Final answer:
The net force on a car coasting up a ramp in a frictionless environment is influenced by gravity and may be part of a centripetal force on banked curves. The car's weight and road's normal force combine to create this centripetal force, with the ideal angle allowing these forces to maintain a constant circular motion without friction.
Step-by-step explanation:
The behavior of the net force (F net) when a car coasts up a ramp in the absence of resistive forces like friction and air drag involves the concept of Newton's laws of motion. In a scenario where the car is coasting up a frictionless ramp, the net force acting on the car would be the component of gravity pulling the car down the ramp, since no other resistive forces are considered. However, if the ramp is banked and the car is moving at a certain speed, there could be a scenario where the normal force from the road and the car's weight combine to create a centripetal force that keeps the car moving in a curved path without the need for friction.
This conceptual setup aligns with a free-body diagram indicating that, on a frictionless banked curve, the only two forces acting on the car are its weight (w) and the normal force of the road (N). If the angle of the banked curve is ideal for the car's speed and the curve's radius, these forces combine to yield a net external force that is equal to the necessary centripetal force required to keep the car on a circular path. The magnitude of this horizontal force towards the center of curvature is given by mv²/r, where m is the mass of the car, v is its velocity, and r is the radius of the curve. Consequently, the vertical component of the normal force, N cos θ, must be equal to the car's weight, mg, signifying that the net vertical force is zero.