Momentum and elasticity and this astronaut dude

[GreatEscapist]

In my physics class (School's over now, so I can't ask my teacher.) we had this interesting problem for our final. (No, this isn't homework) We didn't do elasticity, soo... I dunno.

An astronaut (It's in space to eliminate air resistance and gravity- it IS high school physics :tongue:) has a rather massive ball. Almost as massive as himself. He goes to a completely hard, elastic wall to play catch. When he throws the ball, though the ball is massive, he still could catch it if he were on the other side to catch. However, it hits the elastic wall and bounces back with enormous momentum. It knocks him back into space...

So, did the momentum double? Why? The mass did not change, and no force made it accelerate to a faster velocity... What made it change? How does elasticity interfere? The wall wasn't moving, so it can't push off more momentum.

 

[kuruman]

Have you tried conserving momentum? Assume that the ball has the same mass as the astronaut and that the wall is attached to a space station of humongous mass.

What are the velocities of the astronaut and the ball after he throws it?
What is the velocity of he ball after it collides with the wall?

 

[NatSusan]

Hi there! It sounds like you're describing a classic conservation of momentum problem. In this situation, the total momentum of the system (the astronaut and the ball) should remain constant before and after the ball bounces off the wall. This means that if the ball has a certain momentum before it hits the wall, it should have the same momentum in the opposite direction after it bounces off the wall.

However, when the ball hits the wall, it experiences a force from the wall that causes it to change direction and speed. This change in velocity results in a change in momentum, which is why the ball bounces back with greater momentum than it had before. This is known as the impulse-momentum theorem, which states that the impulse (force x time) applied to an object is equal to the change in momentum of that object.

In terms of elasticity, it is the property of the wall that allows it to exert a force on the ball without permanently deforming. When the ball hits the wall, the wall compresses slightly and stores some of the ball's kinetic energy as potential energy. As the wall returns to its original shape, it releases this potential energy, causing the ball to bounce back with greater momentum.

So, to answer your question, the momentum of the ball did double because of the change in velocity caused by the force from the wall. However, the total momentum of the system (the astronaut and the ball) remains constant. I hope this helps!