On a wet racetrack, the maximum safe speed, to avoid sliding on a level circular curve with a radius of curvature of 56 m, is 73 km/hr. What is the coefficient of friction between the car's tires and the track surface?
To find the coefficient of friction between the car's tires and the track surface, we need to use the formula that relates the maximum safe speed, radius of curvature, and the coefficient of friction. The formula is:
v = sqrt(μ * g * r)
Where:
v = maximum safe speed (73 km/hr)
μ = coefficient of friction
g = acceleration due to gravity (9.8 m/s^2)
r = radius of curvature (56 m)
To solve for μ, we'll need to convert the maximum safe speed from km/hr to m/s.
1 km/hr = 1000 m/3600 s = 5/18 m/s
So, the maximum safe speed is:
v = 73 km/hr * (5/18 m/s) = 20.28 m/s
Now we can solve for μ using the formula:
20.28 m/s = sqrt(μ * (9.8 m/s^2) * (56 m))
First, square both sides of the equation to eliminate the square root:
(20.28 m/s)^2 = μ * (9.8 m/s^2) * (56 m)
Now, divide both sides of the equation by (9.8 m/s^2) * (56 m) to isolate μ:
μ = (20.28 m/s)^2 / (9.8 m/s^2) / (56 m)
Calculating this expression will give us the coefficient of friction.