# M3 Springs

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#1
Question: A particle of mass m is suspended from a fixed point O by a light elastic string of natural length a and modulus of elasticity 4mg. The particle is pulled vertically downwards a distance d from its equilibrium position and released from rest. If the particle just reaches O, find d.

Working:

since the modulus is 4mg, the extension is d and the natural length is a. Since at the highest point all the EPE will be converted into GPE, since the change in height will be a+d. Rearranging into a quadratic we get hence hence or . Since d is greater than 0, d=a. However, according to the mark scheme, d=0.75a. Anyone know where I've gone wrong?
0
6 years ago
#2
(Original post by Chlorophile)
Question: A particle of mass m is suspended from a fixed point O by a light elastic string of natural length a and modulus of elasticity 4mg. The particle is pulled vertically downwards a distance d from its equilibrium position and released from rest. If the particle just reaches O, find d.

Working:

since the modulus is 4mg, the extension is d and the natural length is a. Since at the highest point all the EPE will be converted into GPE, since the change in height will be a+d. Rearranging into a quadratic we get hence hence or . Since d is greater than 0, d=a. However, according to the mark scheme, d=0.75a. Anyone know where I've gone wrong?
I have not checked it but a common mistake at this type of problem is that when string has EPE in the equilibrium position too
2
#3
(Original post by TeeEm)
I have not checked it but a common mistake at this type of problem is that when string has EPE in the equilibrium position too
Oh right, that's definitely it. I thought it meant it was pulled a distance d down from its natural length. Thanks!
0
6 years ago
#4
(Original post by Chlorophile)
Oh right, that's definitely it. I thought it meant it was pulled a distance d down from its natural length. Thanks!
no worries
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