6. A painter weighing 800 newtons stands on a single board scaffold that is supported at each end by a vertical rope from above. If one rope has a tension of 550 newtons and the other has a
tension of 450 newtons, what is the weight of the board?

The weight of the board is 200 N

Explanation:

Translational Equilibrium

An object is in translational equilibrium if the velocity of its translational motion is constant or if it's at rest.

The painter is standing on the single board scaffold, obviously at rest. This means the sum of all translational forces must be zero.

If the tensions of both ropes are T1 and T2, the weight of the painter is Wp, and the weight of the board is Wb, then:

T1 + T2 - Wp - Wb = 0

Both tensions go vertically up and both weights go vertically down.

Solving for Wb:

Wb = T1 + T2 - Wp

Wb = 550 N + 450 N - 800 N

Wb = 200 N

The weight of the board is 200 N