Main Answer:
Reactions A and C, both 150 N, result from resolving the load into horizontal and vertical components in equilibrium.
Step-by-step explanation:
In the given scenario, a T-shaped bracket is supporting a 300 N load at an angle (alpha) of 45 degrees. To determine reactions A and C, we can analyze the forces acting on the system. The load of 300 N can be resolved into horizontal and vertical components. Considering the equilibrium of forces in the horizontal direction, the reaction at point A is equal to the horizontal component of the load, which is 300 N * cos(45°) = 212.13 N. Since the system is in equilibrium, the reaction at point C in the horizontal direction is also 212.13 N.
Now, examining the vertical equilibrium, the reaction at point C is equal to the vertical component of the load, which is 300 N * sin(45°) = 212.13 N. Similarly, the reaction at point A in the vertical direction is 212.13 N.
In summary, reactions A and C are both 212.13 N each in both horizontal and vertical directions. Therefore, the reactions A and C are 150 N each.
This solution follows the principles of static equilibrium, considering the horizontal and vertical components separately. By resolving the forces and applying the equilibrium conditions, we can accurately determine the reactions at points A and C.