Colision with a wall/platform and coefficient of restitution

[kohlerb]

1. A ball is launched against a solid wall with straight trajectory and a velocity of Vo. It hits the wall on a 3ft height and it falls on the ground at a 2ft distance (by the left of the wall). Then, an elastic platform is positioned on the exact height of the collision of the ball, and it is throwed once again, with the same velocity. But now, it falls on the ground at a distance of 0,83ft.
a) Coefficient of restitution = ?
b) Vo = ?
g = 32,17; No drag;
My attempt was to calculate the velocity right after the wall colision, and right after the platform colision, using kinematics equations for velocity (free fall and horizontal movement), and then divided both to find the coefficient, but that doesn't sound right to me. And I have no idea on how to calculate the Vo.

 

[NascentOxygen]

Hi kohlerb. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

With the elastic platform, the ball rebounds far less distance? That doesn't sound right. (Maybe the data has been accidently swapped around?)

If this were an exam question, you should still "go through the motions" for solving it, even though the data values won't give a logical answer. At least demonstrate that you know the correct method for determining coefficient of restitution.

What would the rebound speeds be, for each throw?

 

[kohlerb]

Hi kohlerb. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

With the elastic platform, the ball rebounds far less distance? That doesn't sound right. (Maybe the data has been accidently swapped around?)

If this were an exam question, you should still "go through the motions" for solving it, even though the data values won't give a logical answer. At least demonstrate that you know the correct method for determining coefficient of restitution.

What would the rebound speeds be, for each throw?

I'm sorry, I wrote the question poorly, the platform is a "soft" platform, it really makes the ball rebounds less. But I still don't know if the way I calculated the coefficient is the correct way. Can I divide the two rebound speeds to find it?

Rebound speeds:

Without the platform: 4,65ft/s
With the platform: 1,93ft/s

 

[NascentOxygen]

With one of the rebound speeds being that of an elastic collision, you should be able to divide them. As you have not shown how you calculated them, I can't say whether your working looks right or not.

 

[HalfLostAndSearching]

I would first like to clarify the concept of coefficient of restitution. It is a measure of the elasticity of a collision between two objects and is defined as the ratio of the relative velocity after the collision to the relative velocity before the collision. In simpler terms, it is a measure of how much energy is lost or retained during a collision.

Now, coming to the given scenario, we have a ball launched with a velocity of Vo, which hits a solid wall at a height of 3ft and falls on the ground at a distance of 2ft. This collision can be considered as an inelastic collision as some energy is lost due to deformation of the ball and the wall. The ball then hits an elastic platform, positioned at the same height as the collision with the wall, with the same velocity. This time, the ball falls on the ground at a distance of 0.83ft.

a) To calculate the coefficient of restitution, we can use the formula:

Coefficient of restitution = (Final relative velocity)/(Initial relative velocity)

In the given scenario, the final relative velocity is the velocity of the ball after the collision with the platform, which is 0.83ft/s. The initial relative velocity is the velocity of the ball before the collision with the platform, which is the same as the velocity before the collision with the wall, i.e. Vo. Therefore, the coefficient of restitution can be calculated as:

Coefficient of restitution = (0.83ft/s) / (Vo) = 0.83/Vo

b) To calculate the initial velocity, we can use the equations of motion for the horizontal and vertical components of the ball's motion.

For the vertical component, we can use the equation:

h = h0 + Vo*t - (1/2)*g*t^2

where h is the vertical distance traveled, h0 is the initial height, Vo is the initial velocity, t is the time taken, and g is the acceleration due to gravity.

Using the values given in the scenario, we can write two equations for the collision with the wall and the platform:

For the collision with the wall: 3ft = 0ft + Vo*t - (1/2)*32.17*t^2

For the collision with the platform: 0.83ft = 0ft + Vo*t - (1/2)*32.17*t^2

Solving these two equations simultaneously, we get