Elastic Potential Energy of a Sprin

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  • #1
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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
 

Answers and Replies

  • #2
HallsofIvy
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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.
 
  • #3
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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
 
  • #4
PhanthomJay
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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.
 
  • #5
PhanthomJay
Science Advisor
Homework Helper
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509
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'......
 

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