Finding Impluse through Momentum

[VitaX]

Homework Statement

A 2-kg cart, traveling on a horizontal air track with a speed of 3 m/s, collides with a stationary 4-kg cart. The carts stick together. The impulse exerted by one cart on the other has a magnitude of:

Homework Equations

m1v1i + m2v2i = (m1+m2)vf

The Attempt at a Solution

2*3 * 4*0 = (2+4)vf
vf = 1 m/s
J = Pf - Pi = 6*1 - 2*3 = 0 N*s

But apparently that answer is wrong. What did I do wrong here? I get 3 tries before it won't let me try anymore.

The choices are:

0 (Tried, Wrong)
12 N*s
6 N*s (Tried, Wrong)
9 N*s
4 N*s

 

[VitaX]

I'm kind of thinking its 12 N*s if I just add up the final and initial momentum's. Don't know if it's correct thought.

 

[shyta]

look back at the question. what is it looking for?
The impulse exerted by one cart on the other.

be aware of what values you're substituting into your formula

 

[VitaX]

look back at the question. what is it looking for?
The impulse exerted by one cart on the other.

be aware of what values you're substituting into your formula

Yeah I know it's asking for impulse. When you say be aware of the values I'm substituting in, I don't really understand what you mean. I substituted the values in that I was given into the conservation of momentum equation then solved for the final Velocity. I thought I did everything right. Can you expand on what you mean?

 

[a.ratnaparkhi]

I think your answer is 4N*s.
you have found final velocity correctly.
J=Pi-Pf
=2*3-2*1 (mass is 2Kg in Pi & Pf)
J=4N*s

 

[VitaX]

I think your answer is 4N*s.
you have found final velocity correctly.
J=Pi-Pf
=2*3-2*1 (mass is 2Kg in Pi & Pf)
J=4N*s

But the mass after they collide should be m1 + m2 which is 6 kg. And isn't J = final momentum - initial momentum.

 

[shyta]

ratna is right. look closely at what the question is asking for "The impulse exerted by one cart on the other."

one cart on the other. what does that infer as?
simply put, consider the change in momentum of 1 cart.

 

[Oldblood]

If the answer was 0 there would be no collision at all. In a collision you have 2 magnitudes of implulse. The sum of these are 0, that's the whole point with conservation of momentum. Since the sum is 0 we don't get an increase or decrese of momentum in the 2-cart system. And this is offcourse because of Newtons 3rd law which says that the forces are equal in magnitude and has oposite directions. So the sum is 0 but the two impulses by themself isnt.

So basically what theyre asking for is the magnitude of these impulses. You can find that by looking at either cart, cause the magnutude is equal on both. Let's start looking at the smallest:

Impulse=F*t

We don't know much about the forces or time here but we don't really have to because:

Impulse=ΔP where ΔP is change in mv. Its abit like saying: we want the area of a rectangle, but we don't really care what the sides are cause we can figure it out without them and the sides are not important in this situation, all we care about is the area.

So what is change of momentum on the smallest kart?

ΔP=mΔv= 2kg*(3-1)m/s= 4 Ns

You should get the same answer by looking at the other kart. Change in momentum in that case is:

ΔP=mΔv= 4kg*(1-0)m/s = 4 Ns