Coefficient of Restitution

In summary, the conversation discusses finding the coefficient of restitution in an example involving a block being pushed towards a wall. The block has an initial velocity of 7 m/s and travels 4 meters before rebounding off the wall and stopping after 1 meter. The conversation suggests finding the speeds of the block before and after the collision by using Newton's second law and the formula for accelerated motion. The speaker also notes that this topic should be discussed in the homework help section.
  • #1
SuperGeek
4
0
Hi all,
I am trying to find the coefficient of restitution in this example:
Block m1=2 kg is pushed with initial velocity v=7 m/s for distance
d = 4 meters towards a wall. Kinetic friction b/w floor and block is mK = 0.4. The block rebounds off the wall and travels distance
d2 = 1 m before stopping.

I think I should get the speeds of the block right before and after hitting the wall first but I am really lost on this one. Any help or teaching would be appreciated.
 
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  • #2
Originally posted by SuperGeek
I think I should get the speeds of the block right before and after hitting the wall first but I am really lost on this one. Any help or teaching would be appreciated.
Yes, you need to find the speed of the block before and after the collision. First find the acceleration of the block, using Newton's second law. Then use the formula for accelerated motion to find the speeds:

Vf2 = Vi2 + 2aΔX

(This should really be in the homework help section!)
 
Last edited:
  • #3


The coefficient of restitution is a measure of the elasticity of a collision between two objects. In this example, the coefficient of restitution can be calculated by dividing the final velocity of the block after the collision by the initial velocity before the collision.

To find the final velocity of the block after the collision, we can use the conservation of energy principle. The initial kinetic energy of the block is given by 1/2 * m1 * v^2 = 1/2 * 2 kg * (7 m/s)^2 = 49 J.

After the collision, the block travels a distance d2 = 1 m before stopping. Using the work-energy theorem, we can calculate the work done by the kinetic friction force (mK * d2) and the change in kinetic energy (1/2 * m1 * vf^2) and set them equal to each other. This results in vf = 5.5 m/s.

Therefore, the coefficient of restitution is 5.5 m/s (final velocity after collision) divided by 7 m/s (initial velocity before collision), which is approximately 0.79.

I hope this helps to clarify the concept of coefficient of restitution and how it can be calculated in this example. Keep practicing and you will become more comfortable with these types of problems. Good luck!
 

What is the Coefficient of Restitution?

The Coefficient of Restitution is a measure of the elasticity of a collision between two objects. It is a number between 0 and 1, with 1 representing a perfectly elastic collision and 0 representing a completely inelastic collision.

How is the Coefficient of Restitution calculated?

The Coefficient of Restitution is calculated by taking the ratio of the relative velocity of the objects after the collision to the relative velocity before the collision. This can be represented by the equation e = (V2 - V1) / (U1 - U2), where e is the Coefficient of Restitution, V2 and V1 are the velocities of the objects after the collision, and U1 and U2 are the velocities before the collision.

What factors affect the Coefficient of Restitution?

The Coefficient of Restitution is affected by various factors, including the materials and surfaces of the objects colliding, the angle of collision, and the speed and mass of the objects. Generally, objects made of more elastic materials and colliding at lower speeds tend to have higher Coefficient of Restitution values.

Why is the Coefficient of Restitution important in sports?

The Coefficient of Restitution is important in sports because it affects the performance of equipment such as balls and rackets. A higher Coefficient of Restitution allows for more energy transfer and a faster rebound, resulting in more powerful and efficient shots. This is especially important in sports such as tennis, golf, and baseball.

How does the Coefficient of Restitution relate to the conservation of energy?

The Coefficient of Restitution is closely related to the principle of conservation of energy. In a perfectly elastic collision, where the Coefficient of Restitution is 1, the kinetic energy before and after the collision remains the same. In a completely inelastic collision, where the Coefficient of Restitution is 0, the kinetic energy is not conserved and is converted into other forms of energy such as heat and sound.

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