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Find coefficient of friction, given force and mass

Q: An engine provides 5.0 kN of force to keep a 1600-kg vehicle moving at a uniform speed. (Air resistance is negligible.) What is the coefficient of rolling friction between the tires and the road surface?

A: First convert 5.0 kN to Newtons: F = 5.0 kN = 5000 N. (Just like 5 kg = 5000 grams when measuring mass.)

You know it’s traveling at uniform speed, so this tells us that the right force = left force. There is no net force, because there is no acceleration!

F = 5000 N
m = 1600 kg
g = 9.8
\mu = ?

Use this equation:

F_f = \mu \cdot mg and solve for \mu.

\mu = F_f / mg
\mu = (5000) / (1600)(9.8)
\mu = 0.32

Use the Ti-84 to help you graph

If you graph F_f vs. F_N, the slope of the graph will be the value of \mu, the coefficient of friction.