Calculating Time and Speed of Rebounds with Coefficient of Restitution

In summary, the conversation discusses the time taken for a ball to rebound after being dropped on a smooth table and the calculation of its speed and height using the coefficient of restitution and constant acceleration formulae. It also poses questions about the time taken for the ball to become stationary and its speed after subsequent rebounds.
  • #1
Darth Vader
1
0

Homework Statement


I drop a ball downwards vertically onto a smooth table. The coefficient of restitution is 0<e<1. The ball rebounds upwards vertically with speed x. What is the time taken between the time that the ball was dropped to its nth rebound?

Also, what is the time taken before the ball becomes stationary?

Homework Equations


e = speed of separation/speed of approach
Constant acceleration formulae

The Attempt at a Solution


Say the ball rises to a height h after the first rebound. Then h = x^2/(2g). The time taken to reach this height is t = x/g using the quadratic formula...
 
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  • #2
Darth Vader said:
Say the ball rises to a height h after the first rebound. Then h = x^2/(2g).
Yes.
Darth Vader said:
The time taken to reach this height is t = x/g using the quadratic formula...
That cannot be right because the right hand side has dimension time-squared.

With what speed does it hit the floor the second time? What will be the next rebound speed?
 

FAQ: Calculating Time and Speed of Rebounds with Coefficient of Restitution

What is the Coefficient of Restitution?

The Coefficient of Restitution (COR) is a measure of the elasticity of a collision between two objects. It is a dimensionless quantity that ranges from 0 to 1, with 1 representing a perfectly elastic collision and 0 representing a completely inelastic collision.

How is the Coefficient of Restitution calculated?

The COR is calculated by dividing the relative velocity of the two objects after the collision by the relative velocity before the collision. This can also be expressed as the ratio of the final to initial kinetic energy of the objects.

What factors affect the Coefficient of Restitution?

The COR is affected by several factors, including the materials and surfaces of the objects involved, the angle and speed of collision, and any external forces or friction present. It is also dependent on the point of impact and the deformation of the objects during the collision.

Why is the Coefficient of Restitution important in sports?

In sports, the COR is important as it determines the rebound or bounciness of objects such as balls. A higher COR means a more energetic rebound and can lead to faster and longer shots in sports like basketball and tennis. It also affects the safety and performance of equipment used in sports, such as helmets and padding.

How is the Coefficient of Restitution used in engineering and design?

In engineering and design, the COR is used to predict the behavior of objects in collisions and to ensure the safety and functionality of structures and equipment. It is also used in the development of materials and surfaces with desired COR values for specific applications.

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