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4. A car of mass m is traveling with constant speed v around a circular banked...

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Physics

4. A car of mass m is traveling with constant speed v around acircular banked road of radius R, see the

side view and the free-body diagram.
a) Apply Newton’s 2nd law to the car, i.e. write equations for thecentripetal, angular, and vertical components of the netforce.
b) Determine the angle θ at which the road should be banked so thatno static friction is required to drive the car.
Now, include the static friction force FS in the free-body diagramand Newton’s equations.
c) Find the maximum speed vmax at which the car can travel aroundwithout slipping. Assume the coefficient of maximum static frictionis μs.
In the end, find the expressions for the contact force with whichthe ground is acting on the car, i.e.:
d) The magnitude of the normal force FN and
e) The magnitude of the static friction FS, in terms of the givenquantities m, v, R, g, and θ.

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