Question

3.3 A person is lying on a board, which is supported at both ends. A vertical reaction force VA is acting on the board at point A and passes through the origin of the coordinate system. A vertical reaction force VB is acting at the point located in iB -le I is known that the weight of the person is F and the weight of the board is P. The vector that determines the centroid C of the person is given by: xc -aer +Bey. Determine the reaction forces RA and RB as a function of L, α, β, F and P

The answer is listed below. Please show me how to obtain the answer.

Answer 1

Net force (downwards) = Reaction force (upwards) V_A + V_B = F + P (I) Net torque around centre of board. F times (l/2 - alpha) = V_A times l/2 - V_B times l/2 (II) F l/2 - F alpha = (V_A - V_B)l/2 (II) eq (I) + (II) V_A - V_B = F(l/2 - alpha)2/l = F - 2 alpha/l F 2V_B = P + 2 alpha/l F V_B = P/2 + alpha F/l rightdoublearrow V_A = F - 2 alpha F/l + P/2 + alpha F/l = (1 - alpha/l) F + P/2