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 $6m{s}^{-2}$
2. climbs down with an acceleration of $4m{s}^{-2}$
3. climbs up with a uniform speed of $5m{s}^{-1}$
4. falls down the rope nearly freely under gravity? (Ignore the mass of the rope).

Answer 1

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 = ma
or T = m (g- a)
= 40 (10 - 4)
= 240 N
The rope will not break.
3. when the monkey climbs up with uniform speed then
T = 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.