i need the physic equation?

Question

A car with a mass of 1100 kg travels around a banked curve with a constant speed of 35 m/s (about 78 MPH). The radius of the curve is 40 m.

What is the magnitude of the horizontal component of the normal force that would be required to produce this centripetal acceleration in the absence of any friction?

Answer 1

Force = mass * acceleration

acceleration = (angular velocity^2) * radius
= (velocity^2) / radius

so

force = mass * (velocity^2) / radius
= 1100 * (35^2) / 40
= 33687.5 N

Seems unlikely a real car could do this

Answer 2

The road should be banked so as to provide the necessary centripetal foce = mv^2 / r.

If N is the normal force,the horizontal component must be equal to = mv^2 / r.

1100 *35^2 / 40 = 33687.5 N.

Answer 3

If the road is frictionless (us = 0) because of a cover of ice, the car will not be able to round any curve at all. In order to avoid problems like this, curves on highways are usually banked. We assume that there is no friction between the tires and the road. The normal force N has components both along the radial and the vertical axes. Since there is no motion along the vertical direction, the net force along the vertical axis must be zero.
b = bank angle

N cos(b) = mg>>>>Normal force = N = mg/cos(b)
Radial component of Normal force:
Nr = N sin(b)= sin(b)x mg/cos(b) = mg tan(b)
m V^2/R = Nr= mg tan(b)
tan(b) = 1/g xV^2/R