Final answer:
The maximum speed at which a car can safely travel around a circular track of radius 55 m with a coefficient of friction of 0.350 is 20.8 m/s.
Step-by-step explanation:
The maximum speed at which a car can safely travel around a circular track can be determined using the formula for centripetal force. The centripetal force is given by the equation:
Fc = (mv^2) / r
where Fc is the centripetal force, m is the mass of the car, v is the velocity of the car, and r is the radius of the track.
To find the maximum speed, we need to find the maximum value of the coefficient of friction, μmax. The coefficient of friction can be related to the centripetal force by the equation:
μ = Fc / (mg)
where g is the acceleration due to gravity.
The maximum value of the coefficient of friction, μmax, can be calculated by:
μmax = tan(θ)
where θ is the angle of friction or the maximum angle at which the car can safely negotiate the turn.
Therefore, the maximum speed at which the car can safely travel around the circular track is given by:
vmax = sqrt(μmaxrg)
Substituting the given values, we have:
vmax = sqrt((0.350)(55.0)(9.8))
= 20.8 m/s
So, the maximum speed at which the car can safely travel around the circular track is 20.8 m/s.