(1)A \"swing\" ride at a carnival consists of chairs that are swung in a circle
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(1)A "swing" ride at a carnival consists of chairs that are swung in a circle by 12.0 m cables attached to a vertical rotating pole, as the drawing shows. (? = 69.0
A "swing" ride at a carnival consists of chairs that are swung in a circle by 12.0 m cables attached to a vertical rotating pole, as the drawing shows. (? = 69.0 degree) Suppose the total mass of a chair and its occupant is 204 kg. Determine the tension in the cable attached to the chair. Find the speed of the chair. A centrifuge is a device in which a small container of material is rotated at a high speed on a circular path. Such a device is used in medical laboratories, for instance, to cause the more dense red blood cells to settle through the less dense blood serum and collect at the bottom of the container. Suppose the centripetal acceleration of the sample is 6.85 times 103 times as large as the acceleration due to gravity. How many revolutions per minute is the sample making, if it is located at a radius of 4.30 cm from the axis of rotation?Explanation / Answer
(a) Determine the tension in the cable attached to the chair.
mg = 204 x 9.8 = 1999.2 N
1999.2/sin(30) = 3998.4 N
(b) Find the speed of the chair.
g/tan(34.5) = centripetal acc
9.8/tan(34.5) = 14.25 m/s^2
radius = 12cos(34.5) = 9.8889 m
14.25 x 9.8889 = v^2 = 140.9, sq-root = v = 11.87 m/s
2.acceleration due to gravity = 9.8 m/s^2
centripetal acceleration = 5E3 * 9.8 m/s^2
centripetal acceleration also equals v^2 / r, where they give you r = .0681m
so v^2 / .0681 = 5E3 * 9.8
v = sqrt(.0681 * 5E3 * 9.8)
v is the object tangential speed.
I don't have a calc and don't feel like using my computer's calc, but once you get a number for v, do the following.
v (m/s) * 1 rev / 2piR m * 60 sec/min = speed in rev/min. Rr = .0681m
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