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

(a) climbs up with an acceleration of 6 ms-2

(b) climbs down with an acceleration of 4 ms-2

(c) climbs up with a uniform speed of 5 ms-1

(d) falls down the rope nearly freely under gravity?

(Ignore the mass of the rope).

Asked by Abhisek | 1 year ago |  63

1 Answer

Solution :-

Mass of the monkey = 40 kg

Maximum tension the rope can withstand, Tmax= 600 N

(a) When the monkey climbs up with an acceleration of 6m/s2,

Tension T – mg = ma

T = m (g+a)

T = 40 (10 + 6)

= 640 N

Since T > Tmax, the rope will break

 

(b) When the monkey climbs down with the acceleration of 4m/s2

mg – T = ma

T = mg – ma = m (g – a)

= 40 (10 – 4) = 240 N

Since T <Tmax, the rope will not break

 

(c) When the monkey climbs with a uniform speed 5m/s. The acceleration will be zero. The equation of motion is

T – mg = ma

T – mg = 0

T = mg = 40 x 10 = 400 N

Since T <Tmax, the rope will not break

 

(d) When the monkey falls freely, the acceleration of the monkey will be equal to the acceleration due to gravity

The equation of motion is written as

mg + T = mg

T = m(g-g) = 0

Since T <Tmax, the rope will not break

Answered by Pragya Singh | 1 year ago

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