Bouncing ball elastic collision

In summary, the conversation discusses the concept of elastic collisions between a ball and the floor, where the speed after each collision is e times the speed before collision. The goal is to find the time it takes for the ball to come to rest, given the initial speed before the first bounce. The suggested approach is to use the equation impulse=change in momentum for successive bounces and sum them up as an infinite series, assuming a constant force and using the equation work=change in kinetic energy to find the force. The distance traveled by the ball can also be calculated as a sum of an infinite series. Finally, the value of the force can be substituted to find the time. The question is whether this approach is correct.
  • #1
anand
37
0
A ball drops to the floor and bounces,eventually coming to rest.Collisions between the ball and floor are elastic;the speed after each collision is e times the speed before collision where e<1.If speed just before 1st bounce is v,find the time taken to come to rest.
 
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  • #2
Do you have any thoughts on the question yourself? Could I also ask that in future you would post homework questions using the template provided.
 
  • #3
Here is how I thought of doing it.
Use impulse=change in momentum
for successive bounces and add them all up(infinite series).Assume the force F to be a constant,so that it can be taken out of the integral sign.To find force F,use
work=change in kinetic energy.
The distance traveled by the ball can be found as sum of an infinite series.
Substituting the value of F,time can be found.
Is this approach correct?
 

1. What is a bouncing ball elastic collision?

A bouncing ball elastic collision is a type of collision between two objects where both objects are elastic, meaning they can deform and return to their original shape. In this type of collision, the total kinetic energy of the system is conserved, meaning it remains the same before and after the collision.

2. How does a bouncing ball elastic collision differ from an inelastic collision?

In an inelastic collision, the objects involved stick together after the collision and some kinetic energy is lost. In a bouncing ball elastic collision, the objects involved bounce off each other and no kinetic energy is lost. This is due to the objects being elastic and able to store and release energy during the collision.

3. What factors affect the outcome of a bouncing ball elastic collision?

The outcome of a bouncing ball elastic collision can be affected by factors such as the mass, velocity, and elasticity of the objects involved. The angle and surface of the collision can also play a role in the outcome.

4. How is the coefficient of restitution related to a bouncing ball elastic collision?

The coefficient of restitution is a measure of the elasticity of a collision. In a bouncing ball elastic collision, the coefficient of restitution would be close to 1, indicating a highly elastic collision where no kinetic energy is lost.

5. How can the principles of a bouncing ball elastic collision be applied in real life?

The principles of a bouncing ball elastic collision can be applied in real life situations such as sports, where elasticity is important in the interaction between objects like a basketball and the ground. It can also be applied in engineering and design, where understanding the elasticity of materials is crucial in creating durable and efficient structures.

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