Tension & Torque Homework: 60.8 kg Man on 2.7m Scaffold

[a.a]

Homework Statement

A man of mass 60.8 kg stands on a scaffold supported by a vertical rope at each end. The scaffold has a mass of 17.2 kg and is 2.7 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?

Homework Equations

Torque = F r sin(angle to horizontal)
F = m g

The Attempt at a Solution

clockwise torque = anticlockwise torque
(2.7)(17.2) + (60.8)(9.8)(1.8) = F (2.7)
...
F = 414.4 N

I even tried it without useing the mass of the board and then placing the force caused by the mass (Fg) at the center, but all these thing didn't work.
We are also asked for the tension in the left rope after the tension in the right rope. But I can't figure out the right one first. Thanks in advance...

 

[a.a]

I realized my mistake, got it now, thanks anywas.. sorry I posted too soon.

clockwise torque = anticlockwise torque
(1.35)(17.2)(9.8) + (1.8)(60.8)(9.8) = F (2.7)
...
F = 481.5

 

[nlightner]

As a scientist, it is important to approach problems like this with a systematic and logical approach. First, we need to identify all the given information and understand the problem. From the given information, we know that there is a man standing on a scaffold that is supported by two vertical ropes, with the man standing to the right of the middle of the scaffold. We also know the mass of the man, the mass of the scaffold, and the length of the scaffold.

Next, we need to determine the forces acting on the scaffold. In this case, there are three forces: the weight of the man, the weight of the scaffold, and the tension in the ropes. We can use the equation F = m*g to calculate the weight of the man and the scaffold.

Now, we need to consider the torque, which is the measure of the force's ability to rotate an object. In this case, the scaffold will rotate if the clockwise torque is not balanced by the anticlockwise torque. We can use the equation Torque = F*r*sin(angle to horizontal) to calculate the torques caused by the weight of the man and the scaffold.

Since the scaffold is in equilibrium, the clockwise torque must be equal to the anticlockwise torque. We can set up an equation using the calculated torques and the unknown tension in the right rope. Solving this equation will give us the tension in the right rope.

To determine the tension in the left rope, we can use the fact that the total tension in both ropes must equal the weight of the man and the scaffold. Therefore, we can subtract the tension in the right rope from the total weight to find the tension in the left rope.

In summary, by breaking down the problem into smaller components and using the appropriate equations, we can solve for the unknown tension in the right rope and then use that value to calculate the tension in the left rope. This approach can be applied to various problems involving tension and torque, allowing us to accurately analyze and understand the forces at play in different scenarios.