A 1980kg car starts from rest at point A on a 5° incline and coasts through a distance of 158m to point B. The brakes are then applied, causing the car to come to a stop at point C, 21m from point B. Knowing that slipping is impending during the braking period and neglecting air resistance, determine the coefficient of static friction between the tires and the road.
Vf^2 = V0^2 + 2ad
F = ma
The Attempt at a Solution
I get the velocity at point B by: V = sqrt(0 + 2*(9.81*sin(5))*158) = 16.4371 m/s
I then find the acceleration from point B to point C by: 0 = 16.4371^2 + 2*a*21
∴ a = -6.4328 m/s^2
Then I try and find the coefficient of static friction by:
F = ma = -μmgcos(5)
cancelling the m's: -6.4328 = -μ*9.81*cos(5)
This gives me: μ = .6582 which is not correct. What am I missing? Thanks for any help.