Cloverleaf exits are approximately circular. A 1256 kg automobile is traveling 58 mph while taking a cloverleaf exit that has a radius of 35.4 m. Calculate the centripetal acceleration of the car and the centripetal force on the car. Remember that 1 mph = 0.447 m/s.
To calculate the centripetal acceleration of the car, we can use the formula:
Centripetal acceleration = (velocity^2) / radius
First, we need to convert the velocity from mph to m/s. We know that 1 mph is equal to 0.447 m/s, so we can convert the velocity as follows:
58 mph * 0.447 m/s = 25.926 m/s (rounded to three decimal places)
Now we have the velocity in m/s, and we can plug it along with the given radius into the formula:
Centripetal acceleration = (25.926 m/s)^2 / 35.4 m
Calculating this:
Centripetal acceleration = 671.1134 m^2/s^2 / 35.4 m
Centripetal acceleration ≈ 18.957 m/s^2 (rounded to three decimal places)
To calculate the centripetal force on the car, we can use Newton's second law, which states:
Centripetal force = mass * centripetal acceleration
Given that the mass of the car is 1256 kg, let's plug in the values:
Centripetal force = 1256 kg * 18.957 m/s^2
Centripetal force ≈ 23,786.392 N (rounded to three decimal places)
Therefore, the centripetal acceleration of the car is approximately 18.957 m/s^2, and the centripetal force on the car is approximately 23,786.392 N.