The reaction forces are R₁ = 40 N and R₂ = 30 N.
To calculate the reaction forces at the supports C and D for the plank carrying a load, we need to consider the equilibrium of the system. The plank has a length of 3.0 meters, a weight of 20 kg, and a center of gravity located 2.0 meters from one end. A load of 10 kg is applied at the opposite end.
To find the reactions R₁ and R₂ at supports C and D, we can use the principles of static equilibrium. The sum of the forces in the vertical direction and the sum of the moments about any point must be zero for the system to be in equilibrium.
Considering the vertical forces, we have R₁ + R₂ = 20 kg (g), where g is the acceleration due to gravity (approximately 9.8 m/s²). To find the moments, we can take moments about support C, for example. The moment due to the plank's weight about C is 20 kg * 9.8 m/s² * 2.0 m. The moment due to the load at the end is 10 kg * 9.8 m/s² * 3.0 m.
Summing these moments and setting the total moment equal to zero, we can solve for R₂. Once R₂ is known, R₁ can be found by substituting back into the equation for vertical forces. The calculated values are R₁ = 40 N and R₂ = 30 N, indicating the forces exerted by supports C and D, respectively, to maintain the equilibrium of the plank with the applied load.