4. A 63 kg skier speeds down a trail, as shown in Figure 5-27. The surface is sm

Question

4. A 63 kg skier speeds down a trail, as shown in Figure 5-27. The surface is smooth and inclined at an angle of ? = 24° with the horizontal.

(a) Find the direction and magnitude of the net force acting on the skier.
Magnitude
N Direction
Which direction?:
perpendicular from the slope (into the ground)
away from the center of the earth
towards the center of the earth
perpendicular from the slope (away from ground)
downhill, parallel to slope
uphill, parallel to slope

(b) Does the net force exerted on the skier increase, decrease, or stay the same as the slope becomes steeper?

Explain.

Explanation / Answer

Since the skier is traveling parallel to the surface, the net force is:

Fnet = F(parallel) - Ff where F(parallel) is the parallel component to gravity that is causing the skier to fall and Ff is the force due to friction.

Since there is no friction, Fnet = F (parallel)

F(parallel) is equal to Fw (sin) = 63 *9.81* sin 24 = 251.4N downhill parallel to the slope

As the slope becomes steeper, the angle becomes larger and sin gets closer and closer to one so that the Net Force increases

Hope that helps

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