Safe Parking on Icy Days: Calculating Friction

[bpw91284]

Homework Statement

On an icy day, you worry about parking your car in your driveway, which has an incline of 13°. Your neighbor Ralph’s
driveway has an incline of 8°, and Bonnie’s driveway across the street has one of 5°. The coefficient of static friction
between tire rubber and ice is 0.15. Which driveway(s) will be safe to park in?

Homework Equations

Force of friction=F*u

The Attempt at a Solution

How can we know 'F' without knowning the mass of car?

 

[cristo]

Just let mass=m, and leave it in the equations. When comparing the components of the forces in the horizontal direction, the masses will cancel.

 

[bpw91284]

Here is what I just did...

Sum of Forces in horz direction,
F_f*cos@-F_n*cos(90-@)=0
Since F_f=u*F_n
0=0.15*F_n*cos@-F_n*cos(90-@)
Divide by F_n, solve for @ to be 8.6 degrees. So both Ralph's and Bonnie's driveways will be ok?