You are Here: Home >< Physics

# Stiffness and Length Question! watch

1. 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?
2. Did anyone else think this thread was going to be dirty?
3. (Original post by OMG TOOTHBRUSH)
Did anyone else think this thread was going to be dirty?
Funny guy...
4. It's not the stiffness and length that matters, it's what you do with it.
5. Thought this was about d****
6. (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...
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?
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.
8. (Original post by Stonebridge)
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.
Surely it is 0.4N / 2.5 cm, as the weight is then increased by 0.15N?
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.
10. (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?
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?
Yes that's fine.
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.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: December 5, 2010
Today on TSR

### The most controversial member on TSR?

Who do you think it is...

### Is confrontation required?

Discussions on TSR

• Latest
Poll
Discussions on TSR

• Latest

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE