A man of mass 64.8 kg stands on a scaffold supported by a vertical rope at each end. The scaffold has a mass of 16.8 kg and is 3.9 m long. Suppose the man stands to the right from the middle of the scaffold that is a distance one sixth of the length of the scaffold. What is the tension in the right rope?

http://www.jiskha.com/search/index.cgi?query=A+man+of+mass+64.8+kg+stands+on+a+scaffold+supported+by+a+vertical+rope+at+each+end.+The+scaffold+has+a+mass+of+16.8+kg+and+is+3.9+m+long.+Suppose+the+man+stands+to+the+right+from+the+middle+of+the+scaffold+that+is+a+distance+one+sixth+of+the+length+of+the+scaffold.+What+is+the+tension+in+the+right+rope%3F+http://www.jiskha.com/search/index.cgi?query=A+man+of+mass+64.8+kg+stands+on+a+scaffold+supported+by+a+vertical+rope+at+each+end.+The+scaffold+has+a+mass+of+16.8+kg+and+is+3.9+m+long.+Suppose+the+man+stands+to+the+right+from+the+middle+of+the+scaffold+that+is+a+distance+one+sixth+of+the+length+of+the+scaffold.+What+is+the+tension+in+the+right+rope%3F+

To find the tension in the right rope, we need to analyze the forces acting on the scaffold.

Let's start by drawing a free-body diagram for the scaffold:

<----<---- Scaffold (3.9 m) ---->---->
|_______________|____________|_______________|___________|

^
|
|
Man

There are three forces acting on the scaffold:
1. Weight of the scaffold acting downward (mg).
2. Weight of the man acting downward (mg).
3. Tension in the right rope acting upward.

For equilibrium, the sum of vertical forces must be zero.

1. Weight of the scaffold (Fscaffold) = mass of the scaffold (mscaffold) * acceleration due to gravity (g).
Fscaffold = mscaffold * g = 16.8 kg * 9.8 m/s^2 = 164.64 N (upward)

2. Weight of the man (Fman) = mass of the man (mman) * acceleration due to gravity (g).
Fman = mman * g = 64.8 kg * 9.8 m/s^2 = 635.04 N (downward)

Now, the distance from the middle of the scaffold to the man is 1/6 of the length of the scaffold:
Distance = (1/6) * 3.9 m = 0.65 m

The tension in the right rope (Tright) can be found using the torque equation, since the system is in rotational equilibrium:

Torque about the left rope = Torque about the right rope

(Weight of the man) * (distance from the right rope) = (Weight of the scaffold) * (distance from the left rope)
Fman * 0.65 m = Fscaffold * (3.9 m - 0.65 m)

635.04 N * 0.65 m = 164.64 N * (3.9 m - 0.65 m)
413.28 N = 164.64 N * 3.25

Now, we can solve for the tension in the right rope (Tright):

Tright = Fman + Fscaffold
Tright = 635.04 N + 164.64 N
Tright = 799.68 N

Therefore, the tension in the right rope is approximately 799.68 Newtons.