What is the centripetal force and speed of?A car drives around a circle with a radius of 100 m on a road that is banked (at an angle) to prevent...

When the car is negotiating the curve, the car has a
centripetal force directed towards the centre of the curvature. The radius of curvature
is given to be 100m. The centripetal force if give by Fc = mv^2/r, where m, is the mass
of the car (1500kg) and v is the speed of the car.

To
balance the centripetal force, the normal reaction at the place acts in an opposing
direction which is equal to mgcos x, where x is the angle of banking of the road.
.

Since entire system is in equilibrium and no friction is
there, the equation of forces is: (mv^2)/r = mgcosx.

Given
m =1500 kg,  r = 100meter, x = 20 degrees and angle of slope (or bankig ) x = 20 degrees
and g = 9.81m/s^2 we get:

At the maximum
velocity 1500*v^2/100 = 1500*9.81 cos20.

v^2 = (9.81cos20
deg)100.

v= sqrt{(9.81cos20
deg)100}.

v = 30.3618
meter/second.

Therefore the maximum velocity the car can go
is 30.3618 m/s = 30.3618*60*60.1000 km/hr  = 109.3km/h.