Final answer:
The upward force exerted on the board by the support, which ensures static equilibrium with two children standing on it, is calculated by adding the weight of the board (69.6 N) to the combined weight of the children (467.0 N and 305.0 N). The result is an upward force of 841.6 N.
Step-by-step explanation:
The question pertains to the concept of static equilibrium in physics, where an object is at rest, and all the forces acting on it are balanced. In the given scenario, a long uniform board rests on a support at its midpoint, and two children stand on the board such that the board is balanced. To find the upward force exerted by the support, we add the weight of the board to the combined weight of the two children. Since the board is in static equilibrium, the upward force by the support must equal the total downward force due to the weights.
The weight of the board is 69.6 N, the first child weighs 467.0 N, and the second child weighs 305.0 N. Therefore, the total downward force is the sum of these weights:
Total downward force = Weight of the board + Weight of first child + Weight of second child
Total downward force = 69.6 N + 467.0 N + 305.0 N
Total downward force = 841.6 N
Thus, the upward force exerted on the board by the support is 841.6 N, which is required to maintain balance and keep the board in static equilibrium.