The figure shows a man sitting in a bosun\'s chair that dangles from a massless
ID: 1535677 • Letter: T
Question
The figure shows a man sitting in a bosun's chair that dangles from a massless rope, which runs over a massless, frictionless pulley and back down to the man's hand. The combined mass of man and chair is 62.4 kg. With what force magnitude must the man pull on the rope if he is to rise (a) with a constant velocity and (b) with an upward acceleration of 1.49 m/s2? (Hint: A free-body diagram can really help.) Problem continues below.
If the rope on the right extends to the ground and is pulled by a co-worker, with what force magnitude must the co-worker pull for the man to rise (c) with a constant velocity and (d) with an upward acceleration of 1.49 m/s2? What is the magnitude of the force on the ceiling from the pulley system in (e) part a (f) part b, (g) part c, and (h) part d?
Explanation / Answer
LEt T1 be the tension in the rope attached to the chair
and
T2 be the tension in the rope held by man.
T1 = T2 = T (say) as the thread is mass less
from the equation of net force in vertical direction
2T - mg = ma
(a) as velocity is contant, acceleration = 0
2T = mg
T = mg/2
T = 62.4*9.8/2
T = 305.76 is the force with wich the man must pull the rope.
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(b) Now when acceleration a = 1.49 m/s^2
again from the equation of vertical motion
2T = mg+ma
2T = m(g+a)
2T = 62.4*(9.8+1.49)
T = 352.56 N Force with wich the man must pull the rope
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part C:
in this , only an end of the rope is connected to the man-chair system
Motion equation will be T - mg = ma
When a = 0
T = mg
T = 62.4* 9.8
T = 612.144 N is the force with wich the second man must pull the rope.
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(d) when a = 1.49 m/s^2
T = m(g+a)
T = 62.4* (9.8 + 1.49)
T = 704.496 N is the force with wich the second man must pull the rope.
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(e) Force on the cealing = force due to two parts of the rope = 2T
2T = 64.2* 9.81
2T = 629.802 N
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(f) Force on the cealing = 2T = 2 * 352.56 = 707.12 N
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(g). Force on the cealing = 2T = 2 * 629.802 = 1259.604 N
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(h). Force on the cealing = 2T = 2 * 707.12 = 1414.24 N
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