Final answer:
Centripetal force is the force that keeps an object moving in a circular path and is directed toward the center of the circle. For a 900 kg car taking a 600-m-radius curve at 25.0 m/s, the centripetal force can be calculated using Newton's second law and is found to be 937.5 N, which must be provided by the static frictional force.
Step-by-step explanation:
Understanding Centripetal Force
The concept of centripetal force is crucial in understanding circular motion. It is the force that is necessary to keep an object moving in a circular path and is directed toward the center of the circle. For example, when a car is traveling on a circular track, centripetal force is required to keep it moving along that curved path rather than in a straight line which the car would follow if no force acted on it.
Deriving the Expression for Velocity
To solve an example of a car on a circular track, let's consider a 900 kg car rounding a 600-m-radius curve on horizontal ground at 25.0 m/s.
The centripetal acceleration is a product of the square of the velocity (v^2) and the reciprocal of the radius (1/r), given by the equation a = v^2/r.
Now, using Newton's second law, which states that the force is equal to mass times acceleration (F = ma), we can find the centripetal force exerted by the car.
Multiplying the car’s mass (m) by the centripetal acceleration gives us the centripetal force (Fc): Fc = m * (v^2/r).
Substituting the given values, the centripetal force Fc would be 900 kg * (25.0 m/s)^2 / 600 m, which calculates to 937.5 N.
Static friction must provide this force to prevent the car from slipping, thus the frictional force between the car tires and the road must at least be equal to the centripetal force calculated.