A 2.5-kg block www is held at rest against a spring (k = 1200 N/m), compressing it d = 5.0 cm from its equilibrium position, then released. There is no friction d. A B h except where indicated otherwise. C How much potential energy is stored in the spring just before the block is released? Determine the speed of the block va at point A, just after it departs from the spring. Just to the right of point A, the block traverses a rough section, (represented by the thick line between A and B), losing half of its kinetic energy to friction. What is the block's speed at point B?
A 2.5-kg block www is held at rest against a spring (k = 1200 N/m), compressing it d = 5.0 cm from its equilibrium position, then released. There is no friction d. A B h except where indicated otherwise. C How much potential energy is stored in the spring just before the block is released? Determine the speed of the block va at point A, just after it departs from the spring. Just to the right of point A, the block traverses a rough section, (represented by the thick line between A and B), losing half of its kinetic energy to friction. What is the block's speed at point B?
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![**Title: Understanding Energy, Speed, and Friction in a Spring System**
**Introduction:**
This exercise explores the principles of energy conservation and the effects of friction in a mechanical system involving a spring and a block.
**Scenario Description:**
A 2.5-kg block is compressed against a spring with a spring constant \( k = 1200 \, \text{N/m} \). The block compresses the spring by \( d = 5.0 \, \text{cm} \) from its equilibrium position, then is released. There is no friction affecting the block except in a specified section.
**Diagram Explanation:**
- **A**: Point where the block starts after being released from the spring.
- **B**: Point after the block crosses a rough section, losing energy due to friction.
- **C**: Point at which the block reaches a certain height without any friction.
**Questions and Explanation:**
1. **How much potential energy is stored in the spring just before the block is released?**
The potential energy stored in the spring can be calculated using the formula for elastic potential energy:
\[
U = \frac{1}{2} k d^2
\]
where \( U \) is the potential energy, \( k \) is the spring constant, and \( d \) is the compression distance.
2. **Determine the speed of the block \( v_A \) at point A, just after it departs from the spring.**
As the block leaves the spring, all potential energy is converted into kinetic energy:
\[
\frac{1}{2} m v_A^2 = U
\]
where \( m \) is the mass and \( v_A \) is the velocity at point A.
3. **Just to the right of point A, the block traverses a rough section (represented by the thick line between A and B), losing half of its kinetic energy to friction. What is the block’s speed at point B?**
At this point, the block loses half of its kinetic energy:
\[
\frac{1}{2} \times \frac{1}{2} m v_A^2 = \frac{1}{2} m v_B^2
\]
Solve for \( v_B \).
4. **After point B, there is no longer any friction. At](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F946f068e-22bb-4068-a00a-e22f7e79f207%2F2d74c462-5868-44ce-8256-199ea2b7ee07%2Fu1547g0b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Energy, Speed, and Friction in a Spring System**
**Introduction:**
This exercise explores the principles of energy conservation and the effects of friction in a mechanical system involving a spring and a block.
**Scenario Description:**
A 2.5-kg block is compressed against a spring with a spring constant \( k = 1200 \, \text{N/m} \). The block compresses the spring by \( d = 5.0 \, \text{cm} \) from its equilibrium position, then is released. There is no friction affecting the block except in a specified section.
**Diagram Explanation:**
- **A**: Point where the block starts after being released from the spring.
- **B**: Point after the block crosses a rough section, losing energy due to friction.
- **C**: Point at which the block reaches a certain height without any friction.
**Questions and Explanation:**
1. **How much potential energy is stored in the spring just before the block is released?**
The potential energy stored in the spring can be calculated using the formula for elastic potential energy:
\[
U = \frac{1}{2} k d^2
\]
where \( U \) is the potential energy, \( k \) is the spring constant, and \( d \) is the compression distance.
2. **Determine the speed of the block \( v_A \) at point A, just after it departs from the spring.**
As the block leaves the spring, all potential energy is converted into kinetic energy:
\[
\frac{1}{2} m v_A^2 = U
\]
where \( m \) is the mass and \( v_A \) is the velocity at point A.
3. **Just to the right of point A, the block traverses a rough section (represented by the thick line between A and B), losing half of its kinetic energy to friction. What is the block’s speed at point B?**
At this point, the block loses half of its kinetic energy:
\[
\frac{1}{2} \times \frac{1}{2} m v_A^2 = \frac{1}{2} m v_B^2
\]
Solve for \( v_B \).
4. **After point B, there is no longer any friction. At
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