1. 500 kg racing car completes one lap in 20.9 seconds around a circular track w
ID: 1703825 • Letter: 1
Question
1. 500 kg racing car completes one lap in 20.9 seconds around a circular track with a radius of 80.0 m. The car moves at constant speed. What is the acceleration of the car?2. A 500 kg racing car completes one lap in 20.9 seconds around a circular track with a radius of 80.0 m. The car moves at constant speed. What horizontal force must the track exert on the tires to produce this acceleration?
3. 631.7 kg racing car completes one lap in 14.6 seconds around a circular track with a radius of 52.8 m. The car moves at constant speed. The centripetal acceleration of the car is _____ m/s2?
4 .An athlete whirls a 7.00 kg hammer tied to the end of a 1.1 m chain in a horizontal circle. The hammer makes one revolution in 0.9 s. What is the centripetal acceleration of the hammer?
5 .A merry-go-round completes one revolution in 30 s. What is the speed of a rider located at a distance 3 m from the center of the merry go-round?
Explanation / Answer
1 rev = 2 rad
1. 1 rev in 20.9s ; 1/20.9 rev/s = 0.301 rad/s ; r = 80m
v = r ; v = 0.301 rad/s (80m) = 24.05 m/s
Because it's uniform circular motion, the acceleration of the object is a = v2/r = (24.05 m/s)2 / 80m
a = 7.23 m/s2
2. The force would be equal in magnitude to the centripetal acceleration, so F = mv2/r
F = (500kg)(24.05 m/s)2 / 80m = 3615.2 N
3. = 1/14.6 rev/s = 0.430 rad/s
v = r ; v = 0.430 rad/s (52.8m) = 22.722m/s
a = v2/r = (22.722m/s)2 / (52.8m) = 9.78 m/s2
4. 1/0.9 rev/s = 6.98 rad/s =
v = r ; v = 6.98 rad/s (1.1m) = 7.68 m/s
a = v2/r = (7.68 m/s)2 / (1.1m) = 53.61 m/s2
5. 1rev in 30s, so = 1/30 rev/s = 0.209 rad/s
v = r ; v = 0.209 rad/s (3.0m) = 0.628 m/s
The reason I keep changing my units into rads/s is because the equation v = r is derived using rad/s, if I wanted to use rev/s then I'd need a different equation.
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