The man (75 Kg) is climbing up the rope with acceleration 0.25 m/s2 relative to the rope. MA = 80 Kg. What is the rope tension and aA? Ans: aA = 0.195 m/s2 down, T = 769 N

a = 0.195 m/s²

T = 769.2 N

Explanation:

The sum of the forces (ΣF) acting on the man climbing up the rope is:

where : is the mass of the man, : is the acceleration of the man, T: is the tension and g: is the gravitational constant                                

       (1)                                              

Since the acceleration of the man is relative to the rope, the acceleration of the man is:

         (2)

where : is the acceleration of the man relative to the rope and a: is the acceleration of the rope = acceleration of the block A

By introducing equation (2) into (1) we have:

  (3)

The sum of the forces acting on the block A is:

where : is the mass of the block A

           (4)    

Now, solving equations (3) and (4) for a and T, we have:

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