Calculating Work Needed to Compress Spring

[Chandasouk]

Homework Statement

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.

U_s = 1/2K$$\Delta$$X²

2.96cm = .0296m

4.01cm = .0401m

$$\Delta$$X = .0105m

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

 

[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.

 

[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.

 

[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

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

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

=1.42 J ?

 

[rl.bhat]

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

 

[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.

 

[Tzim]

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

 

[Chandasouk]

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

=20.7J ?