question_answer 32)

A monkey of mass 40 kg climbes on a rope which can stand a maximum tension of 600 N [Fig. 5.134]. In which of the following cases will the rope break : the monkey (i) climbs up with an acceleration of (ii) climbs down with an acceleration of   (iii) climbs up with a uniform speed of (iv) falls down the rope nearly freely under gravity ? Take . Ignore the mass of the rope.   Fig. 5.134                             Fig. 5.135  

Answer:

(i) When the monkey climbs up with an acceleration  the tension T in the string must be greater than the weight of the monkey [Fig. 5.135(fl)],   or             . (ii) When the monkey climbs down with an acceleration,            [Fig. 5.135(b)],   or          T = m(g - a) = 40(10 - 4) = 240 N. (iii) When the monkey climbs up with uniform speed,                T = mg = 40 x 10 = 400 N. (iv) When the monkey falls down the rope nearly )n  freely, a = g             . As the tension in the rope in case (i) is greater than the maximum permissible tension (600 N), so the rope will break in case (i) only.