---
title: "A small cart of mass \\(M\\) moves at a constant speed \\(v_0\\) along a continuous track containing four distinct sections. Point \\(W\\) is at the bottom of a circular dip of radius \\(2R\\), point \\(X\\) is at the bottom of a circular dip of radius \\(R\\), point \\(Y\\) is at the top of a circular crest of radius \\(2R\\), and point \\(Z\\) is on a flat horizontal segment. The speed of the cart satisfies \\(v_0^2 < 2gR\\) so that the cart never loses contact with the track. Which of the following correctly ranks the magnitude of the normal force \\(F_N\\) exerted by the track on the cart at the four points?"
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url: "https://nerd-notes.com/ubq/120589/"
date_modified: "2026-08-23T04:41:44+00:00"
---

# A small cart of mass \(M\) moves at a constant speed \(v_0\) along a continuous track containing four distinct sections. Point \(W\) is at the bottom of a circular dip of radius \(2R\), point \(X\) is at the bottom of a circular dip of radius \(R\), point \(Y\) is at the top of a circular crest of radius \(2R\), and point \(Z\) is on a flat horizontal segment. The speed of the cart satisfies \(v_0^2 < 2gR\) so that the cart never loses contact with the track. Which of the following correctly ranks the magnitude of the normal force \(F_N\) exerted by the track on the cart at the four points?

A small cart of mass \(M\) moves at a constant speed \(v_0\) along a continuous track containing four distinct sections. Point \(W\) is at the bottom of a circular dip of radius \(2R\), point \(X\) is at the bottom of a circular dip of radius \(R\), point \(Y\) is at the top of a circular crest of radius \(2R\), and point \(Z\) is on a flat horizontal segment. The speed of the cart satisfies \(v_0^2 < 2gR\) so that the cart never loses contact with the track. Which of the following correctly ranks the magnitude of the normal force \(F_N\) exerted by the track on the cart at the four points?

![A single continuous track profile is shown as a solid line running horizontally from left to right. On the left, a concave-upward circular arc with center of curvature radius \(2R\) has a point labeled \(W\) at its lowest point. Next, a concave-upward circular arc with radius \(R\) has a point labeled \(X\) at its lowest point. Next, a concave-downward circular arc with radius \(2R\) has a point labeled \(Y\) at its highest point. On the far right, a horizontal straight track segment contains a point labeled \(Z\). At each of the four points, a small rectangular box representing the cart rests on the upper surface of the track. A small horizontal rightward arrow labeled \(v_0\) is drawn above each box. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460104-UG7Ggr.jpg)

- **A.** \(F_{N,X} > F_{N,W} > F_{N,Z} > F_{N,Y}\)
- **B.** \(F_{N,W} > F_{N,X} > F_{N,Z} > F_{N,Y}\)
- **C.** \(F_{N,X} > F_{N,W} > F_{N,Y} > F_{N,Z}\)
- **D.** \(F_{N,Y} > F_{N,Z} > F_{N,W} > F_{N,X}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120589/*