Structures and Materials Questions

[Lols123]

First Q: Two wires, A and B, are of equal length. A has twice the diamter of B. The Young's Modulus of A is twice that of B. If they are subjected to the same load and A stretches by 10mm, the wire B will stretch by x. What is the value of x?

Any help is appreciated.

[madoscar65]

Ok firstly, ( I don't know how to use Latex so what I type here might not be easily seen)

So we know that E=stress/strain

Ea=FL/AadLa and Eb= FL/AbdLb

We know that Young's modulus of A is twice that of B, so we have Ea=2Eb
A has twice the diameter of B, since we are dealing with radius, A=pi(d/2)^2 and therefore wire has 4 times the area of B which is Aa=4Ab

So now we just equate them

Ea=2Eb
FL/4AbdLa=2FL/AbdLb

1/AbdLa=8/AbdLb
1/dLa=8/dLb
dLa=dLb/8
dLb=8dLa

We know dLa=10mm, therefore dLb=8 x 10= 80mm Hope that is correct,
What I typed there may not be clear to you.., lower cases just stand for which wire it is for and d just means delta. If you don't see what I typed clearly, I'm happy to write my work on a piece of paper and scan it down here.

[Lols123]

thanks! but its a little hard to read/understand :/
so if you could upload would be great

i have another question D:
how do you determine the tipping point of a structure (e.g. a cantilever)? Do you use torque? If so, how? :S

[madoscar65]

Hope the picture I scanned makes more sence .

For your second question, if the cantilever reaches its tipping point means that the normal force on the left of the cantilever is 0. Therefore the only thing that is keeping the cantilever is its own mass (centre mass). If there is a mass placed on the cantilever x distance away and its force is greater than the cantilever weight, then the cantilever will tip. In order to determine that, you will need to use torque and balance them out.

[Lols123]

yep the picture helped heaps, thanks!

with what you're saying about the cantilever. how come the left hand side support reaction force is 0 rather than the right hand side?

also having troubles with this question, so any ideas on how to approach it would be great.

[VivaTequila]

Your first question:

First Q: Two wires, A and B, are of equal length. A has twice the diamter of B. The Young's Modulus of A is twice that of B. If they are subjected to the same load and A stretches by 10mm, the wire B will stretch by x. What is the value of x?

Assuming wires A and B are made of the same material (and will hence have the same Young's Modulus), then if A has twice the diameter of B, double the force need to be applied to A to get the same strain as the amount of force that needs to be applied to get the same strain as B.

Put another way, A is twice as strong for any amount of force. It's harder to pull on a thick cord than a thin cord if they are made of the same stuff. In fact, if its double the diameter, then it's doubly hard.

Considering that they are subject to the same load, then A will stretch half as much as B will, for the reasons above.

Therefore 1/2A : B
A:2B

B stretches twice as much as A does, so B will stretch 10mm

i think, double check my answer, but that's how i would do this question


how do you determine the tipping point of a structure (e.g. a cantilever)? Do you use torque? If so, how? :S

Depends on the question and the setup of the question. Give us a specific example.