A 75.5 kg skier encounters a dip in the snow's surface that has a circular cross section with radius of curvature of $r$ = 10.1 m. If the skier's speed at point A in the figure below is 7.82 m/s, what is the normal force exerted by the snow on the skier at point B? h = 1.79 m. Ignore frictional forces.

To determine the normal force exerted by the snow on the skier at point B, we need to consider the forces acting on the skier.

1. Gravitational force (weight): The weight of the skier can be calculated using the formula weight = mass * gravity, where mass is given as 75.5 kg and gravity is approximately 9.8 m/s².

weight = 75.5 kg * 9.8 m/s²

2. Centripetal force: When the skier goes around the curved path, there is a centripetal force acting towards the center of the circle. The formula for centripetal force is F = (mass * velocity^2) / radius of curvature.

centripetal force = (75.5 kg * (7.82 m/s)^2) / 10.1 m

3. Normal force: The normal force is the force exerted by a surface perpendicular to the contact point. At point B, the normal force balances the weight and the centripetal force. Therefore, the normal force can be found by subtracting the weight from the centripetal force (since they have opposite directions).

normal force = centripetal force - weight

Now, you can calculate the normal force by plugging in the values for mass, velocity, radius of curvature, and gravity into the formulas mentioned above.

To find the normal force exerted by the snow on the skier at point B, we can use the principles of circular motion.

1. First, we need to find the skier's acceleration at point B. Since the skier is moving in a circular path, the acceleration can be found using the centripetal acceleration formula:

a = v^2 / r

where a is the acceleration, v is the speed, and r is the radius of curvature.

Plugging in the given values, we have:

a = (7.82 m/s)^2 / 10.1 m
a ≈ 6.048 m/s^2

2. Next, we can calculate the net force acting on the skier at point B. Since the only horizontal force acting on the skier is the normal force, the net force is equal to the centripetal force:

F_net = m * a

where F_net is the net force, m is the mass of the skier, and a is the acceleration.

Plugging in the given values, we have:

F_net = (75.5 kg) * (6.048 m/s^2)
F_net ≈ 457.884 N

3. Finally, we can find the normal force exerted by the snow on the skier at point B. The normal force is equal in magnitude but opposite in direction to the weight of the skier:

F_normal = -m * g

where F_normal is the normal force, m is the mass of the skier, and g is the acceleration due to gravity.

Plugging in the given value for the mass and the approximate value for the acceleration due to gravity (9.81 m/s^2), we have:

F_normal = -(75.5 kg) * (9.81 m/s^2)
F_normal ≈ -741.255 N

Therefore, the normal force exerted by the snow on the skier at point B is approximately 741.255 N.