Safe Parking on Icy Days: Calculating Friction

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AI Thread Summary
The discussion focuses on determining the safety of parking on icy driveways with different inclines: 13° for the user's driveway, 8° for Ralph's, and 5° for Bonnie's. The coefficient of static friction between tire rubber and ice is given as 0.15. By analyzing the forces involved, it is concluded that the critical angle for safe parking is approximately 8.6°. Therefore, both Ralph's and Bonnie's driveways are deemed safe for parking, while the user's driveway is not. The calculations emphasize the importance of friction and incline in assessing parking safety on icy surfaces.
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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?
 
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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.
 
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?
 

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