Let the radius of the circular segment be 92 m,
the mass of the car 2393 kg, and the coefficient
of the static friction between the road and the
tire 0.9.
Find the magnitude of the normal force N which the road exerts on the car at the opti-
mal speed (the speed at which the frictional
force is zero) of 82 km/h. The acceleration
due to gravity is 9.8 m/s2
To find the magnitude of the normal force N, we can start by considering the forces acting on the car when it is moving at the optimal speed (frictional force is zero).
1. First, let's calculate the optimal speed in meters per second (m/s):
Optimal speed = 82 km/h = (82 * 1000) / 3600 m/s
= 22.78 m/s
2. The only force acting on the car at this speed is the normal force (N) exerted by the road. This force is equal in magnitude and opposite in direction to the gravitational force acting on the car.
3. The gravitational force is given by:
F_gravity = mass * acceleration due to gravity
= 2393 kg * 9.8 m/s^2
= 23416.4 N
4. Since the normal force balances the gravitational force when the frictional force is zero, the magnitude of the normal force (N) is equal to the gravitational force:
N = F_gravity
= 23416.4 N
Therefore, the magnitude of the normal force (N) that the road exerts on the car at the optimal speed of 82 km/h is 23416.4 N.