Impact and the Coefficient of Restitution

In summary, the conversation discusses the use of the coefficient of restitution in calculating the speed of a ball bouncing off a wall. It is determined that the coefficient of restitution applies only to the normal velocity component because the energy loss is due to compression and expansion of the object. If there is no friction between the ball and the wall, the compression will only occur in the horizontal direction. However, if there is friction, the ball may start rotating and rolling resistance must be taken into account. This can be seen in the example of superballs, which could acquire so much spin that they would reverse direction when bouncing off a surface.
  • #1
Vladimir_Kitanov
44
14
Homework Statement
V1=50 ft/m
e = 0,75
Relevant Equations
e=(relative velocity after collision)/(relative velocity before collision)
Last post with picture, after this i will use Latex.

She say that correct answer is 41 ft/m.

Capture.PNG

IMG_20220730_194136.jpg

Is this correct?
 
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  • #2
I get answer b). ##41 \ ft/m##
 
  • #3
The coefficient of restitution applies only to the normal velocity component.

PS effectively you just multiplied 50 by 0.75.
 
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  • #4
PeroK said:
The coefficient of restitution applies only to the normal velocity component.
Why only to normal velocity?
And how to calculate x then?
 
  • #5
Vladimir_Kitanov said:
Why only to normal velocity?
Because the energy lost is in the compression and subsequent expansion of the object, and the extent of the compression depends on the velocity component normal to the contact surface.
Vladimir_Kitanov said:
And how to calculate x then?
Resolve the initial velocity into components.
 
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  • #6
Normal component is in x direction, and ball bounce of wall just in x direction.That is why we can use coefficient of restitution in that direction?
And speed in y is same because we need to calculate speed right after collision?
Is that correct?
 
  • #7
I guess one has to assume that there is no friction between the ball and the wall so that the compression is only in the horizontal direction.
 
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  • #8
malawi_glenn said:
I guess one has to assume that there is no friction between the ball and the wall so that the compression is only in the horizontal direction.
Yes, and that.
 
  • #9
malawi_glenn said:
I guess one has to assume that there is no friction between the ball and the wall so that the compression is only in the horizontal direction.
Oblique bouncing with friction is quite complicated. Assuming no slipping, as the ball compresses, the frictional component of the reaction force exerts a torque about the ball's centre, causing it to start rotating. So now we have rolling resistance as a new part of the ball starts to compress and a corresponding part starts to decompress.
Superballs (https://en.wikipedia.org/wiki/Super_Ball), popular in the late '60s, could acquire so much spin that at the next bounce they would reverse direction, bouncing back and forth between two points on the floor.
 
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1. What is the coefficient of restitution?

The coefficient of restitution is a measure of the elasticity of a collision between two objects. It is defined as the ratio of the relative velocity of separation after the collision to the relative velocity of approach before the collision.

2. How is the coefficient of restitution calculated?

The coefficient of restitution is calculated by dividing the relative velocity of separation by the relative velocity of approach. This can be determined by measuring the velocities of the objects before and after the collision.

3. What is the relationship between the coefficient of restitution and the impact force?

The coefficient of restitution is directly related to the impact force. A higher coefficient of restitution means a more elastic collision, resulting in a lower impact force. A lower coefficient of restitution means a more inelastic collision, resulting in a higher impact force.

4. How does the coefficient of restitution affect the rebound height of a ball?

The coefficient of restitution plays a major role in determining the rebound height of a ball. A higher coefficient of restitution means the ball will rebound to a greater height, while a lower coefficient of restitution means the ball will rebound to a lower height.

5. What factors can affect the coefficient of restitution?

The coefficient of restitution can be affected by factors such as the materials and surface properties of the objects involved in the collision, the angle and speed of impact, and external forces such as air resistance or friction. Temperature and humidity can also have an impact on the coefficient of restitution.

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