---
title: "A car of mass \\(m\\) travels at a constant speed \\(v\\) in a horizontal circle of radius \\(R\\) along a track banked at an angle \\(\\theta\\) above the horizontal. Friction between the tires and the track is negligible. Which of the following correctly describes the magnitude of the normal force \\(F_N\\) exerted by the track on the car and provides a correct physical justification?"
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url: "https://nerd-notes.com/ubq/110079/"
date_modified: "2026-03-26T11:47:26+00:00"
---

# A car of mass \(m\) travels at a constant speed \(v\) in a horizontal circle of radius \(R\) along a track banked at an angle \(\theta\) above the horizontal. Friction between the tires and the track is negligible. Which of the following correctly describes the magnitude of the normal force \(F_N\) exerted by the track on the car and provides a correct physical justification?

A car of mass \(m\) travels at a constant speed \(v\) in a horizontal circle of radius \(R\) along a track banked at an angle \(\theta\) above the horizontal. Friction between the tires and the track is negligible. Which of the following correctly describes the magnitude of the normal force \(F_N\) exerted by the track on the car and provides a correct physical justification?

![A cross-sectional view of a car modeled as a rectangular block on a track surface inclined at an angle theta. A dashed horizontal line extends from the car to the center of its circular path, labeled R. A downward arrow from the car represents the gravitational force mg. An arrow perpendicular to the track surface and pointing away from it represents the normal force F_N.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774525646-5pngx9.jpg)

- **A.** The magnitude \(F_N = mg \cos\theta\), because the normal force must balance the component of the gravitational force perpendicular to the surface of the track.
- **B.** The magnitude \(F_N = \dfrac{mg}{\cos\theta}\), because the vertical component of the normal force must balance the gravitational force for the car to maintain a constant vertical height.
- **C.** The magnitude \(F_N = mg \sin\theta\), because the component of the normal force parallel to the surface provides the centripetal acceleration.
- **D.** The magnitude \(F_N = \dfrac{mv^2}{R}\), because the normal force is the only force directed toward the center of the circular path and acts as the centripetal force.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/110079/*