Answer
427.8k+ views
Hint: We have to first generalize by drawing a free body diagram representing all the forces acting on the aircraft.The speed is given in km/h which we will change into m/s to find the radius and there is no need to convert the angle into degree radians.
Complete step by step answer:
Speed of aircraft= 720 km/h
Converting it into m/s, \[720\times \dfrac{5}{18}=200m/s\]
Let us take the acceleration due to gravity to be 10 \[m/{{s}^{2}}\]. The angle of banking is \[{{15}^{0}}\] using the formula which we use during the banking of roads where the car takes a turn.
We can see that mg is balanced by cos component of normal force so,
\[\Rightarrow N\cos \theta =mg\]-------(1)
And the centripetal force is balanced by the sine component of normal force,
\[\Rightarrow N\sin \theta =\dfrac{m{{v}^{2}}}{r}\]--(2)
Dividing eq (2) by (1) we get,
\[\begin{align}
&\Rightarrow \tan \theta =\dfrac{{{v}^{2}}}{rg} \\
&\Rightarrow r=\dfrac{{{v}^{2}}}{g\tan \theta } \\
\end{align}\]
Putting the values, we get,
\[\therefore =\dfrac{{{200}^{2}}}{10\times \tan (15)}=\dfrac{400}{0.26}=14.92m\]
So, the radius of the loop is 14.92 m.
Note:Here while resolving the Normal force we have to be careful and since there is no motion in the vertical direction we have equated the two vertical forces, and also the velocity is taken in m/s so that the radius comes out to be in metres in place of kilometres.
Moreover, banking turns are used to change the aircraft heading. The turn is initiated by banking on one side slightly. It is done by lowering one of the ailerons and raising the other aileron.
Complete step by step answer:
Speed of aircraft= 720 km/h
Converting it into m/s, \[720\times \dfrac{5}{18}=200m/s\]
Let us take the acceleration due to gravity to be 10 \[m/{{s}^{2}}\]. The angle of banking is \[{{15}^{0}}\] using the formula which we use during the banking of roads where the car takes a turn.
![seo images](https://www.vedantu.com/question-sets/e688c3e0-ab1e-41a1-92a0-939469b135486230001307862516282.png)
We can see that mg is balanced by cos component of normal force so,
\[\Rightarrow N\cos \theta =mg\]-------(1)
And the centripetal force is balanced by the sine component of normal force,
\[\Rightarrow N\sin \theta =\dfrac{m{{v}^{2}}}{r}\]--(2)
Dividing eq (2) by (1) we get,
\[\begin{align}
&\Rightarrow \tan \theta =\dfrac{{{v}^{2}}}{rg} \\
&\Rightarrow r=\dfrac{{{v}^{2}}}{g\tan \theta } \\
\end{align}\]
Putting the values, we get,
\[\therefore =\dfrac{{{200}^{2}}}{10\times \tan (15)}=\dfrac{400}{0.26}=14.92m\]
So, the radius of the loop is 14.92 m.
Note:Here while resolving the Normal force we have to be careful and since there is no motion in the vertical direction we have equated the two vertical forces, and also the velocity is taken in m/s so that the radius comes out to be in metres in place of kilometres.
Moreover, banking turns are used to change the aircraft heading. The turn is initiated by banking on one side slightly. It is done by lowering one of the ailerons and raising the other aileron.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)