A monkey of mass 40 kg climbs on a rope which can stand a maximum tension 600 N. In which of the following cases will the rope break? The monkey (a) climbs up with an acceleration of 6m/s2 (b) climbs down with an acceleration of 4m/s2 (c) climbs up with a uniform seed of 5m/s (d) falls down the rope freely under gravity. Take g = 10m/s2 and ignore the mass of the rope.

Answers (1)

(a)    F = T – mg
ma = T – mg
T = ma + mg  
= m(a + g)  
= 40(10 +6)  
=640N
This is greater than the max. tension which the rope can withstand. Hence the rope will break.

(b)F = mg – T
ma = mg – T
T = mg - ma  
=m(g - a)          
= 40(10 - 4)  
= 240N
This is lesser than the max. tension which the rope can withstand. Hence the rope will not break.

( c) F = T – mg   
ma = T – mg       
T = ma + mg          
 = m(a + g)            
= 40(0+ 10)           
=400N
This is greater than the max. tension which the rope can withstand. Hence the rope will not break.

( d) F = mg – T
ma = mg – T
T = mg - ma  
=m(g - g)  
= 0N

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