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?

The man stands 3.9/6=0.65m to the right of the centre of the scaffold.

Let the tensions be L and R respective for the left and right ropes.

L.......16.8...64.8....R

Sum moments about the left end:
16.8*1.95+64.8*(1.95+0.65) - R*3.9 = 0

Solve for R.

where is the 1.95 coming from?

1.95=3.9/2 (half of the length, at the centre of gravity of the plank).

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

Let's denote the tension in the left rope as T1 and the tension in the right rope as T2.

First, let's calculate the weight of the man and the scaffold.

Weight of the man = mass of the man * acceleration due to gravity
= 64.8 kg * 9.8 m/s^2
= 635.04 N

Weight of the scaffold = mass of the scaffold * acceleration due to gravity
= 16.8 kg * 9.8 m/s^2
= 164.64 N

Next, let's consider the forces acting on the scaffold.

1. Tension in the left rope (T1) acts upward.
2. Tension in the right rope (T2) acts upward.
3. Weight of the man (635.04 N) acts downward.
4. Weight of the scaffold (164.64 N) acts downward.
5. The weight of the scaffold acts at its center of mass, which is at a distance of (1/6) * 3.9 m = 0.65 m from the right support.

Since the scaffold is in equilibrium (not accelerating), the sum of the forces in the vertical direction must be zero. Therefore, we can write the equation:

T1 + T2 - 635.04 N - 164.64 N = 0

Now, since the man is standing one sixth of the length of the scaffold to the right from the middle, we can assume the left half of the scaffold to be symmetric. This means that the T1 will be equal to T2.

So, we can write the equation as:

2T2 - 635.04 N - 164.64 N = 0

Combining the forces:

2T2 - 799.68 N = 0

Now, solve for T2:

2T2 = 799.68 N
T2 = 799.68 N / 2
T2 = 399.84 N

Therefore, the tension in the right rope is 399.84 N.