Question

A model airplane of mass 0.6 kg is attached to a horizontal string and flies in a horizontal circle of radius 6 m, making 1.6 revolutions every 5 s. (The weight of the plane is balanced by the upward “lift” force of the air on the wings of the plane.) The accelaration due to the gravity is 9.81 m/s2 . Find the speed of the plane. Answer in units of m/s.

Answer 1

Answer:

$speed= 12.15\frac{m}{s}$

Explanation:

In this question we have given

mass of airplane=.6 Kg

Radius of horizontal circle,r=6m

Time taken to complete 1.6 revolution=5s

Therefore time taken to complete 1 revolution, t=$\frac{5}{1.6}$

t=3.1 s

We have to find the speed of airplane

We will first find the distance covered by airplane in tracing one circle which is equal to circumference of circle

We know that

Circumference,d = $2 \pi \times r$

or $d=2\times 3.14 \times 6$

$d=37.68 m$

We know that speed=$\frac{d}{t}$............(1)

Put value of d and t in equation 1

speed=$\frac{37.68}{3.1}$

$speed= 12.15\frac{m}{s}$