Question

# A monkey of mass 40 kg climbs on a rope (Fig.) which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey 1. climbs up with an acceleration of $$6 \ m s^{-2}$$ 2. climbs down with an acceleration of $$4 \ m s^{-2}$$ 3. climbs up with a uniform speed of $$5 \ ms^{-1}$$ 4. falls down the rope nearly freely under gravity? (Ignore the mass of the rope).

Solution

## 1. When monkey climbs up with an acceleration 'a' then $$T - mg = ma$$Or T = m (g + a) = 40 (10 + 6) = 640 N which exceeds the maximum tension which rope can withstand (600 N), hence rope breaks. 2. when monkey is climbing down with an acceleration a mg - T = maor T = m (g- a) = 40 (10 - 4) = 240 N The rope will not break. 3. when the monkey climbs up with uniform speed thenT = mg = 40 $$\times$$ 10 = 400 N The rope will not break. 4. when the monkey is falling freely, it would be a state of weightlessness. So, there won't be any tension in the rope hence it will not break. Physics

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