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

[Chandasouk]

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?

 

[maladroit]

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!

 

[Chandasouk]

T = mg for the first one and T = mg for the second question it asks me

 

[Chandasouk]

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) ?

 

[maladroit]

right on! very good.