What is the centripetal force on a vehicle rounding a circular curve with a radius of 80 m at a constant speed of 90 km/h if the vehicle's mass is 2,000 kg? (hint: first express the velocity in meters per second.)
a. 20,250 n
b. 625 n
c. 15,625 n
d. 703 n

Centripetal force is the force that needs to be exerted on an
object in order to keep it on a circular path with a certain radius. 
If the force is there but it isn't strong enough, then the object will
travel in a circular curve alright, but it'll be bigger than the radius
you want.  If the force isn't there at all, then the object will move
in a straight line.

To keep a mass ( 'M' ) moving with speed 'S' on a circular path
with radius of 'R', the force on it has to be

                                         Force = M S² / R

and it always has to point from the object toward the center
of the circle.

That formula is pretty simple, but in order to use it just as it
stands, the quantities have to be in SI base units ... meters,
kilograms, and seconds ... so we have to massage the speed,
and change it from  km/hr  to  m/s .

     Speed = (90 km/hr) x (1,000 m/km) x (1 hr / 3,600 sec)

                = (90 x 1,000 / 3,600)  (m / sec)  =  25 m/s .

Now we're ready to use the formula.
Centripetal force = (mass) x (speed)² / (radius)

                           = (2,000 kg) x (25 m/s)² / (80 m)

                           = (2,000 x 625 / 80)  (kg-m / sec²)

                           =            15,625 newtons .
        

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