Laws of Motion
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Question : 33
Total: 40
A monkey of mass 40 kg climbs on a rope as shown in the figure which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey
(a) climbs up with an acceleration of 6 m s– 2
(b) climbs down with an acceleration of 4 m s– 2
(c) climbs up with a uniform speed of 5 m s– 1
(d) falls down the rope nearly freely under gravity?
(Ignore the mass of the rope).
(a) climbs up with an acceleration of 6 m s
(b) climbs down with an acceleration of 4 m s
(c) climbs up with a uniform speed of 5 m s
(d) falls down the rope nearly freely under gravity?
(Ignore the mass of the rope).
Solution:
Here, mass of monkey m = 40
Maximum tension the rope can stand,T = 600
In each case, actual tension in the rope will be equal to apparent weight of monkey (R).
The rope will break when R exceeds T.
(a) When monkey climbs up with a = 6 m s– 2
R = m ( g + a ) = 40 ( 10 + 6 ) = 640 N
Hence the rope will break.
(b) When monkey climbs down with a = 4 m s– 2
R = m ( g – a ) = 40 ( 10 – 4 ) = 240 N
∴ The rope will not break.
(c) When monkey climbs up with a uniform speedv = – 1 a = 0
∴ R = m g = 40 × 10 = 400 N
∴ The rope will not break.
(d) When monkey falls down the rope nearly freely under gravity,
a = g
∴R = m ( g – a ) = m ( g – g ) =
Hence the rope will not break.
Maximum tension the rope can stand,
In each case, actual tension in the rope will be equal to apparent weight of monkey (R).
The rope will break when R exceeds T.
(a) When monkey climbs up with a = 6 m s
Hence the rope will break.
(b) When monkey climbs down with a = 4 m s
∴ The rope will not break.
(c) When monkey climbs up with a uniform speed
∴ The rope will not break.
(d) When monkey falls down the rope nearly freely under gravity,
∴
Hence the rope will not break.
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