A spring has a natural length of 20cm. If a 25-N force is required to keep it stretched to a length of 30 cm, how much work is required to stretch it from 20 cm to 25 cm?

Question

A spring has a natural length of 20cm.  If a 25-N force is required to keep it stretched to a length of 30 cm, how much work is required to stretch it from 20 cm to 25 cm?

lgbasallote · Answer

the formula is $$F = kx$$
25 N is requred to stretch the spring by 10 cm
$$25 = k(10)$$
$$k = \frac{25}{10}$$

now..how much force is required to stretch it by 5 cm..
$$F = kx$$
$$F = (\frac{25}{10}) (5)$$
$$F = \frac{25}{2}$$
does that help?

anonymous · Answer

Ok, that gives me the force which I have computed up until then, however, I get caught on when we need to use that to get the total amount of work done on the spring.

lgbasallote · Answer

oh..you're looking for work

if i remember right..spring work is $$W = \frac 12 kx^2$$
does that help?

anonymous · Answer

Yes much thanks.  I get a total answer of 0.31.  Thank you very much!

lgbasallote · Answer

welcome