# 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. – Brian Moths 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? – jatin 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. – BowlOfRed Mar 23 '16 at 21:47