A highway curve with a radius of 800 m is banked properly for a car traveling 100 km/h. If a 1620- kg Porshe 928S rounds the curve at 220 km/h, how much sideways force must the tires exert against the road if the car does not skid?
To calculate the sideways force exerted by the tires against the road, you need to consider the balance of forces acting on the car as it curves around the banked curve.
First, let's determine the speed of the car in meters per second (m/s). We can convert the given value of 220 km/h to m/s as follows:
Speed (m/s) = (220 km/h) * (1000 m/km) / (3600 s/h)
= (220 * 1000) / 3600
= 220000 / 3600
≈ 61.11 m/s
Next, let's calculate the lateral or sideways acceleration of the car. This acceleration is caused by the centripetal force acting towards the center of the curve:
Acceleration (lateral, a) = (Speed^2) / Radius
= (61.11^2) / 800
≈ 3.74 m/s^2
Now, we can find the net force acting on the car in the lateral direction (sideways force). This net force is the difference between the gravitational force component and the frictional force component. In this case, the gravitational force component pulls the car towards the center of the curve, and the frictional force component counteracts this pull to prevent skidding.
Gravitational Force (Fg) = mass * gravitational acceleration
= 1620 kg * 9.8 m/s^2
≈ 15876 N
The frictional force (Ff) is given by:
Ff = mass * acceleration (lateral)
= 1620 kg * 3.74 m/s^2
≈ 6046.8 N
Finally, the net force acting on the car in the lateral direction (sideways force) is given by:
Sideways Force = Gravitational Force - Frictional Force
= 15876 N - 6046.8 N
≈ 9829.2 N
Therefore, the tires must exert approximately 9829.2 Newtons of force against the road to prevent skidding as the Porshe 928S rounds the curve.