Question

36) A bookshelf is held up by two support brackets (see diagram on board). The shelf is 50 cm wide. A vase weighing 2 kg is placed on the far right end of the shelf. Ignore the mass of the shelf. a) Draw a free body diagram of the shelf. b) write down two equations from the two conditions for static equilibrium (one equation for each condition) as applied to the shelf. Label all forces and torques in your equations with a subscript and tell what each subscript stands for c) Solve the equations for the forces applied by each of the two supports.

Answer 1

b)

using equilibrium of forces

F₁ + F₂ = mg

using equilibrium of torque about the left end

F₂ (L) - mg (L) = 0                where L = length of shelf

F₂ = mg

c)

m = 2 kg

hence F₂ = mg = 2 x 9.8 = 19.6 N