How Does a Climbing Man Affect the Center of Mass in a Pulley System?

AI Thread Summary
In a pulley system with a man climbing a ladder and a counterweight, the center of mass is affected by the man's movement and the weights involved. The system's external forces include the tension from the fixed support and gravitational forces acting on both the man and the counterweight. The relationship between the masses of the man and the counterweight is crucial for determining how they counterbalance each other. The problem lacks clarity on whether the man climbs with constant velocity or acceleration, which impacts the analysis. Understanding these dynamics is essential for calculating the displacement of the center of mass accurately.
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Homework Statement



A pulley fixed to a rigid support carries a rope whose one end is tied to a ladder and a man and the other end to the counterweight of mass M. The man of mass m climbs up a distance of h with respect to the ladder and then stops. If the mass of the rope and the friction in the pulley axle are negligible find the displacement of the center of mass of the system.

The Attempt at a Solution


The external forces acting on the system are:
1. The tension due to the fixed support=2T where T is the individual tension in each segment of the rope.
2. Mg and mg due to gravity
The thing is that I don't know whether mass m and M are equal. If no then how do they counterbalance each other?
The question does not even mention whether the man goes up with an acceleration or constant velocity?? Please help.
 
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