# Laws of motion while climbing a rope

I'm a little confused with the application of laws of motion on a man climbing a rope. Suppose a man of mass Mg is climbing a rope with an acceleration a. Rope is massless. Now if look through the frame of the piece of rope held by the man, there is a force Mg downward by man, ma downward applied by man and T upward. This balances out as the piece is at rest. This equation is correct, though my way of looking at it maybe incorrect. Now if we look through the man's frame, we have Mg downward, T upward, ma upward the reaction by rope, and as we are in an accelerated frame, ma downward. What am I doing wrong and can you explain how is the man able to climb upward i.e. how the forces are acting to give this motion.

• You understand it perfectly. The tension provides an upward force of $mg+ma$. That is how the man is able to go up the rope. In the man's frame you have an additional non-inertial force of $ma$ pointing downwards as you say, so the man does not accelerate in his own frame. Mar 23 '16 at 19:58
• What if we just look at the man through an inertial frame. We'll have T upwards, Mg downwards, ma upwards by the rope, sum of these force gives us acceleration of man in the upward direction so = ma, this equation is clearly wrong, where am I wrong? Mar 23 '16 at 20:05
• @jatin, what do you mean by "ma upwards by the rope"? The only force the rope exerts on the man is T. I'm not sure what equation you find wrong. Mar 23 '16 at 21:47
• Try to convert the system into another similar system, i.e. you can replace the rope by stick with grooves(teeth like gears) and replace the hand pulling by rotating gear trying to climb up the grooved stick Mar 20 '20 at 11:48

If a man moves one hand up very fast he will not be pulled down by gravity as he will using the strength. Of both hands to grip the rope again.If a man moves his hand up slowly gravity will pull him down as he is now gripping the rope with one hand

• Welcome to Physics SE! Could you please clarify your answer as i can't quite make sense of it at the moment Nov 20 '19 at 11:16

Your question looks a bit confusing, but still I would try to answer it (as per my understanding of the question). Clearly in any frame of reference the only force that are acting on the object are:

• Gravitational force on the man,$$F_g$$
• Tension from the rope, $$T$$ (See the note)
• Static Friction (from the rope, assuming that he is moving upward by pulling ),$$f_s$$
• ma

Inertial Frame

Now these forces act together to cause a net acceleration $$a$$. The net force is then $$ma$$ ( Yes! the man does not apply this force its just the effect of all the other forces.).

Therefore the equation can be written as $$F_g + f_s = ma$$.

Non-Inertial Frame

Here you just have to account for the pseudo force $$-ma$$ and the net force equation is as follows: $$F_g + f_s - ma =m0=0$$.