A Ball, A Wall and Momentum. (How is this incorrect?)

[Shamrock87]

Homework Statement

This is a fairly straightforward question I'm sure.

I have a ball. This ball has a mass of mass M. I throw this ball with a velocity v against a wall (perfectly along the x-axis (in the positive direction)). Now suppose the ball stays in contact with the wall for a time $$\Delta$$t. Then the ball will rebound back perfectly along the x-axis (in the negative direction).

Homework Equations

A.) What is the momentum of the ball $$\Delta$$t/2 after originally making contact with the wall?

B.) What is the tennis ball's momentum change between the time BEFORE it hits the wall to the time it is in CONTACT with the wall?

C.) What is the tennis ball's momentum change between the time it is in CONTACT with the wall and AFTER it makes contact with the wall?

The Attempt at a Solution

Well, for A.) I would say something like this:

Firstly I would model the ball and wall as an isolated system. Secondly since it is moving perfectly along the x-axis I would then say:

p=mv

And according conservation of momentum I am lead to believe that the momentum of the ball at $$\Delta$$t/2 is mv.

But I am not confident.

B.) Next I am lead to believe that the change in momentum BEFORE it hits the wall and while it's in CONTACT with the wall is 0 because of conservation of momentum.

C.) I come to the same conclusion as in B.

 

[JazzFusion]

>
>
p=mv

And according conservation of momentum I am lead to believe that the momentum of the ball at $$\Delta$$t/2 is mv.

When Sir Isaac Newton first formulated his laws of motion, he defined force in terms of a change in momentum. F was defined in terms of $$\Delta$$p over $$\Delta$$t. His first law of motion says, "A body at rest tends to stay at rest, and a body in motion tends to stay in motion, unless acted upon by a force." In other words, momentum stays constant, UNLESS the system is acted upon by a force (like, for instance, the normal force of a wall). Momentum can and does change.

Have you covered the 'Impulse-Momentum Theorem' yet?

 

[Shamrock87]

Well, in this summer course we haven't so much covered this as skipped over it and been expected to know it like the back of our hand.

But I took a look around the chapter and sure enough found Impulse. But I should have thougt of this sooner because the project is labeled "Momentum and Impulse".

Ha, thanks for the heads up.

 

[Doc Al]

B.) What is the tennis ball's momentum change between the time BEFORE it hits the wall to the time it is in CONTACT with the wall?

C.) What is the tennis ball's momentum change between the time it is in CONTACT with the wall and AFTER it makes contact with the wall?

While A is clear, these two seem a bit vague. Since contact extends over the time Δt, the statement "the time it is CONTACT" can mean any point along that time interval. Are they referring to the point Δt/2 from part A?

Well, for A.) I would say something like this:

Firstly I would model the ball and wall as an isolated system. Secondly since it is moving perfectly along the x-axis I would then say:

p=mv

And according conservation of momentum I am lead to believe that the momentum of the ball at $$\Delta$$t/2 is mv.

But I am not confident.

Looking at the ball alone, is momentum conserved? What must be the ball's speed at Δt/2?