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

4. A car of mass m is traveling with constant speed v around a circular 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 the centripetal, angular, and vertical components of the net force.
b) Determine the angle θ at which the road should be banked so that no static friction is required to drive the car.
Now, include the static friction force FS in the free-body diagram and Newton’s equations.
c) Find the maximum speed vmax at which the car can travel around without slipping. Assume the coefficient of maximum static friction is μs.
In the end, find the expressions for the contact force with which the 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 given quantities m, v, R, g, and θ.

Solutions

Expert Solution

genius_generous answered 1 year ago

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