Final answer:
Medium banked turns refer to the angle of inclination in roads that allows vehicles to maintain speed with less reliance on friction. The ideal bank angle can be adjusted to enable navigation of curves at specific speeds and is particularly crucial for race tracks with steeply banked curves. Physics concepts of centripetal force and motion on an incline are used to derive expressions for ideal conditions.
Step-by-step explanation:
Understanding Medium Banked Turns
When discussing medium-banked turns, the focus is on the dynamics of how a vehicle navigates a turn on a road with a sloped surface. This utilization of an incline in the road is referred to as a banked curve. The purpose of the banking is to allow the vehicle to maintain speed through the curve with less reliance on friction. For an 'ideally banked curve,' the bank angle is designed so drivers can navigate the curve at a particular speed without requiring friction between the tires and the road surface; this is often used in race tracks. To understand this concept completely, we derive an expression that describes the relationship between the bank angle, the speed of the vehicle, the radius of curvature of the turn, and gravitational force. This expression, which is an important aspect of circular motion in physics, allows us to calculate ideal conditions under which certain speeds can be maintained safely around a curve without slipping.
For instance, if we were to calculate the ideal speed for a steeply banked curve with a 100 m radius and a bank angle of 65.0°, with the absence of friction, we would use the appropriate physics equations that deal with centripetal force and motion on an incline. Similarly, to determine the ideal banking angle for a highway turn, we would again apply these concepts taking into account the desired speed limit and radius of the turn. In both examples, the centripetal force necessary for circular motion is provided by the horizontal component of the normal force due to the road's inclination, rather than by friction.