A man is pulling himself up to a pulley that consists of two disks welded togeth

Question

A man is pulling himself up to a pulley that consists of two disks welded together as shown. The man is currently pulling straight down on the rope in his hands with a force of magnitude 498.2 N. The other rope is also vertical and is attached to the man's waist at his center of mass. The man's mass is 89.8 kg, the pulley's total moment of inertia is 2.93 kg m2, the radius of the small disk is 0.31 m, and the radius of the big disk is 0.60 m.  

With the force given above, what is the magnitude of the acceleration of the man's waist (where the rope is attached)?

How hard does the man have to pull to hold himself stationary?

Explanation / Answer

force equation om man

T + 498.2 - 89.8*9.8 = 89.8*a = 89.8*alpha*0.31

498.2*0.60-T*0.31 = 2.93*alpha

498.2 - 89.8*9.8 + (498.2*0.60)/0.31 = (27.83+9.45)alpha

=> alpha = 15.62 rad/sec^2

a = alpha/R = 15.62/0.31 = 50.38 m/s^2

b)

498.2*0.60-T*0.31 = 0 ( in order to keep stationary, a= 0)

=> T = 964.2 N

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