Friction provides the force needed for a car to travel around a flat, circular race track. What is the maximum speed at which a car can safely travel if the radius of the track is 85.0 m and the coefficient of friction is 0.38?
To find the maximum speed at which a car can safely travel around a circular track, we need to consider the centripetal force provided by friction.
The centripetal force 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
r is the radius of the circular track
In this case, the centripetal force is provided by friction, so we can substitute F with the frictional force:
F_friction = μ * m * g
Where:
F_friction is the frictional force
μ is the coefficient of friction
m is the mass of the car
g is the acceleration due to gravity
Set the two equations equal to each other:
μ * m * g = m * (v^2 / r)
We can cancel out the mass of the car (m) from both sides of the equation:
μ * g = v^2 / r
Now solve for v, the maximum velocity:
v = √(μ * g * r)
Given:
μ = 0.38 (coefficient of friction)
g ≈ 9.8 m/s^2 (acceleration due to gravity)
r = 85.0 m (radius of the track)
v = √(0.38 * 9.8 * 85.0)
v ≈ √316.93
v ≈ 17.82 m/s
Therefore, the maximum speed at which the car can safely travel is approximately 17.82 m/s.