How Does a Man Accelerate While Climbing a Rope?

[metastable]

That's why I thought it must be 2 phases with 2 acceleration and mass terms-- suppose the hands are different mass.

 

[jbriggs444]

That's why I thought it must be 2 phases with 2 acceleration and mass terms-- suppose the hands are different mass.

Suppose they are the same mass.

 

[metastable]

Then one phase lifts the body mass minus the hand mass, and the other phase lifts only the hand mass. The body could be simplified to a telescoping rod with 2 grappling claws. During each phase only one claw is grasping.

 

[jbriggs444]

Then one phase lifts the body mass minus the hand mass, and the other phase lifts only the hand mass. The body could be simplified to a telescoping rod with 2 grappling claws. During each phase only one claw is grasping.

There is one phase where the right hand is grasping and the left hand is rising. There is another phase where the left hand is grasping and the right hand is rising. Both phases are identical. There is no reason to worry about the distinction.

 

[.Scott]

A man tries to climb up a rope with acceleration, $a$. What does he actually do to climb up?

Why make things simple? Let's assume that this man will not only "try" to accelerate up the rope, but is taking on this project with real dedication.

So he will needs to apply the $F=m_m(g+a)$ that I specified earlier. As long as his velocity is up, he is "climbing the rope". But the acceleration doesn't have to be positive. He could start on a trampoline and then grab onto the rope and start climbing with not enough force to maintain his climb. He would reach a maximum height, and then drop back down to the trampoline. If I were that man, I would go with this option.

But most of us probably envisioned this man starting at the bottom of the rope with $V_0=0$. And by "climbing" we probably expect he will get at least a meter or two above the floor. We are also envisioning that the source of the mechanical energy is with the man - so something like a ski lift is out.

This arm movement stuff is also not going to cut it. I have tried climbing up a rope before. Doing it at all requires legs. Using arms to do it with constant velocity would be almost impossible. And doing it with constant acceleration is just not going to work.

He should use a space elevator - one where the "rope" stays in place and the gondola does the climbing. With nice computer controlled stepper motors, he will be able to control his acceleration precisely - and that nice constant acceleration is probably just what the elevator structure is best suited for. And of course, he will be able to maintain a constant acceleration for a much longer distance than most other methods - not just because of the length of the "rope", but because it will be extending into the vacuum of space where high velocities are better managed.

$F=(m_m+m_g)(g+a)$
$m_g$: mass of space gondola