Question

A 5000-lb wrecking ball hangs from a 50-ft cable of density 10 lb/ft attached to a crane. Calculate the work done if the crane lifts the ball from ground level to 50 ft in the air by drawing in the cable.

Answer 1

Answer:

total work is = 52450 J

Explanation:

given data

mass =  5000-lb

density = 10 lb/ft

height = 50 ft

solution

as we will treat here cable and ball are separate  

and

here work need to lift cable is

w = (10Δy )(9.8 y )  j

and

now summing all segment of cable

so passing limit Δy to 0

so total work need

= $\int\limits^{10}_0 {98y} \, dy$    

= $[49 y^2]^{50}_0$

= 2450J

so lifting 5000 lb wrcking 50 m  required additional 5000 + 2450

so total work is = 52450 J