Ball bounces back to same height after Angular Impulse?

In summary, the conversation discusses the behavior of a ball rolling off a frictionless cliff and colliding with a surface with friction at the bottom. It is determined that the x component of the velocity would be reduced and the angular momentum would be fixed clockwise due to the frictional impulse. The possibility of the ball rebounding higher than the initial drop is also explored, with the idea that a perfectly rigid ball could potentially achieve this with the right initial spin. The concept of using a pulley and hammer contraption to convert the ball's original spin into a higher rebound is also discussed.
  • #1
FallenApple
566
61
So Imagine a ball moving off a frictionless cliff with a velocity v to the right, at the bottom of the cliff the surface has friction.

So after the collision, the x component of the velocity would be reduced, and the angular momentum would be fixed clockwise because the frictional impulse acted to the left.

Now clearly the bounce would not be symmetric. But I'm thinking only in the x. The maximum height of the rebound should still be the same, its only the x velocity that was reduced and convered to rotational motion. The y velcocity gets completely reflected back upwards.

This is assuming that the ball is rigid enough that it doesn't deform at all during the collision. It just get torqued up.

Is this correct?
 
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  • #2
FallenApple said:
Is this correct?
yup
 
  • #3
It gets interesting when you ask, if the ball can rebound higher than the drop, given the right initial spin.
 
  • #4
A.T. said:
It gets interesting when you ask, if the ball can rebound higher than the drop, given the right initial spin.

Interesting. I suppose this is possible. I don't know if it can happen if the ball is perfectly rigid since friction horizontal only, the ball's y velocity would still be perfectly reflected regardless of original spin.

Unless the ball wasn't perfectly rigid and is spring like in constitution. So during the collision the ball would be compressed and somehow the loss of spin would further contribute to the vertical compression, of which finally, the compression is released and the ball flies up higher than it started.

I can think of one way to convert the original spin to a higher height though. If the ball has a original spin clockwise and during the collision, the ball torques down on a rope connected to pulley that has the other side of the rope in a tunnel under the floor connected to a vertically hanging hammer( also under the floor. The ball's spin would slow down, the rope would be pulled by Newton's third law, and that rotational energy lost by the ball would be transmitted to rotating the hammer like pendulum, and finally hitting the ball upwards.

If the hammer hits the ball the instant after the floor itself has completed it's impulse( assume that either the floor opens right after or that the hammer is strong enough to break through the floor), the ball would receive another impulse(without any pause following the first one) and therefore reach a final higher height.

The horizontal energy and rotational energy lost by the ball was converted to vertical energy via the pulley hammer contraption.
 
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FAQ: Ball bounces back to same height after Angular Impulse?

1. How does angular impulse affect the height of a bouncing ball?

Angular impulse is the change in angular momentum of a ball. When a ball bounces, it experiences a change in angular momentum due to the force of gravity pulling it down and the force of the ground pushing it up. This change in angular momentum causes the ball to bounce back to the same height.

2. What is the relationship between angular impulse and the coefficient of restitution?

The coefficient of restitution is a measure of how much energy a ball retains after a collision. In the case of a bouncing ball, the higher the coefficient of restitution, the more energy is retained and the higher the ball will bounce. Angular impulse affects the coefficient of restitution by changing the angular velocity of the ball, which in turn affects the energy and height of the bounce.

3. Can a ball bounce back to its original height without angular impulse?

No, angular impulse is necessary for a ball to bounce back to its original height. Without angular impulse, the ball would not have enough energy to overcome the force of gravity pulling it down and would not be able to bounce back to the same height.

4. How does the surface affect the relationship between angular impulse and the height of a bouncing ball?

The surface on which a ball bounces can affect the coefficient of restitution and therefore the height of the bounce. For example, a softer surface may absorb more of the ball's energy, resulting in a lower bounce. This in turn can affect the angular impulse and the height to which the ball bounces.

5. Are there any other factors that can affect the height of a bouncing ball besides angular impulse?

Yes, there are other factors that can affect the height of a bouncing ball, such as the initial height from which the ball is dropped, the mass and elasticity of the ball, and air resistance. These factors can all impact the amount of energy the ball has and how high it can bounce.

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