Calculating the Coefficient of Friction

Most recent answer: 04/30/2020

Is there a way to calculate the coefficient of static friction between a tire and a road, given the car's initial speed of 0 m/s, a final speed of 27.77778 m/s, and a change in time of 2.45 seconds? Is there a way to generate a formula to solve for this component?
- Robert Stewart (age 17)
Bel Air, MD, USA

The coefficient of static friction tells you the maximum acceleration the car can undergo before the tires begin to slip (i.e., "squealing" the tires).  For a given acceleration without slipping, we can only calculate the minimum coefficient that will enable it.

In this problem, a = 27.77778 m/s / 2.45 s = 11.34 m/s2, a bit more than 1 g.  The definition of the friction coefficient is Fmax = mamax = μmg --> μ = amax/g > 11.34/2.45 = 1.16 .  All we know is that μ must be larger than this, because amax > a.

(published on 04/30/2020)