I'm trying to solve a problem that reads:
The coefficient of static friction between a truck's tires and the road is 0.850. What is the maximum acceleration uphill that the truck can have if the road is tilted 12 degrees to the horizontal?
I drew a free body diagram and came up with the following equations:
X direction: $f=ma+mgsin\theta = \mu_sF_n$
Y direction: $F_n = mgcos\theta$
Substituting $mgcos\theta$ into the x direction equation and solving for $a$ gives:
At this point I'm not sure what this last equation means or how to find the maximum acceleration from it. It's saying that the acceleration depends only on the force of gravity, the angle of the incline, and the coefficient of static friction. I'm confused because shouldn't the acceleration depend on things like the horsepower of the engine as well as the variables in the equation? Does this equation give the value of some kind of hard cap as to how much friction can contribute to movement given a certain coefficient of friction?