---
title: "A roller coaster cart of mass \\(M\\) is driven at a constant speed \\(v\\) along a track that includes two circular sections. The first section is a loop-the-loop with a radius of curvature \\(R\\). The second section is a dip with a radius of curvature \\(\\{R\\}/{2}\\). The speed \\(v\\) is the minimum speed required for the cart to maintain contact with the track at the very top of the loop. Which of the following expressions represents the magnitude of the normal force exerted by the track on the cart when it is at the bottom of the dip?"
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url: "https://nerd-notes.com/ubq/109287/"
date_modified: "2026-05-01T22:12:15+00:00"
---

# A roller coaster cart of mass \(M\) is driven at a constant speed \(v\) along a track that includes two circular sections. The first section is a loop-the-loop with a radius of curvature \(R\). The second section is a dip with a radius of curvature \(\{R\}/{2}\). The speed \(v\) is the minimum speed required for the cart to maintain contact with the track at the very top of the loop. Which of the following expressions represents the magnitude of the normal force exerted by the track on the cart when it is at the bottom of the dip?

A roller coaster cart of mass \(M\) is driven at a constant speed \(v\) along a track that includes two circular sections. The first section is a loop-the-loop with a radius of curvature \(R\). The second section is a dip with a radius of curvature \(\{R\}/{2}\). The speed \(v\) is the minimum speed required for the cart to maintain contact with the track at the very top of the loop. Which of the following expressions represents the magnitude of the normal force exerted by the track on the cart when it is at the bottom of the dip?

![A side-view diagram of a roller coaster track. On the left, there is a vertical circular loop of radius R. A cart is at the highest point of this loop. To the right of the loop, the track transitions into a downward-curving dip with a tighter radius of R/2. A cart is shown at the lowest point of this dip. Arrows indicate the constant speed v at both locations.](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/ubq-frq-generatedstem-fig-1-1777673535-yAqMNU.jpg)

- **A.** \(Mg\)
- **B.** \(2Mg\)
- **C.** \(3Mg\)
- **D.** \(5Mg\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109287/*