A small ball of mass m is placed on top of a large ball of mass 3m. Both balls are dropped simultaneously from a height h = 3.75 m as shown in the figure. Assuming the radius of the large ball and small are small and thus negligible in comparison to the height they are being dropped meaning the small ball has the same speed the large ball has when it hits the ground. If the large ball rebounds elastically from the floor, collides with the small ball, stops and then the small ball rebounds elastically from the large ball, find the maximum height the small reaches
A small ball of mass m is placed on top of a large ball of mass 3m. Both balls are dropped simultaneously from a height h = 3.75 m as shown in the figure. Assuming the radius of the large ball and small are small and thus negligible in comparison to the height they are being dropped meaning the small ball has the same speed the large ball has when it hits the ground. If the large ball rebounds elastically from the floor, collides with the small ball, stops and then the small ball rebounds elastically from the large ball, find the maximum height the small reaches
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A small ball of mass m is placed on top of a large ball of mass 3m. Both balls are dropped simultaneously from a height h = 3.75 m as shown in the figure. Assuming the radius of the large ball and small are small and thus negligible in comparison to the height they are being dropped meaning the small ball has the same speed the large ball has when it hits the ground. If the large ball rebounds elastically from the floor, collides with the small ball, stops and then the small ball rebounds elastically from the large ball, find the maximum height the small reaches.
Transcribed Image Text:### Two-Ball Collision Experiment
The diagram illustrates a classic physics experiment involving a two-ball collision to demonstrate the principles of conservation of momentum and energy transfer.
#### Description:
1. **Initial Setup**:
- A large cork ball is placed on a table or flat surface.
- A small rubber ball is positioned directly above the cork ball at a height marked by "h".
2. **Execution**:
- The rubber ball is dropped from the height "h" above the larger cork ball.
- The diagram shows two main phases:
- **Before Collision**: The rubber ball descends towards the cork ball.
- **After Collision**: The rubber ball ascends after hitting the cork ball and the large cork ball remains on the surface.
3. **Outcome**:
- On impact, the rubber ball rebounds upwards. Depending on the parameters (masses, heights, initial velocity), the balls transfer momentum and kinetic energy, causing the smaller ball to bounce higher than the original drop.
#### Explanation:
- **Conservation of Momentum**: The total momentum of the system before and after collision remains constant if no external forces act on it.
- **Energy Transfer**: As the rubber ball hits the cork ball, some kinetic energy is transferred, causing the rubber ball to rebound with greater velocity.
#### Relevant Physics Concepts:
- **Elastic and Inelastic Collisions**: This experiment can demonstrate elastic collisions if energy loss is minimal.
- **Potential and Kinetic Energy**: The potential energy at height "h" converts to kinetic energy as the ball falls, and partially converts back to potential energy after the rebound.
This simple yet powerful experiment visually demonstrates fundamental principles of physics in motion.
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