How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 95 at a speed of 95 ?
Express your answer using two significant figures.
forcefriction=forcecentripetal
mu*mg=mv^2/r
change velocity and radius to SI units.
ok... but I don't have the mass...
the mass cancel each other out.
To solve this problem, we need to use the centripetal force equation and the frictional force equation.
First, let's calculate the centripetal force required to keep the car moving in a circular path:
Centripetal force (F) = mass (m) x velocity squared (v^2) / radius (r)
F = mv^2 / r
Using the given values:
m = mass of the car (not given)
v = velocity of the car = 95 m/s
r = radius of the curve = 95 m
Next, let's determine the maximum frictional force that can be exerted on the car:
Maximum frictional force (f_max) = coefficient of static friction (μ_s) x normal force (N)
The normal force (N) is the force exerted by the surface on the car, which is equal to the car's weight (mg), where g is the acceleration due to gravity.
Now, to determine the coefficient of static friction (μ_s), we need to equate the centripetal force (F) to the maximum frictional force (f_max):
F = f_max
mv^2 / r = μ_sN
Since N = mg, we can substitute it into the equation:
mv^2 / r = μ_smg
Now, rearrange the equation to solve for the coefficient of static friction (μ_s):
μ_s = mv^2 / (rmg)
Substituting the given values:
μ_s = (mass of the car) x (95 m/s)^2 / ((95 m) x (9.8 m/s^2))
The mass of the car is not given, so we cannot get an exact value for the coefficient of static friction without the mass information.