# Compressing a spring

1. Nov 5, 2009

### Chandasouk

1. The problem statement, all variables and given/known data
To stretch a spring a distance 2.96 cm from its unstretched length, an amount of work of 11.3 J must be done.

How much work must be done to compress this spring a distance 4.01 cm from its unstretched length?

I did this but am not sure if it is correct.

Us = 1/2K$$\Delta$$X2

2.96cm = .0296m

4.01cm = .0401m

$$\Delta$$X = .0105m

What do I do from here? Would Us = 11.3J?

2. Nov 6, 2009

### rl.bhat

Using known amount of work done, using relevant equation, find the spring constant k.
Using this value of k, find the work done in the second case.

3. Nov 6, 2009

### warfreak131

With the equation $$U_{s}=\frac{1}{2}kx^2$$, you know all but one value, k. Find out what it is. Then for the second part, you'll have all values except $$U_{s}$$. which you can solve for.

4. Nov 6, 2009

### Chandasouk

11.3J = 1/2K(.0296m)2

K=25794 N/m but that is an insanely high number, so I do not think that is correct.

Regardless

$$U_{s}=\frac{1}{2}kx^2$$

Us = 1/2(25794 N/m)(.0105m)2

=1.42 J ?

5. Nov 6, 2009

### rl.bhat

For the second part, x is from the unstretched length. So x = 4.01 cm.

6. Nov 6, 2009

### Tzim

I think that 1.42j is wrong.If you think that in order to move 2.96 you need 11.3j energy.So in order to move it more you would need more energy.

7. Nov 6, 2009

### Tzim

That's an way to understand that there is a error.I hope i helped

8. Nov 6, 2009

### Chandasouk

Us = 1/2(25794 N/m)(.0401m)2

=20.7J ?