To determine the maximum speed at which a car can round a curve of a given radius on a flat surface road, we can utilize the concept of centripetal force. The centripetal force is responsible for keeping an object moving in a curved path and is provided by the friction force between the tires of the car and the road.
The maximum speed can be calculated using the following formula:
v = sqrt(μ * g * r)
where: v is the maximum speed, μ is the coefficient of friction between the tires and the road, g is the acceleration due to gravity (approximately 9.8 m/s²), and r is the radius of the curve.
Plugging in the given values:
μ = 0.30, r = 25 m, g = 9.8 m/s²,
v = sqrt(0.30 * 9.8 * 25) = sqrt(73.5) ≈ 8.57 m/s
Therefore, the maximum speed at which the car can round the 25 m radius curve on a flat surface road with a coefficient of friction of 0.30 is approximately 8.57 m/s.