In: Physics
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.