Elastic Potential Energy of a Sprin

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

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
Homework Helper
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.

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 Helper
Gold Member

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

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
Homework Helper
Gold Member
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'......