How to calculate rebound speed of ball hitting a wall?

In summary, a ball of mass 0.075 traveling horizontally with a speed of 2.20 m/s strikes a vertical wall and rebounds horizontally. Due to the collision, 20% of the ball's initial kinetic energy is dissipated. Using conservation of energy, it can be shown that the ball rebounds from the wall with a speed of 1.97 m/s. However, there was a misunderstanding in the attempt at a solution, as the final energy is not 1/5 of the initial energy, but rather 80%.
  • #1
MattDutra123
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Homework Statement


A ball of mass 0.075 is traveling horizontally with a speed of 2.20 m/s. It strikes a vertical wall and rebounds horizontally. Due to the collision with the wall, 20% of the ball's initial kinetic energy is dissipated.
Show that the ball rebounds from the wall with a speed of 1.97 m/s.

Homework Equations


Impulse = F*t
Kinetic Energy = 1/2mv2

The Attempt at a Solution


I attempted to use conservation of energy by having the initial kinetic energy (0.075*2.202) be equal to 20% final kinetic energy (0.075*v2*1/5) This gave me a result of 2.2 m/s. I don't know how to reach the desired result of 1.97 m/s.
Apologies in advance for bad formatting.
 
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  • #2
MattDutra123 said:
20% of the ball's initial kinetic energy is dissipated.
That means 20% was lost.
MattDutra123 said:
the initial kinetic energy (0.075*2.202) be equal to 20% final kinetic energy
That would be the ball gaining energy, ending with five times what it had to start with.
 
Last edited:
  • #3
haruspex said:
That means 20% was lost.

That would be the ball gaining energy, ending with five times what it hard to start with.
So if I divide the right hand side by 1/5 as opposed to multiplying it as I did, would my approach work?
 
  • #4
MattDutra123 said:
So if I divide the right hand side by 1/5 as opposed to multiplying it as I did, would my approach work?

No, because the final energy is not 1/5 of the initial energy.

20% of the ball's initial kinetic energy is dissipated.

It lost 20% of its energy. That means 80% is left. The final energy is 80% of the original energy.
 
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  • #5
RPinPA said:
No, because the final energy is not 1/5 of the initial energy.

20% of the ball's initial kinetic energy is dissipated.

It lost 20% of its energy. That means 80% is left. The final energy is 80% of the original energy.
Thank you. Very basic misunderstanding.
 

1. How do I calculate the rebound speed of a ball hitting a wall?

The rebound speed of a ball hitting a wall can be calculated using the following formula: rebound speed = initial speed * coefficient of restitution. The initial speed refers to the speed at which the ball is traveling towards the wall, while the coefficient of restitution is a measure of how much energy is conserved during the collision. This value is typically provided in the problem or can be looked up for different materials.

2. What is the coefficient of restitution?

The coefficient of restitution, also known as COR, is a measure of the elasticity of a collision between two objects. It is defined as the ratio of the relative speed of separation to the relative speed of approach between the two objects. In simpler terms, it is a measure of how much energy is conserved during a collision. Objects with a COR of 1 have a perfectly elastic collision, meaning all of the energy is conserved. Objects with a COR of 0 have a perfectly inelastic collision, meaning none of the energy is conserved.

3. How does the mass of the ball affect the rebound speed?

The mass of the ball does not directly affect the rebound speed. However, it does affect the initial speed of the ball, which is a factor in the rebound speed calculation (as seen in the first question). A heavier ball will have a greater initial speed when hitting the wall, resulting in a higher rebound speed.

4. Is the rebound speed the same as the initial speed?

No, the rebound speed is not necessarily the same as the initial speed. The rebound speed is the speed at which the ball bounces off the wall, while the initial speed is the speed at which the ball is traveling towards the wall before the collision. The two speeds can be different depending on factors such as the coefficient of restitution and the angle of impact.

5. Can the rebound speed be greater than the initial speed?

Yes, the rebound speed can be greater than the initial speed. This can happen if the coefficient of restitution is greater than 1. In this case, the ball gains energy during the collision and bounces off the wall with a greater speed than it had before the collision. However, this is not a common occurrence and is usually only seen in theoretical situations.

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