How Do You Calculate the Coefficient of Restitution from a Collision Example?

[SuperGeek]

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.

 

[Doc Al]

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:

V_f² = V_i² + 2aΔX

(This should really be in the homework help section!)

 

[M98Ranger]

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!