Question

Suppose that 6 J of work is needed to stretch a spring from its natural length of 36 cm to a length of 56 cm.

(a)
How much work (in J) is needed to stretch the spring from 44 cm to 52 cm? (Round your answer to two decimal places.)
(b)
How far beyond its natural length (in cm) will a force of 25 N keep the spring stretched? (Round your answer one decimal place.)

Answer 1

To stretch the spring from 36 cm to 56 cm, we need 6 J of work. Let's call the work needed to stretch the spring from 44 cm to 56 cm W1, and the work needed to stretch it from 36 cm to 44 cm W2.

Since the work needed is proportional to the distance the spring is stretched, we can write:

W1/W2 = (56-44)/(56-36)

Solving for W1, we get:

W1 = W2 * (56-44)/(56-36)

Substituting the values, we get:

W1 = 6 * (56-44)/(56-36) = 1.5 J

So, the work needed to stretch the spring from 44 cm to 52 cm is 1.5 J.

Now, let's move on to part (b).

The force required to stretch a spring is given by:

F = kx

where F is the force applied, x is the distance the spring is stretched beyond its natural length, and k is the spring constant.

We can rearrange this equation to solve for x:

x = F/k

We are given that a force of 25 N is applied to the spring. We need to find the distance the spring is stretched beyond its natural length. To do this, we need to know the spring constant.

Unfortunately, the problem does not give us the spring constant.

Without this information, we cannot solve for x.