1) A toy rocket-launcher contains a spring with a spring constant of 35 N/m. How much must the spring be compressed to store 1.5 J of energy?

2) A box is connected to a spring is extended to 200mm, and it stored 3578J of energy. Find the force.

For number one I got

0.4m

For number two I got

89450N/M

Would this be correct?

0.094m

35,780N

Explanation:

1) Work done = 1/2ke^2

k is the spring constant = 335N/m

e is the extension

Workdone = 1.5J

Substitute

1.5 = 1/2*335*e^2

1.5 = 167.5e^2

e^2 = 1.5/167.5

e^2 = 0.00896

e = √0.00896

e = 0.094m

Hence the spring must be compressed by 0.094m

2) Workdone = 1/2Fe

F is the force = ?

Workdone = 3578Joules

extension e = 200mm = 0.2m

Substitute

3578 = 1/2*0.2F

3578 = 0.1F

F = 3578/0.1

F = 35,780N

Hence the force is 35,780N