Answer to Question #122803 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

Write the equilibrium of forces:

$$0=70\cdot9.8+500+400-R_A-R_B$$

Now write the equilibrium of moments around the point where R_A acts. Remember that the scaffold has 400 N spread across its length. Each inch of the scaffold has a mass, not only its center. We should not represent the 400 N as a point force.

$$0=400\cdot\frac{2}{6}\cdot1-400\cdot\frac{4}{6}\cdot2-500\cdot3+R_B\cdot3.$$

We have two equations, two variables, the solution is

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