A bucket full of water is rotated in a vertical circle of radius 1.004 m (the ap
ID: 2078214 • Letter: A
Question
A bucket full of water is rotated in a vertical circle of radius 1.004 m (the approximate length of a person's arm). What must be the minimum speed of the pail at the top of the circle if no water is to spill out? Answer in units of m/s. A model airplane of mass 0.743 kg flies in a horizontal circle at the end of a control wire of length 57 m with a speed of 39.5 m/s. The forces exerted on the airplane are the pull of the control wire, its own weight, and aerodynamic lift, which acts at 20.7 degree inward from the vertical as shown in the figure. Compute the tension in the wire if it makes a constant angle of 20.7 degree with the horizontal. The acceleration due to gravity 9.8 m/s^2 Answer in units of N.Explanation / Answer
18] Minimum speed will be for which the centripetal force equals the gravitational force.
mg = mv2/r
v = [gr]1/2
=> v = [9.8 x 1.004]1/2 = 3.1367 m/s.
19] The net force in the horizontal direction is equal to the centripetal force.
Thus,
Tcos20.7o + Flift sin20.7o = mv2/r
but Flift cos20.7o = w = mg
therefore Flift = 7.784 N
=> Tcos20.7o + 7.784sin20.7o = mv2/r
=> Tcos20.7o + 7.784sin20.7o = 0.743(39.5)2/57
=> T = 18.80 N.
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