Answer to Question #102860 in Mechanics | Relativity for Elia

Question #102860
A special phototype model aeroplane of mass 400g has a control wire 8cm long attached to its body the other end of the control line is attached to afixed point .when aeroplane flies with its string wing horizontal in a horizontal circle 30degree above the horizontal .draw a diagram showing the four exerted on a plane and determine. a)Tension in the control wire b)the lift on the plane ( g=10m/s pie^2=10)
Expert's answer

Write forces according to Newton's second law. Since the airplane is moving along a circumference with radius equal to the horizontal projection of the string, the net force is the centripetal force. Therefore:

"Ox:T\\text{ cos}30^\\circ=m\\frac{v^2}{r}=m\\frac{v^2}{l\\text{ cos}30^\\circ},\\\\\n\\space\\\\\nOy:T\\text{ sin}30^\\circ-mg=0."

Solve that system of equations by expressing tension from the second equation first:

"T=\\frac{mg}{\\text{sin}30^\\circ}=7.84\\text{ N}."

The speed of the plane:

"v=\\text{ cos}30^\\circ \\sqrt{\\frac{Tl}{m}}=\\text{ cos}30^\\circ \\sqrt{\\frac{gl}{\\text{sin}30^\\circ}}=1.1\\text{ m\/s}."

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