---
title: "A car of mass \\(M\\) travels at a constant speed \\(v\\) through a circular dip in a road that has a radius of curvature \\(R\\). As the car passes through the lowest point of the dip, a passenger of mass \\(m\\) feels as though they are being pressed into their seat. Which of the following correctly shows the free-body diagram of the forces exerted on the car at the lowest point and provides the correct relationship between the magnitude of the normal force \\(F_N\\) and the magnitude of the gravitational force \\(F_g\\)?"
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url: "https://nerd-notes.com/ubq/112734/"
date_modified: "2026-04-30T21:07:36+00:00"
---

# A car of mass \(M\) travels at a constant speed \(v\) through a circular dip in a road that has a radius of curvature \(R\). As the car passes through the lowest point of the dip, a passenger of mass \(m\) feels as though they are being pressed into their seat. Which of the following correctly shows the free-body diagram of the forces exerted on the car at the lowest point and provides the correct relationship between the magnitude of the normal force \(F_N\) and the magnitude of the gravitational force \(F_g\)?

A car of mass \(M\) travels at a constant speed \(v\) through a circular dip in a road that has a radius of curvature \(R\). As the car passes through the lowest point of the dip, a passenger of mass \(m\) feels as though they are being pressed into their seat. Which of the following correctly shows the free-body diagram of the forces exerted on the car at the lowest point and provides the correct relationship between the magnitude of the normal force \(F_N\) and the magnitude of the gravitational force \(F_g\)?

![A car of mass M is at the very bottom of a U-shaped circular dip in a road. The dip is part of a circle with a dashed line indicating the radius R from the center of the circle (located above the car) to the car. A horizontal velocity vector v points to the right from the car's center of mass.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1777583255-CZrwL5.jpg)

- **A.** Diagram A; \(F_N = F_g + \dfrac{Mv^2}{R}\)
- **B.** Diagram B; \(F_N = F_g\)
- **C.** Diagram C; \(F_N = F_g - \dfrac{Mv^2}{R}\)
- **D.** Diagram D; \(F_N = F_g + F_c\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/112734/*