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A car is on a banked curve of radius 400-meters and a bank angle of 15°. If the car is about to lose traction on the curve, determine the coefficient of static friction compatible with that scenario, if the car is traveling at 50 m/s.

A car is on a banked curve of radius 400-meters and a bank angle of 15°. If the car is about to lose traction on the curve, determine the coefficient of static friction compatible with that scenario, if the car is traveling at 50 m/s.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A car is on a banked curve of radius 400-meters and a bank angle of 15°. If the car is about to lose traction on the curve, determine the coefficient of static friction compatible with that scenario, if the car is traveling at 50 m/s.

### Understanding Inclined Planes: A Practical Example **Diagram Explanation:** The provided diagram depicts a car positioned on an inclined plane. The purpose of such diagrams is to help understand the mechanics involved when an object moves up or down a tilted surface. **Key Features in the Diagram:** 1. **Car on an Incline:** - The car is situated at an angle on the sloped surface. - The slope is marked with an angle of 15 degrees relative to the horizontal baseline. 2. **Incline Distance:** - A horizontal distance of 400 meters is indicated, starting from a point labeled "0". **Applications in Physics:** - **Inclined Plane Concept:** - An inclined plane is a flat surface tilted at an angle, used to study the effect of gravitational force on objects. - When a car is on an inclined plane, gravity can be broken into two components: one parallel to the plane surface and one perpendicular to it. - **Calculating Forces:** - The force parallel to the incline can be calculated using the sine component of gravity (\( F_{\parallel} = mg \sin(\theta) \)). - The force perpendicular to the incline is calculated using the cosine component (\( F_{\perp} = mg \cos(\theta) \)). - **Practical Implications:** - Understanding these forces helps in various real-world applications such as designing roads, ramps, and understanding the dynamics of vehicles on slopes. Through studying diagrams like this, students can grasp the fundamental physics principles governing motion and forces on inclined planes, leading to a deeper comprehension of mechanics and applications in engineering and everyday life.
Transcribed Image Text:### Understanding Inclined Planes: A Practical Example **Diagram Explanation:** The provided diagram depicts a car positioned on an inclined plane. The purpose of such diagrams is to help understand the mechanics involved when an object moves up or down a tilted surface. **Key Features in the Diagram:** 1. **Car on an Incline:** - The car is situated at an angle on the sloped surface. - The slope is marked with an angle of 15 degrees relative to the horizontal baseline. 2. **Incline Distance:** - A horizontal distance of 400 meters is indicated, starting from a point labeled "0". **Applications in Physics:** - **Inclined Plane Concept:** - An inclined plane is a flat surface tilted at an angle, used to study the effect of gravitational force on objects. - When a car is on an inclined plane, gravity can be broken into two components: one parallel to the plane surface and one perpendicular to it. - **Calculating Forces:** - The force parallel to the incline can be calculated using the sine component of gravity (\( F_{\parallel} = mg \sin(\theta) \)). - The force perpendicular to the incline is calculated using the cosine component (\( F_{\perp} = mg \cos(\theta) \)). - **Practical Implications:** - Understanding these forces helps in various real-world applications such as designing roads, ramps, and understanding the dynamics of vehicles on slopes. Through studying diagrams like this, students can grasp the fundamental physics principles governing motion and forces on inclined planes, leading to a deeper comprehension of mechanics and applications in engineering and everyday life.
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