A monkey of mass 40 kg climbs on a rope (Fig 5.20 ) which can stand a maximum tension of 600 N. In which of the following cases will the rope break : the monkey
climbs up with an acceleraiton of `6 ms^(-2)`
(b) climbs down with an acceleration of `4 ms^(-2)`
( c) climbs up with a uniform speed of `5 ms^(-2)`
(d) falls down the rope nearly freely under gravity ?
( Ignore the mass of the rope )

Explanation

(a) When the monkey climbs up with an acceleration of `6 ms^(-2)`, the tention in the rope is
`T=m(g+a)=40(9.8+6)=632 N`
It is greater than breaking strength (600 N).
So the rope breaks.
(b) When the monkey climbs up with an acceleration of `4 ms^(-2)`, the tension in the rope is
`T=m(g+a)=40(9.8+4)=552 N`
It is smaller than breaking strength (600 N). So the rope does not break.
(c ) When the monkey climbs up with an uniform speed of `5 ms^(-1)`, the tension in the rope is
`T=m(g)=40(9.8)=392 N`
It is smaller than breaking strength (600 N). So the rope does not break.
(d) When the monkey falls down the rope nearly freely under gravity then the tension is almost zero. So the rope does not break.