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# M3 - fiddly string question watch

1. Question:
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A light elastic string of natural length 0.5m is stretched between two points P and Q on a smooth horizontal table. The distance PQ is 0.75m and the tension in the string is 15N.

a) find the modulus of elasticity of the string

A particle of mass 0.5kg is attached to the mid-point of the string. The particle is pulled 0.1m towards Q and released from rest.

b) find the speed of the particle as it passes through the mid-point of PQ.
Okay, so part a was fine, got it as 30 N, but part b has been problematic.

I understand that you have to find the difference in elastic potential between the stretched point that is 0.1m towards Q, and that in the centre, but they have come up with some weird numbers.

This is the solution:
Attachment 498607498609

please could someone explain how they get this specific line? ie - where 0.225, 0.025 come from?
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2. (Original post by 雷尼克)
I understand that you have to find the difference in elastic potential between the stretched point that is 0.1m towards Q, and that in the centre, but they have come up with some weird numbers.

This is the solution:
Attachment 498607498609

please could someone explain how they get this specific line? ie - where 0.225, 0.025 come from?
In the initial position, both halves of the string are still stretched beyond their natural lengths by 0.475-0.25=0.225 for the left side, and by 0.275-0.25=0.025 for the right side. So each side already has some stored EPE. They are calculating the change from that initial energy, for both sides.

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