The radius of curvature of the path for a passenger car is 9.2m. The mass of the vehicle is 1,483kg. The coefficient of friction is 0.76 and the normal reactionary force for a tyre is 41kN. What is the maximum speed (in terms of km/h) of the car for cornering?
To determine the maximum speed of the car for cornering, we can use the concept of centripetal force.
Centripetal force is the force that keeps an object moving in a curved path and is given by the equation:
F = (m * v^2) / r
Where:
F is the centripetal force,
m is the mass of the car,
v is the velocity of the car, and
r is the radius of curvature.
In this case, the centripetal force is provided by the friction between the car tires and the road surface, which is given by:
F = μ * N
Where:
μ is the coefficient of friction, and
N is the normal reactionary force.
We can equate these two equations:
(μ * N) = (m * v^2) / r
We can solve this equation for v:
v^2 = (r * μ * N) / m
v = sqrt((r * μ * N) / m)
Now, let's substitute the given values into the equation to find the maximum speed of the car:
r = 9.2 m,
μ = 0.76,
N = 41 kN = 41000 N,
m = 1483 kg.
Converting the normal force from kN to N:
N = 41000 N
Substituting the values into the equation:
v = sqrt((9.2 * 0.76 * 41000) / 1483)
Calculating this expression will give us the maximum speed in meters per second (m/s). To convert it to kilometers per hour (km/h), we can multiply by 3.6 (since there are 3.6 km in one hour):
v_km/h = v * 3.6
By evaluating this expression, we can find the maximum speed of the car for cornering.