Solving Exploding Spring: Find Car Speeds

[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!

 

[NateTG]

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

 

[Doc Al]

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

 

[Doc Al]

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. :-)

 

[Doc Al]

Sweet.