A car goes around a flat curve of radius 50m at a speed of 35mph. What must be the minimum coefficient of static friction between the tires and the road for the car to make the turn?
r=50m
v=35mph=15.65m/s
F_sf=?
I know that F+sf= (meu)(F_N)
But the mass of the car isn't given how would I solve this problem?
Is F_sf=(mv^2)/r? But again were aren't given mass.
The centripetal force has to be supplied with the tires.
m*v^2/r= mg*mu
To solve this problem, we can use the equation F_sf = (mv^2)/r, where F_sf is the force of static friction, m is the mass of the car, v is the velocity of the car, and r is the radius of the curve.
Although the mass of the car is not given, we can still solve the problem by using the concept of centripetal force. The force of static friction must provide the necessary centripetal force to keep the car moving in a circular path.
The centripetal force is given by F_c = (mv^2)/r, where F_c is the centripetal force. Since the car is not slipping, the force of static friction provides this centripetal force.
So, set F_c equal to F_sf:
(mv^2)/r = F_sf
Now, we can solve for the minimum coefficient of static friction (μ_s). We can cancel out the mass (m) from both sides of the equation:
v^2/r = μ_s * g
Here, g is the acceleration due to gravity, which is approximately 9.8 m/s^2.
Now, plug in the given values:
v = 15.65 m/s
r = 50 m
g = 9.8 m/s^2
(15.65^2)/50 = μ_s * 9.8
Solving this equation will give you the minimum coefficient of static friction (μ_s) required for the car to make the turn.