A ball is dropped from 1.5 m and rebounds to 1.2m. How many times will it bounce before losing 90% of it's energy? I assumed energy was hight times gravity so when the rebound was only 10% of the original amount, 90% of the energy is lost. Is this the correct idea? I calculated 10 bounces resulted in a bounce hight of .16m.
Your assumption that the energy is proportional to the height times gravity is not accurate. The energy of a bouncing ball involves more factors, such as the elasticity of the ball and the conservation of energy during collisions. However, we can still determine how many times the ball will bounce before losing 90% of its energy using a different approach.
To solve this problem, we can use the concept of energy loss per bounce. Each time the ball bounces, it loses a certain percentage of its energy, resulting in a lower rebound height. We want to find the number of bounces it takes for the rebound height to reach 10% of the original height.
Let's work through the calculations step by step:
1. Calculate the initial energy of the ball when dropped from 1.5 m:
- Initial potential energy = mass x gravity x height
- Since we don't have the mass of the ball, let's assume it's 1 kg for simplicity:
Initial potential energy = 1 kg x 9.8 m/s^2 x 1.5 m
2. Determine the rebound height after one bounce. Let's assume the ball has an average elasticity, so it rebounds to 80% of its previous height:
- Rebound height after one bounce = 0.8 x previous height
3. Calculate the energy of the ball after each bounce:
- Energy after one bounce = 0.8 x initial potential energy
- Energy after two bounces = 0.8 x energy after one bounce
- Energy after three bounces = 0.8 x energy after two bounces
- Repeat this calculation until the energy after n bounces reaches 10% of the initial energy.
4. Determine how many bounces it takes until the energy is reduced to 10%:
- Keep calculating the energy after each bounce until it reaches 10% of the initial energy.
- The bounce number at this point will give you the answer.
Following this approach, you can calculate the number of bounces required for the energy to decrease to 10% and compare it with your result of 10 bounces and a rebound height of 0.16 m.