A plank AB 3m long weighing 20kg with its centre of gravity 2m from the end A carries a load of mass 10kg at the end A. it rests on two supports at C and D

Question

1. compute the values of the reaction forces R1 and R2 at C and D.
2. How far from D, and on what side of it, must a mass 24kg be placed on the plank so as to make the reactions equal ? What are their values ?
3. without this 24kg, what vertical force applied at B will just lift the plank clear of D? What is then the reaction at C?

Answer 1

1. The reaction forces R1 and R2 at C and D can be computed using the equation of equilibrium:

R1 + R2 = 20kg + 10kg = 30kg

R1 = 15kg

R2 = 15kg

2. The 24kg mass must be placed 1m from D on the side of C. The reaction forces will then be equal and their values will be 18kg.

3. The vertical force applied at B to lift the plank clear of D is 30kg. The reaction at C will then be 0kg.