# Exploding string

Juntao
A massless spring of spring constant 20 N/m is placed between two carts. Cart 1 has a mass M1 = 5 kg and Cart 2 has a mass M2 = 2 kg. The carts are pushed toward one another until the spring is compressed a distance 1.7 m. The carts are then released and the spring pushes them apart. After the carts are free of the spring, what are their speeds?

a) velocity of car 1 =?
b) velocity of car 2 =?

I know that for this problem, I got to use conservation of momentum and conservation of energy, but I don't even know how to even start off this problem. Major help needed!

Homework Helper
You need to apply two equations:
1. Conservation of energy.
2. Conservation of momentum.

Mentor
Just give it a try. Here are some hints.

What's the initial momentum of the system? (Hint: the masses start from rest.) What's the final momentum (m1v1 + m2v2)?

What's the initial KE of the masses? (see previous hint).

How much energy is stored in the compressed spring?

What's the final KE of the masses?

Juntao
Baby steps, right?

Ok. Initial momentum equals final momentum.
and I realized objects start from rest, so initial velocity is zero
thus,
initial momentum =0
so 0=(m1v1+m2v2)
or -m1v1=m2v2

Ok, that part wasnt so bad.

Initial KE=0
Final KE= .5m1v1^2+.5m2v2^2

Spring potential energy=.5kx^2

ah, so yea, I guess then .5m1v1^2+.5m2v2^2=.5kx^2

Last edited:
Mentor
Originally posted by Juntao
So for the energy part, is it going to be like the KE of both carts equal the potential energy of the spring?

so like this:
.5*m1v1^2+.5m2v2^2=.5kx^2
Yep. You're half-way home.

Juntao
Awesome, I figured it out...Lol, it took me like 1 hr of frustration, then like 5 mins of guidance here, and I got it in like 10 mins. :-)

Mentor
Sweet.