Calculating Impulse and Momentum in a Colliding Cart System

[dorkymichelle]

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

Momentum=mv
impulse = Favg*delta t
Impulse = final momentum - initial momentum

The Attempt at a Solution

P= momentum
Pi=Pf
m1Vi=(m1+m2)Vf
(2)(3)=(2+4)Vf
Vf=1
Can I say that momentum is conserved so impulse = 0 in this case?
Also, in class, we said that momentum is always conserved so that means Pi=Pf, so how can there be an impulse if impulse is the change in momentum and momentum doesn't change if momentum is always conserved?

 

[da_nang]

You need to think about this one. The conservation of momentum means that the sum of the beginning momenta equals the sum of the final momenta.

So, in this form, the equation becomes
m₁v₁ + m₂v₂ = m₁v₃ + m₂v₃, which is the same as
p_1beginning + p_2beginning = p_1final + p_2final.

The impulse is the change of momentum for one cart. The impulse the 4 kg cart exerts on the 2 kg cart is the difference of the momentum for the latter one, and vice versa.