Question

A worker on a scaffolding 75 ft above the ground needs to lift a 500 lb bucket of cement from the ground to a point 30 ft above the ground by pulling on a rope weighing 0.5 lb/ft. Choose the integral needed to calculate how much work is required?

Answer 1

Answer:

W = 15900 ft.lb

Step-by-step explanation:

From the given information.

Consider y to be the distance from the ground towards the bucket of the cement.

At height y, suppose the bucket is lifted by Δy.

Then, the workdone can be = 500Δy + 0.5(75 - y) Δy

where;

The bucket of the cement =  500Δy

The remaining of the rope =  0.5(75 - y) Δy

However; the workdone (W) can be calculated as:

$W = \int^{30}_{0} \ 500 \ dy + \int^{30}_{0} \ 0.5 (75-y ) \ dy$

$W = 500 \times 30 + 0.5 \bigg(75 \times 30 - \dfrac{1}{2} \times 30^2 \bigg )$

W = 15000 + 0.5 ( 2250 - 450)

W = 15000 + 900

W = 15900 ft.lb