A 65 kg snowboarder travels down a 37° incline at 6.2 m/s. In order to stop before hitting a tree, the snowboarder quickly turns their board to increase the coefficient of kinetic friction to 1.9.

Question

What is the normal force between the snowboarder and the ground?

Answer 1

Normal force, F_N = µ_k*N

In this case, the F_N pushes the snowboarder up, perpendicularly to the surface, with the same magnitude as the force pulling him down into the surface. Most of the information in this question is superfluous.

The force pulling the snowboarder down (perpendicular to the surface) is a component of the force from gravity, mg. If we draw the triangles and work out the components, we can see that this value is equal to mg*cos(37). Since the normal force must be equal and opposite to this value, the F_N = mg*cos(37).

Plug in m = 65kg and g = 9.8 m/s/s to find the exact answer.