Answer to Question #122805 in Physics for Dr. Horus

Question

A 70kg painter stands 2m from one end of a 6m long scaffold while his apprentice weighing 500N stands 1m from the other end. Given that the scaffold weigh 400N and rests on two supports directly below the position of the two men, calculate the force on each support.

Answer 1

Since the scaffold is in equilibrium, the forces and torque acting on it are in equilibrium. Write one equation for the equilibrium of forces and the other for equilibrium of torques (around point where R_B is).

$$\sum F=0=700+500+400-R_A-R_B,\\ \sum\tau=0,\\\space\\ 0=-400\cdot\frac{1}{6}\cdot0.5-R_A\cdot3+400\cdot\frac{5}{6}\cdot2.5+700\cdot3$$

The solution is

$$R_A=967\text{ N},\\R_B=633\text{ N}.$$

You might be tempted to consider the weight of the scaffold 400 N as a point force, but every single millimeter of the scaffold has a mass, not only its centre. That is why, representing the beam like this would lead to the wrong answer: