A car moves around a 4.5 km circular track at a rate of 40.0 m/s. What is the magnitude of the force that keeps a 1000-kg car in circular motion?
To find the magnitude of the force that keeps the car in circular motion, we can use the centripetal force formula. The centripetal force (F) is equal to the mass of the object (m) multiplied by the square of its velocity (v), divided by the radius of the circular path (r):
F = (m * v^2) / r
In this case, the mass of the car (m) is given as 1000 kg, and the velocity (v) is given as 40.0 m/s. The car moves around a circular track, so we can assume that the radius (r) is half the diameter of the track.
Given that the track has a diameter of 4.5 km, we can convert it to meters by multiplying by 1000: 4.5 km * 1000 m/km = 4500 m.
Since the radius is half the diameter, we divide the diameter by 2: r = 4500 m / 2 = 2250 m.
Now we can substitute the given values into the centripetal force formula:
F = (1000 kg * (40.0 m/s)^2) / 2250 m
Calculating the equation gives:
F = (1000 kg * 1600 m^2/s^2) / 2250 m
= 1,600,000 kg⋅m^2/s^2 / 2250 m
= 711.11 N
Therefore, the magnitude of the force that keeps the 1000-kg car in circular motion is approximately 711.11 Newtons.