An engineer wants to design a circular racetrack of radius R such that cars of mass m can go around the track at speed U without the aid of friction or other forces other than the perpendicular contact force from the track surface. Find an expression for the required banking angle 0 of the track, measured from the horizontal. Express the answer in terms of m, R, U, and g. Suppose the race cars actually round the track at a speed W > U. What additional radial force F, is required to keep F, = the cars on the track at this speed? Express the answer in terms of m, R, U, W, and g.
An engineer wants to design a circular racetrack of radius R such that cars of mass m can go around the track at speed U without the aid of friction or other forces other than the perpendicular contact force from the track surface. Find an expression for the required banking angle 0 of the track, measured from the horizontal. Express the answer in terms of m, R, U, and g. Suppose the race cars actually round the track at a speed W > U. What additional radial force F, is required to keep F, = the cars on the track at this speed? Express the answer in terms of m, R, U, W, and g.
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter4: Motion In Two And Three Dimensions
Section: Chapter Questions
Problem 64P: A runner taking part in the 200-m dash must run around the end of a track that has a circular arc...
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Step 1: Given information:
The mass of the car "m"
The radius of the track "R"
The velocity with which the car takes the turn "U'
Let us draw the free body diagram of the given scenario:
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