Question

If the work required to stretch a spring 2 ft beyond its natural length is 12 ft-lb, how much work is needed to stretch it 12 in. beyond its natural length?

Answer 1

Answer:

The work required to stretch a spring 12 ft beyond its natural length is 432 ft-lb

Explanation:

The work to stretch a spring is calculated using the formula:

$W = \frac{1}{2}kx^{2}$       Equation (1)

W = work in ft-lb

k = spring constant in lb/ft

x = spring deformation in ft

we clear k from the equation (1)

$k = \frac{2W}{x^{2}}$    Equation (2)

We replace x = 2ft, W = 12 ft-lb in the equation (2)

$k = \frac{2*12}{2^{2}} = 6 \frac{lb}{ft}$

Calculation of work required to stretch spring 12 ft

We replace k = 6 lb/ft and x = 12ft in the equation (1)

$W = \frac{1}{2} * 6 * 12^{2} = 432 ft-lb$