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Elastic Potential Energy Problem (M2)

I have come across a modelling problem in a question in an AQA textbook

An elastic string has modulus of elasticity 12N and natural length 0.5m. A particle of mass 0.5kg is attatched to one end of the string. The other end of the string is attatched to fixed point P. The particle is pulled down until it is 1.5m below P.

After calculating the energy in the system to be 12J, the problem comes here.

biii) calculate the maximum height above P.

I believe that as soon as the string goes more than 0.5m above P, EPE should take effect again and so

EPE + GPE = 12

However, the book seems to show that GPE= 12, with the reasoning that EPE remains 0 even as the string goes more than 0.5m above P.

Can anyone help me out and explain what is going on? Thankyou.
Reply 1
Avatar for lilliehear
lilliehear
8
Original post by Kyyp
I have come across a modelling problem in a question in an AQA textbook

An elastic string has modulus of elasticity 12N and natural length 0.5m. A particle of mass 0.5kg is attatched to one end of the string. The other end of the string is attatched to fixed point P. The particle is pulled down until it is 1.5m below P.

After calculating the energy in the system to be 12J, the problem comes here.

biii) calculate the maximum height above P.

I believe that as soon as the string goes more than 0.5m above P, EPE should take effect again and so

EPE + GPE = 12

However, the book seems to show that GPE= 12, with the reasoning that EPE remains 0 even as the string goes more than 0.5m above P.

Can anyone help me out and explain what is going on? Thankyou.


Its a string not spring. Strings will only store energy when being stretched, squash them more than their natural length and they will become slack. Think of an actual piece of string if it helps. So after its passed its natural length, it stores no EPE and all energy is KE or GPE
Reply 2
Avatar for Kyyp
Kyyp
OP
2
So even though when the string passes its natural length.a second time, because it has become slack, it stays slack?

This was posted from The Student Room's Android App on my HTC One S
Reply 3
Avatar for lilliehear
lilliehear
8
Original post by Kyyp
So even though when the string passes its natural length.a second time, because it has become slack, it stays slack?

This was posted from The Student Room's Android App on my HTC One S


Oh sorry I misread your question first time :colondollar:
But no presumably it should 'stretch' if it is extended past its natural length, implying work is done to it and it therefore stores energy. Is this the advancing for mechanics text book? There are a quite a few mistakes in it, may just be one of those?
Reply 4
Avatar for Kyyp
Kyyp
OP
2
Possibly, but the answer implies that ke is 0 and epe is 0 at maximum height, but the maximum height occurs at a position above its natural length

This was posted from The Student Room's Android App on my HTC One S

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