Question

32) Predict/Calculate A 65-kg skier speeds down a trail, as shown in FIGURE 5-36. The surface is smooth and inclined at an angle of 22° with the horizontal. (a) Find the direction and magnitude of the net force acting on the skier. (b) Does the net force exerted on the skier increase, decrease, or stay the same asthe slope becomes steeper? Explain.

Answer 1

ANSWER:

(a) 238.87 N

(b) increase

STEP-BY-STEP EXPLANATION:

(a)

From the figure we can establish the following:

$\begin{gathered} F=m\cdot a \\ F=m\cdot g\cdot\sin \theta \\ \text{ replacing} \\ F=65\cdot9.81\cdot\sin 22 \\ F=238.87\text{ N} \end{gathered}$

(b)

Since net force is directly proportional to sin (Θ), so, with Θ increase, sin (Θ) also increase, thus net force inceases.