Question

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

Answer 1

Breaking the summation of the forces into its components of "x" and "y"
\[\sum F_{y} = ma_{y}\]\[N_{A}+N_{B} - W = 0\]\[N_{A}+N_{B} =W\]call this equation #1 then we do summation of the forces in the "x" direction with the direction to the right as positive:\[\sum F_{x} =ma_{x}\]\[F_{Engine}-f_{A}-f_{B}=0\]the reason why we set it equal to zero is because there's no acceleration as the car is moving at "constant" speed, we then break down the equation into this:\[m(3.125 \frac{ meter }{ s^2 })-\mu_{s} N_{A}-\mu_{s} N_{B}=0\]\[m(3.125\frac{ meter }{ s^2 })-\mu_{s} (N_{A} + N_{B}) = 0\]refer back to equation #1 and plug it into the normal forces. From here you can solve for the static friction.