**Problem Statement:**A 902 kg automobile is moving at a maximum speed of 37 m/s on a level circular track of radius 216 m. What is the coefficient of friction?**Analysis:**This problem involves understanding the forces acting on the automobile as it moves in a circular path. The key force here is the frictional force, which provides the centripetal force needed to keep the car moving in a circle.**Solution:**1. **Data Given:** - Mass of the automobile, \( m = 902 \, \text{kg} \) - Speed of the automobile, \( v = 37 \, \text{m/s} \) - Radius of the circular track, \( r = 216 \, \text{m} \)2. **Centripetal Force Requirement:** \[ F_c = \frac{m \cdot v^2}{r} \]3. **Frictional Force:** - The frictional force \( F_f \) is given by: \[ F_f = \mu \cdot m \cdot g \] where \( \mu \) is the coefficient of friction and \( g = 9.81 \, \text{m/s}^2 \), the acceleration due to gravity.4. **Equating Forces:** \[ \frac{m \cdot v^2}{r} = \mu \cdot m \cdot g \]5. **Solving for \(\mu\):** \[ \mu = \frac{v^2}{r \cdot g} \] \[ \mu = \frac{37^2}{216 \cdot 9.81} \]6. **Calculation:** \[ \mu \approx \frac{1369}{2118.96} \approx 0.646 \]**Conclusion:**The coefficient of friction required to maintain the car's motion on the track is approximately 0.646.

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Answered: A 902 kg automobile is moving at a…

A 902 kg automobile is moving at a maximum speed of 37 m/s on a level circular track of radius 216 m. What is the coefficient of friction?

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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