SCIENCE: Physics - Mechanical work (variable force)

Work

- amount of energy transferred by a force acting through a distance

- Work can be zero even when there is a force


W = S(a b) F * dx


where:

W = mechanical work done

F = variable force applied

dx = differential distance (delta x, change in x)

S(a b) = integral from a to b

a = lower limit, initial point

b = upper limit, final point



1. Springs - as springs get stretched, the harder it is to pull

The car suspension system steel spring has a spring constant of 12 lb/in. Find the work needed to stretch from an initial amount of 2 in to a final amount of stretch of 4 in.


find:

W = work done by stretching the spring 2 in to 4 in amount of stretch


given:

k = 12 lb/in

a = 2 in

b = 4 in


solution:

The force needed to stretch the spring increases as the spring gets extended

F = kx ---> equation1


W = S(a b) F * dx


substituting,

W = S(a b) kx * dx

W = k * S(a b) x * dx

W = 12 * S(a b) x dx

W = 12/2 [x^2, (2 4)]

W = 6 * (4^2 - 2^2)

W = 6 * (16 - 4)

W = 6 * 12

W = 72 in.lb


thus,

W = 1/2 k (b^2 - a^2)  ---> for springs