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# M3 elastic springs and strings question BOOK answer wrong? watch

1. A light elastic string of modulus 49N and natural length 1.5m has one end attached to Point A of a ceiling. A particle P of mass 0.5kg is attached to the other end of the string.

a) Find the length of the string when P is hanging in equilbrium(answer 1.65m)

The particle P is released from rest at A and falls vertically.

Find

b) the speed of P as P passes through the equilibrium position(answer 5.56ms^-1)

c) the length of the string when P is momentarily at rest ( I get 2.58m but the book says 2.34m)

Thank you
3. (Original post by ghostwalker)

thank you
4. (Original post by sulexk)

thank you
Doesn't work that way. If you post your working someone can check it, but I'm not typing up loads of details. I'll give you the initial equation, and if you're got that correct, then you've almost certainly just made an arithmetic slip.

If x is the extension, then using loss in GPE = gain in EPE, we have:

5. (Original post by ghostwalker)
Doesn't work that way. If you post your working someone can check it, but I'm not typing up loads of details. I'll give you the initial equation, and if you're got that correct, then you've almost certainly just made an arithmetic slip.

If x is the extension, then using loss in GPE = gain in EPE, we have:

I did
[/QUOTE]

My slip was squaring the 1.5 at the bottom

Is it possible if you could help me with one more question please?

I have completed the question although I obtain an answer of 1.1625J and the book has given the answer as 1.2J

The book usually gives to 3sf. So I may be wrong?

A light elastic string of natural length 50cm is stretched between two points A and B on a smooth horizontal table.
The distance AB is 75cm and the tension in the string is 15N.

a) Find, in newtons, the modulus of elasticity of the string. ( answer is 30N)

The midpoint of the string is pulled 10cm towards B. The string still lies along the straight line AB.

b) find in joules, the change in elastic energy of the string.(this is where they get 1.2j)

My thinkng:

if the string still lies along AB then there is stretching and a compression. So epe =

2 * ( modulus * (0.125 + 0.10)^2)/2l

Thus change in epe = (3.0375 from top) - 1.875(this is initial) = 1.1625J

What do you think?

Thank you
6. (Original post by sulexk)

A light elastic string of natural length 50cm is stretched between two points A and B on a smooth horizontal table.
The distance AB is 75cm and the tension in the string is 15N.

a) Find, in newtons, the modulus of elasticity of the string. ( answer is 30N)

The midpoint of the string is pulled 10cm towards B. The string still lies along the straight line AB.

b) find in joules, the change in elastic energy of the string.(this is where they get 1.2j)

My thinkng:

if the string still lies along AB then there is stretching and a compression. So epe =

2 * ( modulus * (0.125 + 0.10)^2)/2l

Thus change in epe = (3.0375 from top) - 1.875(this is initial) = 1.1625J

What do you think?

Thank you
Books right. This is a somewhat more complicated problem than your working implies.

When the mid-point is moved, you need to treat the string as two separate strings, each of unstretched length 0.25, and work out the EPE of each and add to find the total energy.
7. (Original post by ghostwalker)
Books right. This is a somewhat more complicated problem than your working implies.

When the mid-point is moved, you need to treat the string as two separate strings, each of unstretched length 0.25, and work out the EPE of each and add to find the total energy.
Thank you- I really appreciate your help. I am finding something complicated in M3 at the moment. Just one concept. It is that if a string is attached to a ceiling between two points say, A and B. Where it's new length is greater than its natural length.

Then a particle is attached to the midpoint, and now the paticle hangs xm below AB(the ceiling).

If I were to calculate the epe in the string, note the particle is in equilbrium, I could not use mgh = 2(lx^2/2l) . Initially it struck me as to why?

But then from previous questions the particle has Ke at the equilibirum so I would need to take this into account. But would I include the initial epe(I.e. before the particle was attached?)

This is all for now- many thanks! You are an outstanding M3 teacher(personally)!
8. (Original post by sulexk)

...
Best to post an actual question that covers what you want to ask, as I'm not clear from that what you are asking and what the situation is. It's a bit jumbled.

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