To analyze the scenario of a 15-kilogram block at rest on a flat surface, we need to determine the downward force required to prevent the block from moving when a horizontal force of 300 N is applied. The key concept here is the role of static friction, which must counteract the applied force to keep the block stationary.

First, we establish a free body diagram for the block. The forces acting on the block include its weight (mg), the applied downward force (F_down), the normal force (N), and the applied horizontal force (F = 300 N). The weight of the block can be calculated using the formula:

mg = 15 kg × 9.8 m/s² = 147 N.

Since the block is not moving vertically, the sum of the vertical forces must equal zero. This gives us the equation:

ΣF_y = N - mg - F_down = 0.

Rearranging this, we find:

F_down = N - mg.

Next, we need to consider the horizontal forces. The static frictional force (F_s) must equal the applied force to prevent movement. The maximum static friction can be expressed as:

F_{s max} = μ_s × N,

where μ_s is the coefficient of static friction. Given that the applied force is 300 N, we set:

F_{s max} = 300 N.

From this, we can solve for the normal force:

N = F_{s max} / μ_s = 300 N / 0.7 ≈ 428.57 N.

Now that we have the normal force, we can substitute it back into our equation for F_down:

F_down = N - mg = 428.57 N - 147 N ≈ 281.57 N.

Rounding this value, we find that the required downward force to keep the block from moving is approximately 282 N. This calculation illustrates the balance of forces necessary to maintain static equilibrium in the presence of an applied force.