A car travels at a constant speed around a circular track whose radius is 2.66 km. The car goes once around the track in 200 s. What is the magnitude of the centripetal acceleration of the car?
distance = 2 pi r = 2 pi*2660 meters
speed v = 2 pi 2660/200 meters/s
Ac = v^2/r
To find the magnitude of the centripetal acceleration of the car, we can use the formula:
ac = v^2 / r
Where ac is the centripetal acceleration, v is the velocity, and r is the radius.
First, let's find the velocity of the car. We know that the car travels around the track in 200 seconds and the track has a circumference of 2πr.
Circumference = 2πr
Circumference = 2π(2.66 km)
Circumference = 16.72 km
Since the car completes one lap in 200 seconds, we can find the velocity by dividing the circumference by the time:
Velocity = Circumference / Time
Velocity = 16.72 km / 200 s
Velocity = 0.0836 km/s
Now we have the velocity, let's find the centripetal acceleration:
ac = (0.0836 km/s)^2 / 2.66 km
ac = 0.006 km/s^2
Therefore, the magnitude of the centripetal acceleration of the car is 0.006 km/s^2.