Calculating Tension in a Vertical Rope with Variable Mass: A Scientific Inquiry

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SUMMARY

The discussion focuses on calculating the tension in a vertical rope when a gymnast of mass m interacts with it under various conditions. When climbing at a constant rate or hanging motionless, the tension is expressed as T = mg, where g is the acceleration due to gravity. If the gymnast accelerates upward with acceleration a, the tension is T = m(g + a). Conversely, when sliding downward with acceleration a, the tension is T = m(g - a). These calculations are grounded in Newton's Second Law and require a clear understanding of free body diagrams.

PREREQUISITES
  • Understanding of Newton's Second Law
  • Ability to draw and interpret free body diagrams
  • Knowledge of basic physics concepts such as mass and acceleration
  • Familiarity with gravitational force calculations
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  • Study the implications of Newton's Second Law in different physical scenarios
  • Learn how to construct and analyze free body diagrams in various contexts
  • Explore the effects of variable mass systems in physics
  • Investigate real-world applications of tension in ropes and cables
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Physics students, educators, and anyone interested in understanding dynamics involving tension in ropes, particularly in scenarios involving variable forces and accelerations.

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Homework Statement




A gymnast of mass m climbs a vertical rope attached to the ceiling. You can ignore the weight of the rope.

Calculate the tension in the rope if the gymnast climbs at a constant rate.

Calculate the tension in the rope if the gymnast hangs motionless on the rope.

Calculate the tension in the rope if the gymnast accelerates up the rope with an acceleration of magnitude a.

Calculate the tension in the rope if the gymnast slides down the rope with a downward acceleration of magnitude a.


For the first one, they want you to answer in terms of m, well, in variables in general.

I know for the first one that if you travel at a constant velocity, there is no acceleration and no net force so they will both equal zero. But how would I express that using the variable m which is her mass?
 
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Think about Newton's 2nd law...draw a free body diagram of the situation. because they want the answer in variables, don't consider the magnitude of the acceleration!
 
T = mg for the first one and T = mg for the second question it asks me
 
Correct me if I am wrong, but for these two questions

Calculate the tension in the rope if the gymnast accelerates up the rope with an acceleration of magnitude a.

Calculate the tension in the rope if the gymnast slides down the rope with a downward acceleration of magnitude a.

The first would be T = M(g+a) and second would be T = M(g-a) ?
 
right on! very good.
 

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