Rope Loop
Robin Hood?
The drawing shows Robin Hood (mass = 85 kg) about to escape from a dangerous situation. As you can see, currently the chandelier (mass = 219 kg) is held 2.5 m off the floor by a rope looped over the beams and tied to the floor. When Robin cuts the rope free from the floor, the chandelier will fall and he hold on to the rope, being pulled safely up to the balcony 2.1m above the floor. (Ignore the friction between the rope and the beams over which is slides and take a co-ordinate system where up is positive y.)
a)What is the magnitude of acceleration at which Robin Hood pulled upwards after the rope has been cut?
b) What is the tension in the rope as Robin Hood is accelerating upwards?
Force on chandelier:
F = F_grav – T
= 219*g – T
= 219*a
=>
a = g – T/219
Force on RH:
F = T – F_grav
= T – 85*g
= 85*a
=>
a = T/85 – g
Therefore,
T/85 – g = a = g – T/219
T*(1/85 + 1/219) = 2*g = 2*9.8 = 19.6
T = 19.6/(1/85 + 1/219)
= 19.6*219*85/(219 + 85)
= 1200 (N)
and
a = T/85 – g
= 1200/85 – 9.8
= 4.3 (m/s^2)
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