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## #1 Re: Help Me ! » Calculation of the modulus of elasticity of a stretched string » 2018-07-13 03:06:53

Hi, Thanks for all the help. I sourced some help on this, It can be done as follows.

In the final position let the tension in AC be

and the tension in CB be

Then, using Hooke's Law

we have:

and

Now - here's the one thing I'm not fully convinced of yet - R must act normally to the surface - which is to say at

to the vertical.

That said. we now just resolve forces:

Horizontally:

and vertically:

which is to say:

Horizontally:

and vertically

and

I went on and solved the second part for the reaction again by now knowing that

but I didn't assume the angle and indeed I got the same answer for the reaction and a confirmation of the angle of reaction from the vertical of
. I just can't, for some reason, "see" that
to the tangent is
from the vertical.

It was because I wasn't sure of the angle of the reaction that I went down a conservation of energy route in the first place. I still don't really see why one result differs from the other.

## #2 Re: Help Me ! » Calculation of the modulus of elasticity of a stretched string » 2018-07-12 22:22:11

The reason I put the right angle in there is because points A and B lie on the diameter of a circle and point C on the circumference of that circle and so ACB is the angle subtended by the diameter of the circle which is 90 degrees.

I can't rest easy with saying that my answer is correct. I feel I should arrive literally at

or the book is wrong.

If I am wrong then could it be in my assumption that the weight falls vertically so that C lies below its initial position?

Might C not be moved to the left or right by the string as it falls?

Thanks,
Mitch.

## #3 Help Me ! » Calculation of the modulus of elasticity of a stretched string » 2018-07-10 22:57:28

glendismollinew
Replies: 6

Hi,

It is the proof that the modulus of elasticity = W that I cannot achieve. If I assume this then the second part is fine.

I appreciate this is not a purely mathematical question, my error may be physical not mathematical - but my suspicion at the moment is that the question is in error.

My reasoning is that elastic potential energy (EPE) will be put in to the string in the act of stretching it over the bowl - I will calculate this, call it E1. Then further EPE will be introduced when the weight W descends to meet the bowl - call the total EPE in the string after the weight has descended E2 -I will calculate this too. Then E2 - E1 = loss of potential energy of weight.

= modulus of elasticity

Formula:

EPE in a string of natural length a with extension x =

My diagram:

My working:

We are told that for the weight attached to the unstretched string that AC =

and CB =
so that means that AB =
= natural length of string

Length once stretched over the diameter is

and so extension due to this is

and so the elastic potential energy in the string due to only the stretching over the diameter is

I'll leave it in this form for convenience later on.

Ok. from the diagram:

therefore

therefore

call this equation 1

also

and

and so

and

And so, from equation 1, we have:

therefore

and so

and

So the new length, due to stretching over diameter AND falling of weight =

So the extension is now:

So energy now stored in string is:

=

So, the change in elastic potential energy in going from just stretched across the diameter to streched across the diameter AND having the weight fallen is:

and this can be equated to the loss in gravitational potential energy of the weight W giving:

So I have λ in terms of w BUT I do not have λ=w

Is my physical reasoning incorrect?

If not, have I made a mathematical mistake(s)?

Thanks for any help, Mitch.