Max Speed & Acceleration for Climbing Rope

[asdf1]

If a man, weighing m1g is tryingting to climb up or down a rope, and the max tension T that the rope can withstand is 2m1g/3, then find the maximum speed and acceleration with which the man can climb without breaking the rope.

My work:
2m1g-m1g=m1a
=>a=-1g/3

doesn't this mean that the rope will break?

 

[Chi Meson]

Apparrantly the man can not climb this rope. If he weighs w, and the rope can only hold (2/3)w, he can not even hang on to the rope, nevermind climbing it.

He can, however, slide down the rope at a constant acceleration of (1/3)w

BTW, "find the maximum speed" is nonsense for this problem unless the length of the rope is given.

 

[HallsofIvy]

He can climb down the rope just by letting go- no tension at all!

As Chi Meson said, if the rope can only support 2/3 of the man's weight, he cannot climb up at all- he can't even hang on.

 

[asdf1]

thank you very much!