Momentum Questions: Ratio of Carts' Speed, Mass, Impulse & Acceleration

[TheLegace]

Homework Statement

Two heavy frictionless carts are at rest. They are held together by a loop of string. A
light spring is compressed between them. When the string is burned, the spring expands
from 2 cm to 3 cm, and the carts move apart from one another. Both hit the bumpers
fixed to the table at the same instant, but cart A moved 0.45 metre while cart B moved
0.87 metre.
What is the ratio of :
A. The speed of A to the of B after the interaction?
B. Their masses?
C. The impulses applied to the carts?
D. The accelerations of the carts while the spring pushes them apart?

Homework Equations

This is an Explosion, therefore momentum before is going to be 0.
0 = m1v1 + m2v2.
The impulse will also equal 0
Ft = 0.

The Attempt at a Solution

Well I wish I knew where to being, right now the only that I can think about is the displacement of the respective carts, and that they hit at an instant. But I cannot figure out much on the ratio and the solution. Any help would be appreciated.

Thank You.

 

[rosstheboss23]

Alright I can help you with the masses: Thinking back to the units that make up momentum p=(kg times m)/s So this can be broken down further to be p=(mass times distance)/time. Time is the same for both so. m1d1=m2d2. m1/m2=.87/.45 so I hope that helps.

 

[rosstheboss23]

I would say the impulses are the same based on the fact that they are moving at different velocities... and have different masses. Impluse if based on change in momentum so I believe the an equal impulse is given to each cart in an opposite direction (so they do cancel out). So there are parts B and C. :)

 

[TheLegace]

Thank you for the quick reply. Well to figure out the velocity ratio, this is what I derived.

Because of you I was able to figure out the velocity ratio.

va/vb = da/t * t/db (*Note: the velocities are just equal to their respective d/t equations, where time will cancel out, therefore you are just left with the ratio of displacements.)

va/vb = .45m/.87m = .51

I just want to know how exactly I could prove the impulse, and acceleration, but I will keep working at it.