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Tensile force from a swinging weight.


A one pound weight is attached to a string.  If it is being swung in a horizontal circle so that the string sweeps a cone with an apex angle of 120 degrees, what is the tension in the string?


Ans: 2 pounds


The half angle of the cone is 60 degrees.  The force that the weight exerts on the string is the vector sum of its vertical gravitational weight (1 lb), and its horizontal centrifugal force.  This tensile force is equal to the hypotenuse of the right triangle formed by the above two component forces.  Since the angle between the vertical weight vector and the tensile force is 60 degrees, cosine(60deg) = W / T =½.


This is exactly the same relationship that exists between bank angle and g load for a level turn in an airplane:  g= 1/cos(bank angle).  (60deg bank = 2 g)


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