---
title: "A vehicle of mass \\(m\\) travels at constant speed in a horizontal circle of radius \\(R\\) along a track banked at an angle \\(\\theta\\) above the horizontal. The coefficient of static friction between the vehicle’s tires and the track surface is \\(\\mu_s\\), where \\(\\mu_s < \\cot\\theta\\). Which of the following expressions represents the maximum speed \\(v_{\\text{max}}\\) at which the vehicle can navigate the curve without sliding up the incline?"
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url: "https://nerd-notes.com/ubq/123979/"
date_modified: "2026-09-28T13:29:52+00:00"
---

# A vehicle of mass \(m\) travels at constant speed in a horizontal circle of radius \(R\) along a track banked at an angle \(\theta\) above the horizontal. The coefficient of static friction between the vehicle’s tires and the track surface is \(\mu_s\), where \(\mu_s < \cot\theta\). Which of the following expressions represents the maximum speed \(v_{\text{max}}\) at which the vehicle can navigate the curve without sliding up the incline?

A vehicle of mass \(m\) travels at constant speed in a horizontal circle of radius \(R\) along a track banked at an angle \(\theta\) above the horizontal. The coefficient of static friction between the vehicle's tires and the track surface is \(\mu_s\), where \(\mu_s < \cot\theta\). Which of the following expressions represents the maximum speed \(v_{\text{max}}\) at which the vehicle can navigate the curve without sliding up the incline?

![A cross-sectional diagram of a vehicle traveling on a banked track. An inclined surface rises from left to right at an angle labeled \(\theta\) relative to a horizontal dashed ground line. A rectangular box representing the vehicle rests on the inclined surface. A vertical dashed line representing the axis of circular motion passes to the left of the incline. A horizontal solid line with arrowheads at both ends extends from the vertical dashed axis to the center of the vehicle and is labeled \(R\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602192-PIusGW.jpg)

- **A.** \(\sqrt{Rg\left(\dfrac{\sin\theta + \mu_s \cos\theta}{\cos\theta - \mu_s \sin\theta}\right)}\)
- **B.** \(\sqrt{Rg\left(\dfrac{\sin\theta - \mu_s \cos\theta}{\cos\theta + \mu_s \sin\theta}\right)}\)
- **C.** \(\sqrt{Rg\left(\dfrac{\sin\theta + \mu_s \cos\theta}{\cos\theta}\right)}\)
- **D.** \(\sqrt{Rg\left(\dfrac{\cos\theta + \mu_s \sin\theta}{\sin\theta - \mu_s \cos\theta}\right)}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123979/*