A uniform beam of mass 20 kg and length 2.4 m is supported at its ends. A load of mass 30 kg is placed 1.0 m from one end. Calculate the forces exerted by the supports.

To solve this problem, we will apply the conditions for static equilibrium: the net force in both horizontal and vertical directions must be zero, and the net torque about any point must be zero.

First, let's identify the forces and distances:

• Mass of beam ($m_B$) = $20 \, \text{kg}$
• Length of beam ($L$) = $2.4 \, \text{m}$
• Weight of beam ($W_B$) = $m_B g = 20 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 196 \, \text{N}$. This acts at the center of the beam, $L/2 = 1.2 , \