Question

A force of 14 lb is required to hold a spring stretched 4 in. beyond its natural length. How much work W is done in stretching it from its natural length to 10 in. beyond its natural length?

Answer 1

`W = 19.8 J`

Step-by-step explanation:

14 lb force is required to stretch the spring by 4 inch distance

So we have

`F = 14 lbf`

`F = 6.35 * 9.8 N`

`F = 62.3 N`

stretch in the spring is given as

`x = 4 in = 0.1016 m`

now we will have

`F = kx`

`62.3 = k(0.1016)`

`k = 613.125 N/m`

Now we need to find the work to stretch it by x = 10 in = 0.254 m

so we have

`W = (1)/(2)kx^2`

`W = (1)/(2)(613.125)(0.254)^2`

`W = 19.8 J`