Final answer:
Yes, the car will be able to drive at a speed of 55.7 m/s and stay on the track.
Step-by-step explanation:
To determine whether the car will be able to drive at a certain speed and stay on the track, we need to calculate the centripetal force exerted on the car. The formula for centripetal force is Fc = m*v^2/r, where Fc is the centripetal force, m is the mass of the car, v is the speed of the car, and r is the radius of the circular track.
Using the given values, we have:
Mass (m) = 1305 kg
Speed (v) = 55.7 m/s
Radius (r) = circumference / 2π = 2150 m
Plugging these values into the formula, we get:
Fc = (1305 kg) * (55.7 m/s)^2 / 2150 m = 19061.4 N
The centripetal force (Fc) must be provided by the frictional force between the tires and the track. The maximum frictional force is given by the equation Ffric = μ * Fn, where μ is the coefficient of friction and Fn is the normal force.
The normal force (Fn) is equal to the weight of the car, which is given by the equation Fn = m * g, where g is the acceleration due to gravity.
Using the given values:
Fn = (1305 kg) * (9.8 m/s^2) = 12759 N
Now we can calculate the maximum frictional force:
Ffric = (1.20) * (12759 N) = 15310.8 N
Since the calculated centripetal force (19061.4 N) is greater than the maximum frictional force (15310.8 N), the car will be able to drive at a speed of 55.7 m/s and stay on the track.