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

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Homework Help Overview

The problem involves calculating the tension in a vertical rope as a gymnast of mass m interacts with it under various conditions, including climbing at a constant rate, hanging motionless, accelerating upwards, and sliding downwards. The context is rooted in classical mechanics, specifically Newton's laws of motion.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss applying Newton's second law and drawing free body diagrams to analyze the forces acting on the gymnast. There is an exploration of expressing tension in terms of the gymnast's mass and acceleration.

Discussion Status

Some participants have provided expressions for tension under different scenarios, while others are verifying these expressions and discussing the underlying principles. There appears to be a productive exchange of ideas regarding the calculations involved.

Contextual Notes

Participants are required to express their answers in terms of variables rather than numerical values, which influences the approach to the problem. There is an emphasis on not considering the magnitude of acceleration in the initial conditions.

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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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