Help with Impulse? Answers Here!

[led23]

Hey guys, could anyone please explain this to me?

Homework Statement

Two girls with masses of 50kg and 70kg are at rest on frictionless in line skates. The larger girl pushes the smaller girl so that the latter rolls away at a speed of 10m/s.
What is the effect of the action on the larger girl?
What is the impulse that each girl exerts on the other?

Homework Equations

p=mv
I= F delta T

The Attempt at a Solution

50(10)=500
V=10m/s

70-50=20kg/10s=2kgm/s

So, 500kgm/s on girl 2, 700kgm/s on girl 1

 

[AC130Nav]

Homework Statement

Two girls with masses of 50kg and 70kg are at rest on frictionless in line skates. The larger girl pushes the smaller girl so that the latter rolls away at a speed of 10m/s.
What is the effect of the action on the larger girl?
What is the impulse that each girl exerts on the other?

Homework Equations

p=mv
I= F delta T

The Attempt at a Solution

50(10)=500
V=10m/s

70-50=20kg/10s=2kgm/s

So, 500kgm/s on girl 2, 700kgm/s on girl 1

You have calculated the momentum of the smaller girl (500). By conservation that momentum is also the (equal but opposite) momentum of the larger girl. You can get her new v (= p/m).

You missed a formula: I = delta p.

 

[cepheid]

Welcome to PF led23!

I don't understand your second last step in which you take the difference between the girls' masses.

Think about the answer you got some more: does it make sense that one girl has a greater impulse (change in momentum) than the other? Think about this in terms of conservation of momentum and Newton's Third Law of Motion.

 

[led23]

Oh, so they would both have the same impulse?

 

[cepheid]

Oh, so they would both have the same impulse?

The magnitudes would be the same, but the directions would have to be opposite, so that the two final momenta would be equal and opposite. That way you start out with 0 total momentum, and you end up with 0 total momentum.

If this were not true, momentum would not be conserved.

But don't just take my word for it. You can SHOW that momentum is conserved by starting with Newton's Third Law: the force exerted by girl 1 on girl 2 is equal in magnitude and opposite in direction to the force exerted by girl 2 on girl 1. Therefore, since those forces are both exerted over the same time interval (which is the time during which they are in contact), the total impulse supplied to girl 2 by girl 1 is equal and opposite to the total impulse supplied to girl 1 by girl 2. From this, it follows that they have the same change in momentum, and hence momentum is conserved.

Don't forget to answer the first question you were asked as well -- what is the effect on the larger girl? (although the answer is sort of implicit in what I said above).

 

[led23]

Thanks guys.