Predict the period of the airplane’s motion

Question

A toy airplane is attached to the ceiling by a 68-cm string. As the airplane travels in a circle at constant speed, the string makes an angle of 55° with the vertical. Predict the period of the airplane’s motion

Answer 1

Predict the period of the airplane’s motion

A toy airplane is attached to the ceiling by a 68-cm string. As the airplane travels in a circle at constant speed, the string makes an angle of 55° with the vertical. Predict the period of the airplane’s motion

T Cos θ = mg........................................... Eq 1... ( We have equated vertical components of forces)

and T sin θ = Centripetal force = mv²/r .........Eq 2, ( We have equated the horizontal components of forces)

Where r= Radis of circle , m= Mass of toy airplane

Dividing Eq 2 By Eq 1

tanθ= v²/rg , Where θ =55 degree

tan 55 = v²/rg

v² = rg( tan55)

But Time period T' = 2Π r/v , R= radius of circular path of airplane , g = acceleration due to gravity

T '= (4Π²r / gtanθ)^1/2 But r= l tan 55

T ' = ( 4Π^2* l *sin55/g *tan55)1/2 As Sin55/tan 55 = Cos 55

T' = ( 4Π^2* l* Cos 55 /g) ^1/2 , Where l = Length of string

So to get T' = Time Period

plug in l= 0.68 m, g= 9.8 m/s² , Cos 55 =0.573

You will get T' in sec