Final answer:
The question revolves around scaffold stability and using principles of static equilibrium to calculate cable tensions and mass of objects on the scaffold in Physics.
Step-by-step explanation:
The question is asking about the stability of a rolling scaffold in terms of its height relative to its base dimension. The rule of thumb for scaffolding stability states that a rolling scaffold's height cannot exceed a certain multiple of its narrowest base dimension to ensure safety unless it is secured to a stable structure. For the problems provided, we are applying principles of static equilibrium to calculate the tensions in the cables that support the scaffold. We'll use the sum of forces and the sum of torques (or moments) around a point to find the unknown tensions and, in the given scenario, the mass of the painter's equipment.
By setting the sum of the torques around one end of the scaffold to zero, and considering that the tension in the left cable is twice that in the right cable, we can solve for both tensions. Similarly, by knowing the distances of the person and the equipment from a pivot point and the weights involved, we can find the mass of the equipment using the torque equation.
The problems described pertain to the mechanical balance and forces acting on a structure, and how these can be calculated through formulas in classical mechanics, a part of Physics. This is crucial information for ensuring the safety and functionality of structures like scaffolds.