The required work done is 62400 J.
work done to lift a 1500 N object from the ground to the top of a 40 m building if the cable weighs 3 N per m
work done, is define as the product of force and displacement.
since,
work done to lift 1500N to height of 40 m is:
W= FS
= 1500 x 40 = 60000J
now work done for rope
is given by
w = mgΔx(40-x)
w= [tex]\int _0^{40}\left mg(40-x\right)dx[/tex]
w=[tex]3\int _0^{40}\left(40-x\right)dx[/tex]
w= 3[tex][40x-x^2/2]\left \{ {{40} \atop {0}} \right.[/tex]
w= 3[1600-800]
w = 2400
Total work done for lifting 1500N to 40m height
= 6000+2400=62400J
Thus the required work done to lift 1500N weight to 40m is 62400J.
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