Question

In Fig. (i), the man walks 2 m carrying a mass of 15 kg on his hand. In Fig. (ii), he walks the same distance
pulling the rope behind him. The rope goes over a pulley, and a mass of 15 kg hangs at its other end
in which case is the work done by gravity is greater ?
15 kgf
15 kg​

Answer 1

case (i) : force applied on 15 kg mass , F = mg = 15kg × 9.8 m/s² = 147 N [ vertically downward ]

displacement of mass , s = 2m [ horizontally west direction ]

so, angle between force and displacement vector, Φ = 90°

we know,

work done = F.scosΦ

= 147 × 2 × cos90° = 0

case (ii) : force applied on mass, F = tension in rope = weight of body = mg

= 147 N [ horizontally west direction ]

displacement , s = 2m [ horizontally west direction ]

so, angle between F and s , Φ = 0°

so, work done = F.scosΦ

= 147 × 2 × 1 = 294 J

hence, in case (ii), more work is done.

Answer 2

Explanation:

work done in second case is greater

in case 1 displacement horizontal and force downward(mg)

thus @= 90°

work done= 0

in case 2 displacement and force horizontal

in same direction

thus @ = 0°

work done not equal to zero