Climbing with Tension: Exploring Muscle vs. Mechanical Energy

[Crystal037]

Homework Statement

A light rope fixed a one end of a wooden clamp on the ground passes over a tree branch and hangs on the other side. It makes an angle 30 degrees with the ground. The wooden clamp can come out of the ground if an upward force greater than 360N is applied to it. Find the max acceleration with which the man can climb safely. Neglect friction on the tree branch

Relevant Equations

T-mg=ma

Here the upward force on the camp is Tsinx <=360
Therefore T(max)=720N
Here they have taken the equation that T-mg=ma
This shows that the man is climbing due to tension. But I can't visualise how tension helps in climbing. Isn't it our own energy that helps us to climb. The muscle energy gets converted to mechanical energy when we lift our hands, then how tension would lift us up.

 

[haruspex]

This shows that the man is climbing due to tension.

Whether it is 'due' to the tension depends on your point of view.
If you view the man, arms included, as the climbing object then the acceleration is due to the net of external forces acting, i.e. tension minus gravity.
Of course, the excess of the tension over the force of gravity is a result of the man contracting his muscles.

 

[Crystal037]

I don't understand how the man is creating excess of tension. Can you show it with some force vector diagrams

 

[jbriggs444]

The man is free to exert whatever force he likes on the rope. He can pull gently or strongly. However hard he pulls, Newton's third law applies. That is to say that the force the man applies to the rope is equal and opposite to the force the rope applies to the man.

You have already computed that the tension on the rope may not exceed 720 N. It is clear from the problem that the tension on the rope is uniform throughout its length. It follows that the man may not apply more than 720 N to the rope.

To maximize his upward acceleration, the man will want to apply 720 N to the rope so that the rope can apply 720 N to him. If he is light enough, this upward force of 720 N will exceed the downward force of gravity on the man and an upward acceleration will result.

Normally, the student is expected to produce the free body diagram.

 

[Crystal037]

Oh thanks now I get that the force that the man applies will be equal and opposite to that what rope applies so when the man applies a force downwards so the rope applies an upward force which helps him to climb and we don't consider the force exerted by the man since we consider the man as the system.