Question

A cable that weighs 4 lb/ft is used to lift 1000 lb of coal up a mine shaft 700 ft deep. Find the work done.

Answer 1

980000ft-lbs

Step-by-step explanation:

Step one:

given data

mass of cable= 4lb/ft

mass of coal= 1000lb

dept of mine= 700ft

Step two:

Required

the work-done to lift the coal and the rope combined

Work-done to lift coal

Wc=1000*700= 700,000 lb-ft

Work-done to lift rope

`Wr=\int\limits^(700) _0 {4(700-y)} \, dx \\\\Wr=4(700y-(1)/(2)y^2 )\limits^(700)_0`

substitute y=700 we have, since y=0 will result to 0

`Wr=4(700*700-(1)/(2)*700^2 )\\\\Wr=4(490000-245000)\\\\Wr=4(245000)\\\\Wr=980000ft-lbs`