Question

A construction crane lifts a bucket of sand originally weighing 145 lbs at a constant rate. Sand is lost from the bucket at a constant rate of .5lbs/ft. How much work is done in lifting the sand 80ft?

Answer 1

Answer: $10,000\ lb.ft$

Step-by-step explanation:

Given

Initial weight of the bucket is $145\ lb$

It is lifted at constant rate and rate of sand escaping is $0.5\ lb/ft$

At any height weight of the sand is $w(h)=145-0.5h$

Work done is given by the product of applied force and displacement or the area under weight-displacement graph

from the figure area is given by

$\Rightarrow W=\int_{0}^{80}\left ( 145-0.5h \right )dh\\\\\Rightarrow W=\left | 145h-\dfrac{0.5h^2}{2} \right |_0^{80}\\\\\Rightarrow W=\left [ 145\times 80-\dfrac{0.5(80))^2}{2} \right ]-0\\\\\Rightarrow W=11,600-1600\\\\\Rightarrow W=10,000\ lb.ft$