Answer to Question #199522 in Mechanics | Relativity for nela

Question

An aerobatic aircraft is performing circular loops at the speed of sound, covering spectacularly 340 meters every single second in a flight exhibition. All participants have been warned that they keep their acceleration below 8 times that of the gravitational acceleration to avoid getting dizzy. What is the diameter of the smallest loop that these participants can safely do? Here you may use 10 m/s/s as the gravitational acceleration.

Answer 1

Speed of aircraft in circular loop, $v=340\space m/s$

Maximum acceleration permissible $= 8g=80\space m/s^2$

Let the radius of the smallest loop $=R$

Diameter, $D=2R$

$R=\dfrac{D}{2}$

Centripetal acceleration, $a_c=\dfrac{v^2}{R}$

$R=\dfrac{v^2}{a_c}$

$D=\dfrac{2v^2}{a_c}=\dfrac{2\times(340)^2}{80}$

$D=2890\space m$