Question

When a skier skis down a hill, the normal force exerted on the skier by the hill is

a. greater than the weight of the skier.
b. equal to the weight of the skier.
c. less than the weight of the skier

Answer 1

c. The normal force exerted on the skier by the hill is less than the weight of the skier.

Step-by-step explanation:

Hi there!

Please see the attached figure for a better understanding of this explanation:

The vertical forces that act on the skier are the normal force (N) and the vertical component of the weight (wy) (see figure). Since the skier is not being accelerated in the vertical direction (perpendicular to the surface), the resulting net force acting in the vertical direction is zero:

∑Fy = 0

N - wy = 0

N = wy

The vertical component of the weight is calculated using trigonometry of right triangles:

cos θ = adjacent / hypotenuse

cos θ = wy / W

W · cos θ = wy

Since:

cos θ < 1

Then:

W · cos θ < W

Then:

wy < W

and then:

N < W

The correct answer is "c": the normal force exerted on the skier by the hill is less than the weight of the skier.