10: A 8.00-kg metal ball is hanging from a long, taut, and very light flexible wire when it is struck by a 1.00-kg stone traveling horizontally to the right at 9.0 m/s. You may model this as a perfectly elastic collision. The stone rebounds to the left, and the ball swings to a maximum height h above its original level. Hint: m, – m, 2m, -(V,,), m, + m, (V2, ), m, + m, Perfectly elastic collision with object 2 initially at rest A) What is the momentum of the stone after the collision? B) What is the kinetic energy of the ball after the collision? C) Find the value of the maximum height h the ball rises to after the collision.

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**Problem Statement:**

A 8.00-kg metal ball is hanging from a long, taut, and very light flexible wire when it is struck by a 1.00-kg stone traveling horizontally to the right at 9.0 m/s. You may model this as a perfectly elastic collision. The stone rebounds to the left, and the ball swings to a maximum height \( h \) above its original level.

**Equations Provided:**

1. \( (v_{1x})_f = \frac{m_1 - m_2}{m_1 + m_2}(v_{1x})_i \)

2. \( (v_{2x})_f = \frac{2m_1}{m_1 + m_2}(v_{1x})_i \)

Where:
- \( m_1 \) = mass of the stone
- \( m_2 \) = mass of the ball
- \( (v_{1x})_i \) = initial velocity of the stone

**Note:** Perfectly elastic collision with object 2 initially at rest.

**Questions:**

A) What is the momentum of the stone after the collision?

B) What is the kinetic energy of the ball after the collision?

C) Find the value of the maximum height \( h \) the ball rises to after the collision.

**Diagram Explanation:**

There is no diagram included in the image. However, the equations provided are essential for solving the momentum and kinetic energy changes during the collision. They describe the final velocities of both the stone and the ball post-collision.
Transcribed Image Text:**Problem Statement:** A 8.00-kg metal ball is hanging from a long, taut, and very light flexible wire when it is struck by a 1.00-kg stone traveling horizontally to the right at 9.0 m/s. You may model this as a perfectly elastic collision. The stone rebounds to the left, and the ball swings to a maximum height \( h \) above its original level. **Equations Provided:** 1. \( (v_{1x})_f = \frac{m_1 - m_2}{m_1 + m_2}(v_{1x})_i \) 2. \( (v_{2x})_f = \frac{2m_1}{m_1 + m_2}(v_{1x})_i \) Where: - \( m_1 \) = mass of the stone - \( m_2 \) = mass of the ball - \( (v_{1x})_i \) = initial velocity of the stone **Note:** Perfectly elastic collision with object 2 initially at rest. **Questions:** A) What is the momentum of the stone after the collision? B) What is the kinetic energy of the ball after the collision? C) Find the value of the maximum height \( h \) the ball rises to after the collision. **Diagram Explanation:** There is no diagram included in the image. However, the equations provided are essential for solving the momentum and kinetic energy changes during the collision. They describe the final velocities of both the stone and the ball post-collision.
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