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    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:

    EPE=\frac{4mg \times d^2}{2a} 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, \frac{2mgd^2}{a}=mg(a+d) since the change in height will be a+d. Rearranging into a quadratic we get 2d^2-ad-a^2=0 hence (2d+a)(d-a)=0 hence d=-\frac{a}{2} or d=a. Since d is greater than 0, d=a. However, according to the mark scheme, d=0.75a. Anyone know where I've gone wrong?
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    (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:

    EPE=\frac{4mg \times d^2}{2a} 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, \frac{2mgd^2}{a}=mg(a+d) since the change in height will be a+d. Rearranging into a quadratic we get 2d^2-ad-a^2=0 hence (2d+a)(d-a)=0 hence d=-\frac{a}{2} or d=a. 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
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    (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!
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    (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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