Physics question

Question

On an icy day, you worry about parking your car in your driveway, which has incline of 12 degrees. your neighbor's driveway has na incline of 9.0 degrees, and the driveway across the street is at 6.0 degrees. the Coefficient of static friction between tire rubber and ice is 0.15. which driveway(s) will be safe to park in?

Answer 1

Draw a horizontal line representing a level plane. Draw another line at an incline to the first and label the angle between the horizontal and the incline as Theta. 

 

Draw a box on the incline representing the car, add a vertical arrow from the centroid of the box pointing down representing the weight vector W. Add another arrow from the same centroid pointing down the incline representing the component of the weight vector that is parallel to the incline, label this as Fp. Draw another arrow normal to Fp so that the point touches the point of the weight vector. Label this as Fn. 

 

Study your diagram to see that the angle between W and Fn is also equal to theta. Now note that Fp = Wsin(theta) and Fn=Wcos(theta). Recall that Force of friction (f)= Fn *(coefficient of static friction).  Note that for the car to move Fp > f. Use these equations and Algebra to see that, for the car to slide, the coefficient of static friction > tan(theta). 

 

Since atan(.15) = 8.5 degrees and only one driveway is less than that (6 degrees), use that driveway.