A 1200 kg car travels at a constant speed of 22 m/s along a circular track. What is the radius of the track if the car’s centripetal acceleration is 6 m/s2? The same car doubles its speed upon entering another circular track with a radius twice that of the first track. What is its centripetal acceleration now?
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The free-body diagram (part a) is shown at the right.
The acceleration of the car can be computed as follows:
a = v2/R = (18.0 m/s)2/(12.0 m) = 27.0 m/s2 (part b)
The net force can be found in the usual manner:
Fnet = m•a = (500. kg)•(27.0 m/s2) = 13500 N (part b)
Since the center of the circle (see diagram) is above the riders, then both the net force and the acceleration vectors have an upward direction. The force of gravity is downwards, so the net force is equal to the upward force minus the downward force:
Fnet = Fnorm - Fgrav
where Fgrav = m • g = (500. kg) • (9.8 m/s/s) = 4900 N
Thus,
Fnorm = Fnet + Fgrav = 13500 N + 4900 N = 18400 N (part c)
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