A car is driving around a curve that can be approximated as being circular. In which direction does the centripetal force point? towards the center of the circle in the direction of motion away from the center of the circle tangential to the circle perpendicular to the plane of the circle The centripetal force (????C) of an object can be calculated using the equation ????C=m????2???? where m is the object's mass, ???? is the object's velocity, and ???? is the radius of the circle. If the radius of the circle changes by a factor of 0.5, the force changes by a factor of 0.8 3 0.3 0.5 2 1 If the velocity changes by a factor of 4, the force changes by a factor of 5 4 6 1 16 12

When an object moves in circular motion, a centripetal force acts on the objects, keeping it in a circular path: for that to happen, the direction of the force must be towards the centre of the circle.

The magnitude of the centripetal force is given by

[tex]F=m\frac{v^2}{r}[/tex]

where

m is the mass of the object

v is its velocity

r the radius of the circle

In the first part of the problem, the radius is changed by a factor 0.5:

r' = 0.5 r

So the new centripetal force is

[tex]F'=m\frac{v^2}{r'}=m\frac{v^2}{0.5r}=2(m\frac{v^2}{r})=2F[/tex]

So the force changes by a factor 2.

Similarly, when the velocity changes by a factor of 4:

v' = 4 v

the new centripetal force is

[tex]F'=m\frac{v'^2}{r}=m\frac{(4v)^2}{r}=16(m\frac{v^2}{r})=16F[/tex]

So the force changes by a factor 16.