A sports car of mass 950 kg (including the driver) crosses the rounded top of a hill (r = 88 m) at 27 m/s.

Determine the normal force exerted by the road on the car.

Determine the normal force exerted by the car on the 72-{\rm kg} driver.

To determine the normal force exerted by the road on the car, we need to consider the forces acting on the car at the top of the hill.

First, we need to calculate the acceleration of the car at the top of the hill. Since the car is traveling in a circular path, its acceleration can be found using the equation:

a = v^2 / r

Where:
a = acceleration
v = velocity
r = radius of curvature

Plugging in the values given, we have:

a = (27 m/s)^2 / 88 m
a = 729 m^2/s^2 / 88 m
a ≈ 8.29 m/s^2

The net force acting on the car at the top of the hill is the centripetal force, given by:

F_net = m * a

Where:
F_net = net force
m = mass of the car

Plugging in the values, we have:

F_net = 950 kg * 8.29 m/s^2
F_net ≈ 7876 N

At the top of the hill, the normal force and the force due to gravity are the only vertical forces acting on the car. Since the car is not moving vertically, these forces must balance out. Therefore, the normal force exerted by the road on the car is equal to the force due to gravity:

F_normal = mg

Where:
F_normal = normal force
m = mass of the car
g = acceleration due to gravity (approximately 9.8 m/s^2)

Plugging in the values, we have:

F_normal = 950 kg * 9.8 m/s^2
F_normal ≈ 9310 N

So, the normal force exerted by the road on the car is approximately 9310 N.

To determine the normal force exerted by the car on the driver, we need to consider that the driver is inside the car and moves together with it. Therefore, the normal force exerted by the car on the driver is equal to the normal force exerted by the road on the car. Hence, the normal force exerted by the car on the driver is also approximately 9310 N.