Two blocks of masses m and 3m are placed on a frictionless, horizontal surface. A light spring is attached to the more massive block, and the blocks are pushed together with the spring between them as shown the figure below. A cord initially holding the blocks together is burned; after that happens, the block of mass 3m moves to the right with a speed of Vam = 1.65 m/s. 3m Before a 3m After (a) What is the velocity of the block of mass m? (Assume right is positive left is negative.) -4.9 v m/s (b) Find the system's original elastic potential energy, taking m = 0.470 kg. Enter a number. is the elastic potential energy transferred after the string is cut? J (c) Is the original energy in the spring or in the cord? • in the spring in the cord (d) Is the momentum of the system conserved in the bursting-apart process? • Yes No (e) If the spring was compressed by 5.30 cm, what is the spring constant of the spring?

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**Educational Website Content: Analyzing Elastic Potential Energy and Momentum Conservation**

**Problem Scenario:**
Two blocks with masses \( m \) and \( 3m \) are placed on a frictionless, horizontal surface. A light spring is attached to the more massive block, and the blocks are compressed together with the spring between them. A cord initially holds the blocks together, which is then burned. Upon release, the block with mass \( 3m \) moves to the right with a speed of \( v_{3m} = 1.65 \, \text{m/s} \).

**Diagram Explanation:**
1. **Before Release:**
   - The two blocks, \( m \) and \( 3m \), are held together by a spring on a horizontal line with no motion.
2. **After Release:**
   - Block \( m \) moves to the left, while block \( 3m \) moves to the right.

**Questions:**

**(a) Velocity of Block \( m \):**
- Determine the velocity of block \( m \), assuming the right direction is positive and the left is negative.
- **Answer:** \(-4.9 \, \text{m/s}\)

**(b) Elastic Potential Energy:**
- Calculate the system's original elastic potential energy, taking \( m = 0.470 \, \text{kg} \).

**(c) Energy Source:**
- Determine if the original energy is stored in the spring or the cord.
- **Answer Choices:**
  - In the spring (correct)
  - In the cord

**(d) Momentum Conservation:**
- Is the momentum of the system conserved during the process?
- **Answer Choices:**
  - Yes (correct)
  - No

**(e) Spring Constant Calculation:**
- If the spring was compressed by \( 5.30 \, \text{cm} \), determine the spring constant.
- **Answer Prompt:** Enter answer in N/m

**Instructions:**
Use the information and formulas related to elastic potential energy and momentum conservation to complete the calculations above. Understanding these principles is crucial in solving problems involving mechanical energy and dynamic systems.

**Resources for Further Learning:**
Explore topics like Hooke's Law, conservation laws, and kinetic energy to develop a deeper understanding of the underlying physics principles.
Transcribed Image Text:**Educational Website Content: Analyzing Elastic Potential Energy and Momentum Conservation** **Problem Scenario:** Two blocks with masses \( m \) and \( 3m \) are placed on a frictionless, horizontal surface. A light spring is attached to the more massive block, and the blocks are compressed together with the spring between them. A cord initially holds the blocks together, which is then burned. Upon release, the block with mass \( 3m \) moves to the right with a speed of \( v_{3m} = 1.65 \, \text{m/s} \). **Diagram Explanation:** 1. **Before Release:** - The two blocks, \( m \) and \( 3m \), are held together by a spring on a horizontal line with no motion. 2. **After Release:** - Block \( m \) moves to the left, while block \( 3m \) moves to the right. **Questions:** **(a) Velocity of Block \( m \):** - Determine the velocity of block \( m \), assuming the right direction is positive and the left is negative. - **Answer:** \(-4.9 \, \text{m/s}\) **(b) Elastic Potential Energy:** - Calculate the system's original elastic potential energy, taking \( m = 0.470 \, \text{kg} \). **(c) Energy Source:** - Determine if the original energy is stored in the spring or the cord. - **Answer Choices:** - In the spring (correct) - In the cord **(d) Momentum Conservation:** - Is the momentum of the system conserved during the process? - **Answer Choices:** - Yes (correct) - No **(e) Spring Constant Calculation:** - If the spring was compressed by \( 5.30 \, \text{cm} \), determine the spring constant. - **Answer Prompt:** Enter answer in N/m **Instructions:** Use the information and formulas related to elastic potential energy and momentum conservation to complete the calculations above. Understanding these principles is crucial in solving problems involving mechanical energy and dynamic systems. **Resources for Further Learning:** Explore topics like Hooke's Law, conservation laws, and kinetic energy to develop a deeper understanding of the underlying physics principles.
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