A 870-kg race car can drive around an unbanked turn at a maximum speed of 41 m/s without slipping. The turn has a radius of 180 m. Air flowing over the car's wing exerts a downward-pointing force (called the downforce) of 11000 N on the car. (a) What is the coefficient of static friction between the track and the car's tires? (b) What would be the maximum speed if no downforce acted on the car?
down force = F = 870*9.81 + 11000
mu F = m v^2/R
mu (870*9.81 + 11000) = 870 (41)^2/180
for part b, same mu
mu(870*9.81) = 870 v^2/180
v^2 = 180*9.81*mu
part a: 0.43
part b: 27.56
To find the coefficient of static friction between the track and the car's tires, we need to use the given information about the car's maximum speed and the downforce.
(a) The centripetal force that keeps the car moving in a circle is provided by the friction between the tires and the track. The maximum static friction force that can be exerted between two surfaces is given by the equation:
Fs_max = μs * N
Where Fs_max is the maximum static friction force, μs is the coefficient of static friction, and N is the normal force.
In this case, the downward force exerted by the car's weight is balanced by the upward normal force:
N = mg
Where m is the mass of the car and g is the acceleration due to gravity.
Given:
Mass of the car, m = 870 kg
Downforce, Fd = 11000 N
Acceleration due to gravity, g = 9.8 m/s^2
First, let's find the normal force:
N = mg = 870 kg * 9.8 m/s^2 = 8526 N
Next, let's calculate the frictional force:
Fs_max = μs * N
We know that the maximum speed without slipping is 41 m/s, so we can set up an equation using the centripetal force:
Fs_max = m * (v^2 / r)
Where v is the velocity and r is the radius of the turn.
Substituting the values:
Fs_max = 870 kg * (41 m/s)^2 / 180 m
Now we can equate the two equations for Fs_max:
μs * N = 870 kg * (41 m/s)^2 / 180 m
Rearranging, we can find the coefficient of static friction:
μs = (870 kg * (41 m/s)^2 / 180 m) / (8526 N)
Calculating this expression gives us the value of the coefficient of static friction between the track and the car's tires.