Question

An aircraft executes a vertical turn of radius $R=500\text{m}$ with a constant velocity $v=360\text{km/h}$. The normal reaction on the pilot of mass $m=70\text{kg}$ at the lower, upper and middle points of the loop will respectively be :-

• A. $2100\text{N},700\text{N},1400\text{N}$
• B. $1400\text{N},700\text{N},2100\text{N}$
• C. $700\text{N},700\sqrt{5}\text{N},2100\text{N}$
• D. $2100\text{N},700\text{N},700\sqrt{5}\text{N}$

Answer 1

The correct option is D $2100\text{N},700\text{N},700\sqrt{5}\text{N}$

Given $v=360\text{km/hr}=100\text{m/sec}$


At lower point, $N-mg=\frac{m{v}^2}{R}$
where $N=$ Normal reaction on the pilot
$N=mg+\frac{m{v}^2}{R}=70\times 10+\frac{70\times \left(10000\right)}{500}=2100\text{N}$

At upper point, $N+mg=\frac{m{v}^2}{R}$
$N=\frac{m{v}^2}{R}-mg=1400-700=700\text{N}$

At middle point, $N=\frac{m{v}^2}{R}=1400\text{N}$
Resultant Normal reaction at middle point:
$=\sqrt{N^2+(mg{)}^2}=\sqrt{{700}^2+{1400}^2}=700\sqrt{5}\text{N}$