Final answer:
The upward force exerted on the board by the support in static equilibrium is the sum of the weight of the board and the children, totaling 824.1 N.
Step-by-step explanation:
The question is asking about the concept of static equilibrium in physics, where an object is at rest, and all the forces acting on it are balanced. In this particular scenario, a long uniform board is balanced on a support at its midpoint, and two children of different weights are standing on the board. To determine the upward force exerted on the board by the support, we must consider that this force will balance out the weight of the board itself and the weights of both children. In static equilibrium, the sum of all upward forces must equal the sum of all downward forces.
Therefore, the upward force provided by the support (F) must equal the combined weights of the board and the children:
F = weight of the board + weight of child 1 + weight of child 2. So, F = 52.1 N + 281.0 N + 491.0 N, resulting in F = 824.1 N. Thus, the support must exert an upward force of 824.1 N to keep the board balanced.