Final answer:
To find the tensions in the cables of a scaffold in static equilibrium, you must consider the torques and forces acting on the scaffold. Equations are created to solve for unknowns like cable tensions and additional loads based on the principles of equilibrium in physics.
Step-by-step explanation:
The question relates to physics, specifically to static equilibrium and the forces in a system. To find the tensions in the cables, we must consider the torques about a point and the forces acting upon the scaffold and any additional loads such as a person or equipment.
For the first scenario, the 80-kg painter exerts a downward force of 800 N (assuming g=10 m/s2), and the mass of the equipment can be found using the condition that the sum of the torques about any point must be zero.
After establishing a point of rotation, usually at one of the points where the scaffold contacts a cable, we can create equations based on the sum of torques and the sum of vertical forces to solve for unknowns like cable tensions and equipment mass. A similar approach is applied for the second scenario involving a 50-kg person on a 70-kg scaffold.