Question

A model airplane of mass 1.2 kg is attached to a horizontal string and flies in a horizontal circle of radius 6.5 m, making 1.6 revolutions every 8 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:v=8.17 m/s

Explanation:

Given

mass of airplane $m=1.2 kg$

Radius of circle $r=6.5 m$

1.6 revolution in 8 s  

i.e. 1 revolutions in 5 s

time period of 1 revolution is 5 s

and $T\omega =2\pi$

where $T=time\ period$

$\omega =angular\ velocity$

$\omega =\frac{2\pi }{5}=1.25 rad/s$

Speed of plane $v=\omega \times r$

$v=1.25\times 6.5=8.17 m/s$

Answer 2

The speed of the model airplane is equal to 8.17 m/s.

Given the following data:

• Mass of airplane = 1.2 kg

• Radius = 6.5 m

• Revolutions = 1.6 revs

• Time = 8 seconds

• Acceleration due to the gravity = 9.81 $m/s^2$

To determine the speed of the airplane:

First of all, we would determine the time period.

1.6 revs = 8 seconds

1 revs = X seconds

Cross-multiplying, we have:

$1.6X = 8\\\\X = \frac{8}{1.6}\\\\X = 5$

Time period = 5 seconds.

Next, we would find the angular velocity:

$\omega = \frac{2\pi }{T} \\\\\omega = \frac{2\times 3.142 }{5} \\\\\omega = \frac{6.284}{5} \\\\\omega = 1.26 \;rad/s$

Now, we can determine the speed of the airplane:

$Speed = r\omega\\\\Speed = 6.5 \times 1.26$

Speed = 8.17 m/s

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