Question

Suppose that 2 J of work is needed to stretch a spring from its natural length of 32 cm to a length of 49 cm.

(a) How much work is needed to stretch the spring from 40 cm to 44 cm?
(b) How far beyond its natural length will a force of 15 N keep the spring stretched?

Answer 1

The work needed to stretch the spring from 40 cm to 44 cm is 0.64 J.

Step-by-step explanation:

To find the work needed to stretch the spring from 40 cm to 44 cm, we can use the formula for work done by a spring force:

Work = (1/2)k(x2^2 - x1^2)

Where k is the spring constant, x1 is the initial position, and x2 is the final position.

Given that 2 J of work is needed to stretch the spring from 32 cm to 49 cm, we can calculate the spring constant:

2 = (1/2)k(49^2 - 32^2)

From this we find k = 0.04 N/cm.

Now, we can calculate the work needed to stretch the spring from 40 cm to 44 cm:

Work = (1/2)(0.04)(44^2 - 40^2)

Work = 0.64 J.

Therefore, the work needed to stretch the spring from 40 cm to 44 cm is 0.64 J.