Question

A special prototype model airplane of mass 400g has a control wire 8cm long attached to its body. the other end, of the control line is attached to a horizontal circle with its wings horinzontal. the wire OX is inclined at 60 degree to the horizontal and fixed to a point O and X takes 4s to fly once round its circular path. calculate; (i) the tension T in the control wire (ii) the upward force on X due to the air

Answer 1

$m\vec g+\vec T+\vec F+\vec{F_c}=\vec0,$

$Ox: -T\text{cos}\alpha+m\omega^2 l=0,$

$Oy: -mg-T\text{sin }\alpha+F=0,$

1)

$T=\frac{4\pi^2ml}{t^2\text{cos}\alpha}\approx0.168~\text{N},$

2)

$F=mg+\frac{4\pi^2ml\text{tan}\alpha}{t^2}\approx 4.057~\text{N}.$