Question

The coefficient of static friction between hard rubber and normal street pavement is about 0.90. On how steep a hill (maximum angle) can you leave a car parked?

Answer 1

First thing to do is to draw the system described above. Then, write an equation for the forces present.

ΣF = Fg - Ff
0 = mgsin∅ - umgcos∅0 = gsin∅ - ugcos∅
u = tan∅
∅(max) = tan^-1 (u)

Answer 2

Answer: Ok, first, if the mass of the carr is M, and the angle of the hill is a (counting counterclockwise from the ground), the equations for the forces are:

Gravity force Fg = - Mg*sin(a)

Knowing that the normal force that the ground is doing in the car is N = Mg*cos(a)

then the Friction force is: Ff  = 0.9*Mg*cos(a)

if the car is parked, then the sum of the forces must be equal to zero, this is

0.9*Mg*cos(a) - Mg*sin(a) = 0

Mg( 0.9*cos(a) - sin(a)) = 0

so

0.9*cos(a) = sin(a)

0.9 = sin(a)/cos(a) = Tg(a)

a = aTg(0.9) = 41.9°

so the maximum angle is 41.9°, if is smaller or equal, then your car will be fine.