A monkey of mass 40 kg climbs on a rope which stands a maximum tension of 600 N. In which of the following cases will the rope break. (i) When the monkey climbs up with an acceleration of 6 ms-2 (ii) When the monkey climbs down with an acceleration 4 ms-2 (iii) When the monkey climbs up with a uniform speed of 5 ms-1 (iv) When the monkey falls down the rope nearly freely under gravity
When the monkey climbs up with an acceleration a, then T - mg = ma Where T represents the tension T = m g + ma = m (g + a) T’ = 40kg (10 + +6) ms-2 = 640 N But the rope can withstand a maximum tension of 600 N. so the rope will break. (ii) When the monkey is climbing down with an acceleration then mg – T = ma T = mg – ma = m (g – a) T = 40 kg x (10 – 4) ms-2 = 240 N The rope will not break (iii) When the monkey climbs up with uniform speed T = mg = 40 kg x 10 ms-2 = 400 N The rope will not break. (iv) When the monkey is falling freely, it would be state of weightlessness. So tension will be zero and the rope will not break.
