A car with a uniform speed of 60km/h enters a circular flat curve whose radius is .50 km. If the friction between the road and the car's tires can supply a central accekeration of 1.25 m/s^2, dies the car negotiate the curve safely? Prove your answer.
To determine if the car can negotiate the curve safely, we need to compare the centripetal acceleration of the car to the maximum acceleration it can handle (given by the friction between the road and the car's tires).
To calculate the centripetal acceleration of the car, we use the formula:
ac = v^2 / r,
where ac is the centripetal acceleration, v is the velocity of the car, and r is the radius of the curve.
Given:
- Velocity (v) = 60 km/h = 60,000 m / 3600 s = 16.67 m/s (converted from km/h to m/s)
- Radius (r) = 0.50 km = 500 m (converted from km to m)
Substituting the values into the formula, we have:
ac = (16.67 m/s)^2 / 500 m
= 277.8 m^2/s^2 / 500 m
= 0.556 m/s^2
The centripetal acceleration of the car is calculated to be 0.556 m/s^2.
Now, we compare this with the maximum acceleration the car can handle, which is given as 1.25 m/s^2.
Since the centripetal acceleration (0.556 m/s^2) is less than the maximum acceleration the car can handle (1.25 m/s^2), the car can negotiate the curve safely.
In conclusion, the car can safely negotiate the curve due to the centripetal acceleration being less than the maximum acceleration the car can handle.