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

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SUMMARY

The discussion focuses on a physics problem involving a pulley system where a man of mass m climbs a ladder attached to a rope, counterbalanced by a mass M. The key forces at play include the tension in the rope (2T), gravitational forces (Mg and mg), and the need to determine the displacement of the center of mass of the system. The ambiguity regarding whether the masses m and M are equal and the climbing conditions (acceleration or constant velocity) is highlighted as a critical point for solving the problem.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Basic principles of center of mass calculations
  • Knowledge of tension in pulley systems
  • Familiarity with gravitational force concepts
NEXT STEPS
  • Study the principles of center of mass in multi-body systems
  • Learn about the dynamics of pulley systems and tension forces
  • Explore the effects of acceleration versus constant velocity in climbing scenarios
  • Review examples of similar physics problems involving mass and displacement
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators seeking to clarify concepts related to pulley systems and center of mass calculations.

ritwik06
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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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