# Basic Impulse-Momentum Question for a Biomechanics Class

## Homework Statement

I was assigned a worksheet for a biomechanics class that had a simple impulse-momentum problem. My instructor and I disagree about the means to solve the problem.

"A pitched ball with a mass of 150g (.15kg) reaches a catcher's glove traveling at a velocity of 28m/s.
-How much momentum does the ball have?
-How much impulse is required to stop the ball?
-If the ball is in contact with the catcher's glove for 0.5 seconds during the catch, how much average force is applied by the glove?"

FΔt=mΔv
p=mv

## The Attempt at a Solution

To me, it seems that the question implies that the ball has a positive momentum (when you solve for p=.15kg*28m/s, it's 4.2N*s), and the second part asks what impulse the glove applies to the ball (since the impulse of the ball on the glove would have nothing to do with stopping the ball). Thus, the answer to the second question in my mind would reflect the need for the force from the glove to be in the opposite direction (-4.2N*s). The final part of the question is simply the impulse divided by the time (-4.2N*s/.5s), and results in a measure of -8.4N.

I feel petty arguing about only losing one point of 26 for this, but my instructor insists that my signs on the second and third parts of the problem are wrong, and that if you solve for those using the velocity only, you would get positive values. I argued with him for twenty minutes about how the impulse could not possibly be positive if the ball was indeed to be stopped. Am I wrong? How else could I approach him about this?

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I don't think it is worth approaching him, I think he was trying to make a point (and he didn't succeed) but I'm not sure the point was worth one point (no pun intended)
It doesn't really mean much 'positive momentum' or 'negative momentum' if you think about it, positive with respect to what ?
if you define your origin from the ball's launcher, and the catcher has 'positive x' then your view of the positive momentum is correct, and it would be negative if the origin was the catcher with positive x for the launcher.
But look at the ball, it does not go straight, it follows a parabola
so there is some positive in the x, and what ? some negative or positive in the y direction ?
What I am getting at is, momentum, like force, is a vector, asking 'how much' about it, really means 'what is the magnitude ?', and it is always positive by definition.
So how much force did you have to apply on the ball to stop it in that much time is 8.4N
But it doesn't mean you were profoundly wrong, again, I'm not sure what was your teacher's point in having you lose one point over it, in other cases, tracking signs (as you do correctly in fact) is very very important.
(what bothers me more is how in 20 minutes of arguing you didn't manage to understand each other in fact Just don't get mad at it and keep on the good work ;)

We are conveniently ignoring ballistics for the purpose of the assignment - but the momentum of the ball is positive if you set up your reference frame to reflect that the ball moves in a positive direction along the x-axis. Thus, the velocity is in the positive direction, the momentum is in that same direction and the force from the impulse of the ball on the glove is in that direction.

From there I tried to argue that any force that would stop the ball would have to be in the negative direction along the x-axis. Newton's third law and such. No such luck, he claimed I was not using the impulse-momentum theorem correctly. But I'll give up and save the battle for another day. He is just a doctoral student after all.

Yes, you are correct, but really, there is no such thing as 'negative momentum' or 'negative force'
momentum and force are directional, and when you talk about 'how much of it', it really is wrong to say 'I am applying -10N' to do whatever (stop the ball)
You apply 10N (in the opposite direction of the incoming ball)