Physics help on conditions for Static Equilibrium
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Physics help on conditions for Static Equilibrium

[From: ] [author: ] [Date: 11-06-14] [Hit: ]
I will be SO GRATEFUL. 1. A 100 kg man places his hands 0.6 m from his center of mass and places his feet 1.7 m from his hands, intending to do push-ups.......
I am stuck on my physics homework. I was given answers, but I'm totally stumped on how to solve them, and get through step-by-step with a reason why. If someone could show me the way clearly, and show how I got to the next step. I will be SO GRATEFUL.

1. A 100 kg man places his hands 0.6 m from his center of mass and places his feet 1.7 m from his hands, intending to do push-ups. Find the forces exerted on his hands and feet by the floor prior to pushing himself upward. (Answer: 634 N, 346 N)

2. Two 75 kg painters stand on a scaffold (20 kg and 4 m long) supported at the ends by two ropes. If one painter stands 1 m from the right end of the scaffold, how close can the second painter get to the right end of the scaffold before the rope, capable of supporting 1100 N of force, breaks?
(Answer: 1.55 m)

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1.

F_h: Force on hands
F_f: Force on feet

Since the rotation rate of the body is zero, the net torque around any point along the body must be zero. To solve for forces, we choose a point along his body (preferably at a point where a force is being applies to we have one fewer torque to worry about) and sum all the torques to zero. You also have to choose a rotation direction to be positive.

I'll choose the point at his hands and clockwise to be positive. At 0.6 meters away, 980N (his weight) is trying to rotate the man clockwise. This is 0.6m x 980N = 588 Nm of torque. At a distance of 1.7m away, the force on his feet is trying to rotate the man COUNTERclockwise:

-1.7m x F_f <---Note this is negative because it is COUNTERclockwise


Summing all the torques to zero:

588 Nm -1.7m x F_f = 0

So F_f = 588 Nm / 1.7m = 346 N


Since the man is not accelerating, the net force on him must be zero.

So F_h -980N + 346N = 0

So F_h = 634N


Note: Instead of starting at the point of his hands, I could have chosen the point of his feet and gotten the same answers.
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