Question

A plank ab 3.0 long weighing 20kg and with its centre gravity 20m from the end carries a load of mass 10kg at the end rests on two supports at c and d. Calculate: (1) Compute the values of the reaction forces r1 and r2 at c and d. (2) How far from d and on which side of it must a mass of 24kg be placed on the plank so as to make the reactions equal? What are their values?

Answer 1

To compute the values of the reaction forces and determine the position where the 24kg mass must be placed, you need to consider the equilibrium of the system. Solve the torque equations to find the values of r1 and r2. Set r1 equal to r2 to find the position of the 24kg mass.

Step-by-step explanation:

To compute the values of the reaction forces at C and D, we need to consider the equilibrium of the system. Since the plank is at rest, the sum of the forces acting on it must be zero, and the sum of the torques about any point must also be zero.

(1) To solve for r1 and r2, we can use the equations ΣFx = 0 and Στ = 0. Considering the torque equations:

τC = r1(20 kg)(9.8 m/s2) - (10 kg)(20 m)(9.8 m/s2) = 0,

τD = -r2(10 kg)(9.8 m/s2) + (10 kg)(30 m)(9.8 m/s2) = 0.

In the above equations, g is acceleration due to gravity. By solving the equations simultaneously, we can find the values of r1 and r2.

(2) To make the reactions equal, we can use the equation r1 = r2. By solving the equation r1 = r2, we can find the distance from D where a mass of 24 kg must be placed on the plank.