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Stiffness and Length Question!

A piece of elastic cord is fixed at one end and a weight of 0.25N is attached to the free end. The length of the cord is 32 cm. The weight is then increased by 0.15N and the new length of the cord is 34.5 cm. Assuming elastic changes to the cord, calculate:

1) The length of the cord when the weight hanging from its end is 0.50N.

Right, so I calculated the stiffness, which is 16, and then I did 0.50 / 16 = 0.03125 m as the extension, but how do I find the original length of the cord, to which I can just add this extension value to?

Reply 1

OMG TOOTHBRUSH

Did anyone else think this thread was going to be dirty?

Reply 2

adil12

Original post by OMG TOOTHBRUSH

Did anyone else think this thread was going to be dirty?

Funny guy...

Reply 3

talon1579

It's not the stiffness and length that matters, it's what you do with it.

Reply 4

Bubbles0ox

Thought this was about d****

Reply 5

adil12

Original post by talon1579

It's not the stiffness and length that matters, it's what you do with it.

I know that but I don't know what to do with it, hence I am asking the question here...

Reply 6

Stonebridge

Original post by adil12

The elastic constant is from F=kx where x is extension, so k = F/x = 0.15N / 2.5cm (in N per cm units) [you got it upside down I think]
From this find the extension that the original 0.25N force was producing and subtract from the original extended length to find the unextended length.

Reply 7

adil12

Original post by Stonebridge

Surely it is 0.4N / 2.5 cm, as the weight is then increased by 0.15N?

Reply 8

Stonebridge

Original post by adil12

Surely it is 0.4N / 2.5 cm, as the weight is then increased by 0.15N?

You have to work in terms of the increase in length (2.5cm) caused by the increase in the force (0.15N) because they are proportional.
This is what's happening. (L is original length)

You are effectively finding the extension x for the force of 0.25N
This gives the original length by subtraction.
The gradient is the spring constant and is found from the small triangle.

Reply 9

adil12

Original post by Stonebridge

You have to work in terms of the increase in length (2.5cm) caused by the increase in the force (0.15N) because they are proportional.
This is what's happening. (L is original length)

You are effectively finding the extension x for the force of 0.25N
This gives the original length by subtraction.
The gradient is the spring constant and is found from the small triangle.

Right, so k = 0.15N / 2.5 cm = 0.06. Then I would find the extension for the first one, so I would do 0.25N / 0.06 = 4.17 cm, and then do 32 - 4.17 = 27.83 cm (original length) Then find the extension of the line with the new length by doing 0.5N / 0.06 = 8.33 cm, and then 8.33 + 27.83 = 36.16 cm which is the answer? :smile:

Reply 10

Stonebridge

Original post by adil12

Yes that's fine. :smile:

I thought the question actually asked for the original length of the cord but when I checked I found it didn't. [I was working from some notes I had written last night and not looked back at your post.]
It is possible to do it without finding the original length (there are a number of ways, actually), but it's best to start this way and do the shortcuts when you feel more confident.