When a painter weighs 500N and the tensions in each supporting rope are 400N, what is the weight of the scaffold if it is in mechanical equilibrium?

To determine the weight of the scaffold when it is in mechanical equilibrium, we first need to consider what mechanical equilibrium means. In this context, it indicates that the sum of all forces acting on the system must equal zero. This is a fundamental principle in physics concerning the balance of forces.

In this scenario, the painter weighs 500 N, and there are two ropes supporting both the painter and the scaffold. Each rope exerts a tension of 400 N. Therefore, the total upward force provided by the ropes is 400 N + 400 N = 800 N.

Since the painter is static and the system is in mechanical equilibrium, the total downward force (the weight of the painter plus the weight of the scaffold) must be equal to the total upward force provided by the ropes.

This can be expressed with the equation:

[ \text{Weight of the painter} + \text{Weight of the scaffold} = \text{Total upward force from the ropes} ]

Substituting in the known values:

[ 500 N + \text{Weight of the scaffold} = 800 N ]

To find the weight of the scaffold, we rearrange the equation:

[ \text{Weight of the scaffold} =