Elastic Potential Energy of a Sprin

[testme]

Homework Statement

Two trolleys, of mass 1.2 kg and 4.8 kg, are at rest with a compressed spring between them, held that way by a string tied around both. When the string is cut, the trolleys move apart, if the force constant fo the spring is 2400 N/m, by how much must it have been compressed in order that the 4.8 kg cart move off at 2.0m/s

Cart: 4.8 kg, 2 m/s
Cart 2: 1.2 kg
Spring constant, k: 2400 N/m

Homework Equations

Ee = 1/2kx^2
Ek = 1/2mv^2

The Attempt at a Solution

E = E'
1/2kx^2 = 1/2mv^2
kx^2 = mv^2
2400x^2 = 4.8(2)^2
x^2 = 4.8(4)/2400
x = 0.09 m

 

[HallsofIvy]

Why are you not including the kinetic energy of the 4.8 kg cart. The 1.2 kg cart moves too. You can use "conservation of momentum" to find its speed.

 

[testme]

So then would I find the velocity of the other cart like this:

mava + mbvb = mava' + mbvb'
0 = 4.8(2) + 1.2vb'
vb' = 8

then we put that back in so

1/2kx^2 = 1/2mv^2 + 1/2mv^2
2400x^2 = 4.8(2)^2 + 1.2(8)^2
x = 0.2 m

 

[PhanthomJay]

Homework Statement

Two trolleys, of mass 1.2 kg and 4.8 kg, are at rest with a compressed spring between them, held that way by a string tied around both. When the string is cut, the trolleys move apart, if the force constant fo the spring is 2400 N/m, by how much must it have been compressed in order that the 4.8 kg cart move off at 2.0m/s

Cart: 4.8 kg, 2 m/s
Cart 2: 1.2 kg
Spring constant, k: 2400 N/m

Homework Equations

Ee = 1/2kx^2
Ek = 1/2mv^2

The Attempt at a Solution

E = E'
1/2kx^2 = 1/2mv^2
kx^2 = mv^2
2400x^2 = 4.8(2)^2
x^2 = 4.8(4)/2400
x = 0.09 m

you have left out the KE of the smaller mass. It also must move out a certain velocity, using momentum conservation to find that velocity.

 

[PhanthomJay]

So then would I find the velocity of the other cart like this:

mava + mbvb = mava' + mbvb'
0 = 4.8(2) + 1.2vb'
vb' = 8

then we put that back in so

1/2kx^2 = 1/2mv^2 + 1/2mv^2
2400x^2 = 4.8(2)^2 + 1.2(8)^2
x = 0.2 m

Looks like you and HallsofIvy have already worked this out...correctly...
I posted after you 'spoke'...