A car goes around a flat curve of radius #50# #m# at a speed of #14# #ms^-1#. What is the minimum coefficient of friction between the tires and the road for the car to make the turn?
Centripetal acceleration is given by
The minimum friction coefficient required is
(friction coefficients have no units)
To find a force we need to know something about a mass, and we haven't been told the mass of the car. Let's just call it '
The centripetal force is given by
We have values for the velocity and the radius, so:
The frictional force must be equal to or greater than this force in order for the car to successfully make it around the curve without sliding out.
The frictional force will be given by:
We can equate these two forces, the frictional force and the centripetal force:
We can cancel out a factor of
Substituting in the value