Answer to Question #102860 in Mechanics | Relativity for Elia

Question

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)

Answer 1

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:

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

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:

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