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

Mass of the monkey = 40 kg

Maximum tension the rope can withstand, T_{max}= 600 N

**(a) **When the monkey climbs up with an acceleration of 6m/s^{2},

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/s^{2}

mg – T = ma

T = mg – ma = m (g – a)

= 40 (10 – 4) = 240 N

Since T ＜T_{max}, 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 ＜T_{max}, 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 ＜T_{max}, the rope will not break

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