Calculating Tension For A Massless String

[Yosty22]

Homework Statement

A gymnast of mass 59.0kg hangs from a vertical rope attached to the ceiling. You can ignore the weight of the rope and assume that the rope does not stretch. Use 9.81 m/s^2 for the value for the acceleration of gravity.
Calculate the Tension, T, in the rope if the gymnast climbs the rope at a constant rate.

Homework Equations

None (that I can think of)

The Attempt at a Solution

Since the rope is massless, I was thinking that the tension on the rope if she hangs there motionless should be the same as if she is climbing it. Solving for the Tension of the rope while she was sitting there, I just used mass times gravity, in this case; 59kg*9.81m/s^2=578.79N. Would this answer be the same if she was climbing up the rope as well?
Thanks a lot in advance.

 

[mfb]

Since the rope is massless, I was thinking that the tension on the rope if she hangs there motionless should be the same as if she is climbing it.

Right, but that is true for a massive rope as well.

Would this answer be the same if she was climbing up the rope as well?

Yes. You can use momentum conservation to show this, for example.

 

[Yosty22]

Right, but that is true for a massive rope as well.

This is true as long there is no acceleration, correct? As long as the velocity is constant, that is always true?

 

[mfb]

Yes - if we assume that the gravitational force does not depend on the height (a very good approximation here...).

 

[Nickie]

Yes, your approach is correct. The tension in the rope while the gymnast is hanging motionless is equal to her weight (mg), which in this case is 578.79N. This is because the rope is massless and therefore does not contribute any additional weight or tension.

When the gymnast starts climbing the rope at a constant rate, the tension in the rope will increase to support her weight as well as the additional force she is exerting to climb. This tension can be calculated using the same formula, T=mg, where m is the mass of the gymnast and g is the acceleration due to gravity.

So in this case, the tension in the rope while the gymnast is climbing at a constant rate would be 59kg*9.81m/s^2 = 578.79N + force exerted by the gymnast to climb.

Hope this helps!