Physics Friction problem-Need help for future exam

Question

A 310 N sled of slides down a frictionless hillside that rises at 27' above the horizontal. What is the magnitude of the force that the surface of the hill exerts on the sled?

Answer 1

Draw a free-body diagram:

F_N is the normal force, which is what you are solving for.

The weight (W) is the 310 N

Break the weight into two components Wy (weight in the y-direction) and W_X (weight in the x-direction.

Wy = Wcos(27°) = 310cos(27°) = 276.2 N

Summing the forces in the y-direction:

∑Fy = 0 = F_N - W_y therefore F_N = Wy = 276.2 N Round the result to 2 sig figs. F_N = 280 N