A highway curve with a radius of 750 m is banked properly for a car traveling 150 km/h. If a 1560- kg Porshe 928S rounds the curve at 240 km/h, how much sideways force must the tires exert against the road if the car does not skid?
To find the sideways force exerted by the tires, we can use the concept of centripetal force.
Centripetal force is the force that keeps an object moving in a curved path and is directed towards the center of the curve. In this case, the centripetal force is provided by the friction between the tires and the road.
First, let's convert the given speeds to meters per second:
Speed of the car traveling at 150 km/h = 150 km/h * (1000 m/1 km) * (1 h/3600 s) = 41.67 m/s
Speed of the Porsche traveling at 240 km/h = 240 km/h * (1000 m/1 km) * (1 h/3600 s) = 66.67 m/s
The centripetal force can be calculated using the following formula:
Centripetal force = (mass of the car) * (velocity of the car squared) / (radius of the curve)
Given:
Mass of the Porsche = 1560 kg
Radius of the curve = 750 m
Centripetal force required for the Porsche:
Centripetal force = (1560 kg) * (66.67 m/s)^2 / (750 m)
Centripetal force = 1860804.23 N
Since the car does not skid, the sideways force exerted by the tires must be equal to the centripetal force. Therefore, the sideways force exerted by the tires is approximately 1860804.23 N.
To determine the sideways force exerted by the tires against the road, we need to calculate the required centripetal force.
The centripetal force is given by the equation:
F = (m * v^2) / r
Where:
F is the centripetal force
m is the mass of the car (1560 kg)
v is the velocity of the car (240 km/h)
r is the radius of the curve (750 m)
First, we need to convert the velocity from km/h to m/s:
240 km/h * (1000 m/1 km) * (1 h/3600 s) = 66.67 m/s
Now we can plug the values into the equation to find the centripetal force:
F = (1560 kg * (66.67 m/s)^2) / 750 m
F = (1560 kg * 4444.44 m^2/s^2) / 750 m
F = 9279998.4 N
Therefore, the tires must exert a sideways force of approximately 9,280,000 N against the road to prevent the car from skidding.