2 Nm of work is required to stretch a spring from its natural length 30 cm to 42 cm.

How much work is needed to stretch the spring from 35 cm to 40 cm?

Question

2 Nm of work is required to stretch a spring from its natural length 30 cm to 42 cm.

How much work is needed to stretch the spring from 35 cm to 40 cm?

anonymous · Answer

Ok, so the first thing you must do is find the spring constant of this spring.
In order to do that, we must remember that
$$F=-kx$$
and that
$$W=Fd$$
so
$$W=-kx^2$$
inputting the given information, we get
$$2=-k*.12^2$$
So $$k=138.9 N/m$$

anonymous · Answer

Now note that 40 cm - 35 cm= 5 cm
So
$$W=138.9*.05^2=.347Nm$$

anonymous · Answer

You need to rethink this... the spring force is not constant, so while the force applied to stretch a spring is f = kx, the work done is 1/2 kx^2, not kx^2. Use this equation to find k. Then use k to calculate the work done to stretch the spring from 35 to 40 cm, but be careful here - you have to calculate the work to stretch it to 35, the work to stretch it to 40 and then subtract the two - again because the force is not constant!