axis represents the position of the ball in centimeters (cm).
  - The range extends from 0 cm to 40 cm.
- **X-Axis (Time in ms):** This axis measures time in milliseconds (ms).
  - The range extends from 0 ms to 30 ms.

The graph shows the oscillatory motion of the ball with periodic peaks and troughs, indicative of simple harmonic motion.

#### Important Measurements from the Graph:
- **Amplitude (A):** The peak displacement from the equilibrium position.
  - From the graph, A ≈ 40 cm.
- **Period (T):** The time taken to complete one full cycle of oscillation.
  - From the graph, T ≈ 25 ms (estimated from peak to peak).

#### Solutions:
**a. Determining the Mass of the Ball:**

Given:
- Spring constant \( k = 2000 \) N/m
- Amplitude \( A \approx 40 \) cm \( = 0.4 \) m (converted to meters)
- Period \( T \approx 25 \) ms \( = 0.025 \) s (converted to seconds)

Using the formula for the period of a spring-mass system:
\[ T = 2\pi \sqrt{\frac{m}{k}} \]

Rearranging to solve for mass \( m \):
\[ m = \frac{T^2 k}{4\pi^2} \]

Substituting in the known values:
\[ m = \frac{(0.025)^2 \cdot 2000}{4\pi^2} \approx 0.00398 \text{ kg} \]

**b. Maximum Potential Energy:**

The potential energy stored in a spring at maximum displacement (amplitude
Transcribed Image Text:### Simple Harmonic Motion of a Spring-Ball System #### Problem Statement: 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 Description: The graph on the right presents the displacement (x) versus time for the small ball attached to a spring. Key features to note in the graph include: - **Y-Axis (Displacement x in cm):** This axis represents the position of the ball in centimeters (cm). - The range extends from 0 cm to 40 cm. - **X-Axis (Time in ms):** This axis measures time in milliseconds (ms). - The range extends from 0 ms to 30 ms. The graph shows the oscillatory motion of the ball with periodic peaks and troughs, indicative of simple harmonic motion. #### Important Measurements from the Graph: - **Amplitude (A):** The peak displacement from the equilibrium position. - From the graph, A ≈ 40 cm. - **Period (T):** The time taken to complete one full cycle of oscillation. - From the graph, T ≈ 25 ms (estimated from peak to peak). #### Solutions: **a. Determining the Mass of the Ball:** Given: - Spring constant \( k = 2000 \) N/m - Amplitude \( A \approx 40 \) cm \( = 0.4 \) m (converted to meters) - Period \( T \approx 25 \) ms \( = 0.025 \) s (converted to seconds) Using the formula for the period of a spring-mass system: \[ T = 2\pi \sqrt{\frac{m}{k}} \] Rearranging to solve for mass \( m \): \[ m = \frac{T^2 k}{4\pi^2} \] Substituting in the known values: \[ m = \frac{(0.025)^2 \cdot 2000}{4\pi^2} \approx 0.00398 \text{ kg} \] **b. Maximum Potential Energy:** The potential energy stored in a spring at maximum displacement (amplitude
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