A man of mass 76.1kg stands on a scaffold supported by a vertical rope at each end. The scaffold has a mass of 23.9kg and is 3.0m 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?
b).what is the tension in the left rope?
Sum moments about the right end.
Tl*3-23.9g*1.5-76.1g(d)=0 where d is where the man is standing.
1/6 length scaffold is .5m, so the man is standing at 1.5-.5=1.0 or d=1.0 check that.
solve for tension left Tl
A uniform rod of length 10m and mass 50kg is suspended from two verticle ropes attached to its ends.
a) A woman of mass 70kg stands at the middle of the rod. What is the tension in each rope?
b) The ropes break if the tension in them exceeds 750N. how far to the right can the woman walk before the rope breaks?
To find the tension in the right rope, we need to consider the forces acting on the scaffold.
Let's assume that the man is standing on the right side of the scaffold, that is, 1/6 of the length away from the middle. This means that the distance from the right end of the scaffold to the man is (1/6)*(3.0m) = 0.5m.
1. First, we need to find the force exerted by the man's weight. The weight of an object is given by the formula: weight = mass * acceleration due to gravity. In this case, the mass of the man is 76.1kg, and the acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the weight of the man is: weight = 76.1kg * 9.8m/s^2.
2. Next, we need to find the weight of the scaffold. The weight of the scaffold is simply the mass of the scaffold multiplied by the acceleration due to gravity. In this case, the mass of the scaffold is 23.9kg, and the acceleration due to gravity is 9.8m/s^2. Therefore, the weight of the scaffold is: weight = 23.9kg * 9.8m/s^2.
3. Now we need to find the total weight acting on the right side of the scaffold. This will be the sum of the man's weight and the scaffold's weight.
4. Since the scaffold is in equilibrium, the sum of all the vertical forces acting on it must be zero. So, the tension in the right rope will be equal to the total weight acting on the right side of the scaffold.
To find the tension in the left rope, we can use the same reasoning. Since the scaffold is symmetrical, the tension in the left rope will also be equal to the total weight acting on the left side of the scaffold.
By applying these steps, you can now calculate the tension in both the right and left ropes.