Final answer:
The normal force on a skier on a slope is calculated using the skier's mass, the acceleration due to gravity, and the cosine of the slope angle. For a skier with a mass of 73.7 kg coming down a 29° slope, the normal force exerted by the skis is approximately 630.21 N.
Step-by-step explanation:
To find the force normal to the slope exerted by the skis, we must first understand that the skier is acted upon by gravity, which can be decomposed into components parallel and perpendicular to the slope. The normal force is the component of the skier's weight that acts perpendicular to the slope. To calculate this, we can use the formula N = m × g × cos(θ), where N is the normal force, m is the mass of the skier, g is the acceleration due to gravity (9.81 m/s2), and θ is the angle of the slope.
Plugging in the skier's mass (73.7 kg) and the angle of the slope (29°), we calculate the normal force exerted by the skis:
N = 73.7 kg × 9.81 m/s2 × cos(29°) ≈ 73.7 × 9.81 × 0.8746 ≈ 630.21 N
The normal force exerted by the skis on the skier, perpendicular to the slope and neglecting friction, would be approximately 630.21 Newtons.