Solving Momentum Problems: Cart Interactions and Impulses

[beckster]

1. Homework Statement [/b]

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. Both hit the bumpers fixed to the table at the same instant but cart A moved 0.45 m while cart B moved 0.87m. What is the ratio of:
a) the speed of A to that of B after the interaction?
b) their masses?
c) the impulses applied to the carts?
d) the acceleration of the carts while the spring pushes them apart?

Homework Equations

mava+ mbvb= mava' + mbvb'

1/2 mv²= FfΔd

The Attempt at a Solution

First you will have to figure out everything you know about the carts before the string is burnt. You would then use the other part of the equation to solve after the string is burnt.
You would use the second equation that is shown by filling in the knowns.

 

[PeterO]

1. Homework Statement [/b]

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. Both hit the bumpers fixed to the table at the same instant but cart A moved 0.45 m while cart B moved 0.87m. What is the ratio of:
a) the speed of A to that of B after the interaction?
b) their masses?
c) the impulses applied to the carts?
d) the acceleration of the carts while the spring pushes them apart?

Homework Equations

mava+ mbvb= mava' + mbvb'

1/2 mv²= FfΔd

The Attempt at a Solution

First you will have to figure out everything you know about the carts before the string is burnt. You would then use the other part of the equation to solve after the string is burnt.
You would use the second equation that is shown by filling in the knowns.

Part c should be easy.

Impulse = force x time

We don't know how strong the force was, and we don't know how long it lasted for, but with our understanding of Newton's Third Law, we do know that the spring was pushing on each cart with the same sized force at any instant.