Final answer:
The ideal speed to take a level curve on a highway without going into a skid is determined by factors such as the curve's angle of banking and radius. On steeply banked curves, tire friction and stable car configurations allow for higher speeds. For example, on a 100 m radius curve banked at a 65.0° angle, the ideal speed can be calculated as approximately 165 km/h.
Step-by-step explanation:
The maximum speed that a car can take a level curve on a highway without going into a skid is known as the ideal speed. Ideal speed is the maximum safe speed at which a vehicle can turn on a curve without the aid of friction between the tire and the road. It is determined by factors such as the curve's angle of banking and radius.
For example, on steeply banked curves like those found on test tracks or race courses, tire friction and stable car configurations allow for higher speeds. On a curve with a 100 m radius banked at a 65.0° angle, the ideal speed can be calculated if the road is frictionless. The formula to calculate the ideal speed is:
ideal speed = √(radius * gravitational acceleration * tangent(angle of banking))
Using the given values:
- radius = 100 m
- angle of banking = 65.0°
- gravitational acceleration = 9.8 m/s²
Plugging these values into the formula gives us:
ideal speed = √(100 * 9.8 * tan(65.0°)) = 165 km/h
This means that on this particular curve, the maximum speed a car can take without going into a skid is approximately 165 km/h.