A highway curve with a radius of 750 m is banked properly for a car traveling 100 km/h. If a 1600- 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 determine the sideways force exerted by the tires against the road, we need to consider the concept of centripetal force. Centripetal force is the force that keeps an object moving in a curved path, and it is directed towards the center of the curve.
The formula for centripetal force is given by:
F_c = (m * v^2) / r
Where:
F_c represents the centripetal force
m is the mass of the car (1600 kg in this case)
v is the velocity of the car in meters per second (convert km/h to m/s)
r is the radius of the curve (750 m)
Let's calculate the required values step by step:
1. Convert the given velocities from km/h to m/s:
100 km/h = 100 * 1000 / 3600 = 27.78 m/s (velocity for proper banking)
220 km/h = 220 * 1000 / 3600 = 61.11 m/s (velocity of the Porsche 928S)
2. Plug the values into the formula for centripetal force for both cases:
For the properly banked car:
F_c1 = (m * v1^2) / r = (1600 kg * (27.78 m/s)^2) / 750 m
For the Porsche 928S:
F_c2 = (m * v2^2) / r = (1600 kg * (61.11 m/s)^2) / 750 m
3. Calculate the centripetal forces for both cases:
F_c1 ≈ 10468 N
F_c2 ≈ 100775 N
So, to prevent skidding, the tires must exert a sideways force of approximately 10468 N for the car traveling at 100 km/h and around 100775 N for the Porsche 928S at 220 km/h.