Solve for Spring Compression: Physics 11 Momentum and Energy Problem

[roxxyroxx]

Homework Statement

A 1.1 kg cart and a 2.2 kg cart are at rest with a compressed string between them. the force constant of the spring is 600 N/m. when the spring is released, the carts rapidly separate. how far must the spring have been compressed for the 2.2 kg cart to end up moving at 1.5 m/s?
(involves both momentum and energy)

Homework Equations

p = mv
E_k = 0.5mv²
E_p = 0.5kx²

The Attempt at a Solution

i don't even know where to start !

 

[Doc Al]

Figure out the total KE of the carts. Hint: What's the momentum of the system?

 

[roxxyroxx]

Figure out the total KE of the carts. Hint: What's the momentum of the system?

ok so i got:
0.5(1.1)(3^2) = 4.95 J for Cart 1
0.5(2.2)(1.5^2) = 2.475 J for Cart 2

 

[jgens]

Using what you know about the system, apply the law of conservation of energy now.

 

[roxxyroxx]

Using what you know about the system, apply the law of conservation of energy now.

ok so
0.5mv²
= 0.5(7.425)(1.5)²
=8.35

but the answer should be 0.16 m.. did i do something wrong or is there another setp now?

 

[jgens]

Well, your total kinetic energy is the sum of the kinetic energy of each kart, so KE = 7.425. You know that the resultant KE must equal the initial potential energy so KE = .5(k)(x^2).

 

[roxxyroxx]

great thanks !

 

[jgens]

You're welcome.