8] Find the minimum stopping distance for a car moving at 108km/h if the coefficient of static friction between the tires and road is a) 0.9
108,000m/hr * 1hr/3600s = 30 m/s
friction force= -.9 m g
= -.9 * 9.81 m = -8.83 m
F = m a
-8.83 m = m a
a = -8.83 m/s^2
v = Vi + a t
0 = 30 - 8.83 t
t = 4 seconds
To find the minimum stopping distance, we need to use the equation that relates stopping distance to velocity and the coefficient of friction.
The equation is given by:
Stopping Distance = (Velocity^2) / (2 * coefficient of friction * acceleration due to gravity)
In this case, the velocity is given as 108 km/h. However, we need to convert it to m/s since the equation requires velocity in meters per second.
1 km/h = 1000 meters/3600 seconds
So, 108 km/h = (108 * 1000) / 3600 = 30 m/s
The coefficient of static friction is given as 0.9.
The acceleration due to gravity is approximately 9.8 m/s^2.
Now, we can plug in these values into the equation to find the stopping distance:
Stopping Distance = (30^2) / (2 * 0.9 * 9.8) = 105.102 m
Therefore, the minimum stopping distance for a car moving at 108 km/h with a coefficient of static friction of 0.9 is approximately 105.102 meters.