To find the work done in extending a spring

[gnits]

Homework Statement

To find the work done in extending a spring

Relevant Equations

W.D. = F * d

Hi,

Could I please ask where I am going wrong with this very simple question:

Here's my answer (units implied):

A force of 20 extends the spring by 1/100 and so the Work Done in performing this extension is 20 * 1/100 = 1/ 5

Now, the work done in extending a spring is given by the formula W.D. = (Y * x^2) / (2a) where 'Y' is the Modulus Of Elasticity of the spring, 'x' the Extension and 'a' the Natural Length of the spirng.

So we have 1/5 = (Y * 1/10000) / (2a) and so from this we have:

Y/(2a) = 2000

Now, using the same formula, the work done in extending the spring by b is:

(Y * b^2) / (2a) and substituting for Y/(2a) from the previous formula gives:

W.D. = 2000 * b^2 = 2x10^3 * b^2 which is twice the book answer of 1x10^3 * b^2

Thanks for any help,
Mitch.

 

[Blur]

Let me see
F/A =Y x/l ==>x is elongation
So F= kx
Now work
dW = F .dx
dW = kx .dx
Integrating both we get,
W=1/2(kx^2)Hope that helps.

 

[PeroK]

Homework Statement:: To find the work done in extending a spring
Homework Equations:: W.D. = F * d

Hi,

Could I please ask where I am going wrong with this very simple question:

View attachment 253923

Here's my answer (units implied):

A force of 20 extends the spring by 1/100 and so the Work Done in performing this extension is 20 * 1/100 = 1/ 5

Now, the work done in extending a spring is given by the formula W.D. = (Y * x^2) / (2a) where 'Y' is the Modulus Of Elasticity of the spring, 'x' the Extension and 'a' the Natural Length of the spirng.

So we have 1/5 = (Y * 1/10000) / (2a) and so from this we have:

Y/(2a) = 2000

Now, using the same formula, the work done in extending the spring by b is:

(Y * b^2) / (2a) and substituting for Y/(2a) from the previous formula gives:

W.D. = 2000 * b^2 = 2x10^3 * b^2 which is twice the book answer of 1x10^3 * b^2

Thanks for any help,
Mitch.

Why not simply use $F = kx$ and $W = \frac 1 2 k x^2$?

 

[gnits]

Thanks all for your help, I see it now. Thanks, Mitch.