I hope I have put a pretty good title for this question. I was watching Professor Walter Lewin’s lecture on classical mechanics (lecture 7, I think).
Let’s say a person is hanging from a string (by holding onto it) and the string is hanging from the ceiling. That person would feel a tension force $T$ which is equal to his weight, let’s say $mg$. These are the only two forces acting on the person and since he’s not accelerating, $T$ = $mg$ in this case. This tension force $T$ would give him the perception of his weight, that’s what Professor Lewin said. He said that the tension force $T$ by definition is the weight of the person.
Let’s say the person starts accelerating downwards with $a$ ($a$ $<$ $g$). In this case $T$ = $m(g-a)$ and since $m(g-a)$ $<$ $mg$, the person would feel less heavy, as if he has lost weight (that’s what he said). He further said that if that person started accelerating downwards with an acceleration equal to $g$, the tension force $T$ would be $zero$ in that case and he would feel completely weightless. I followed everything up until this point.
But what if the person accelerated at a rate greater than $g$? In order for that to happen, we will need another force pulling him downwards. Let’s say there’s a string tied to his legs pulling him downwards with a force $T_1$ such that he accelerates at a rate higher than $g$, let’s say he is accelerating at $(g+k)$ where k is some number. Writing the equation in this case (according to Newton’s 2nd law),
$T$ - $mg$ - $T_1$ = $-m(g+k)$
$=>$ $T$ = $T_1$ $-mk$
This is what I get. If my math is correct, my question is, what would this tension force $T$ feel like for the person? In the first case when the system was not accelerating, the person feels his weight because of $T$. When the system was accelerating at the rate $a$ $(<g)$, the person felt less heavy. When the system was in free fall, he felt weightless. Now when the system is accelerating at a rate greater than $g$, what would it feel like? Would he feel heavier? Or less heavy? I am sure he would not feel weightless. This is my question. Thanks