Question

During a plane showcase, a pilot makes circular "looping" with a speed equal to the sound speed (340 m/s). However, the pilot can fall when the acceleration is more than 8g, with g being the gravitational constant. Find the radius of the smallest circle that the pilot can take. (HINT: Think about the centripetal acceleration).

Answer 1

Answer:

r= 1474.5 m

Explanation:

We must use the centripetal acceleration formula and equate it to the limit acceleration (i.e 8g) in order to solve the resulting equation for the radius r.

The centripetal acceleration is given by:

$a=\frac{v^2}{r}$

Thus equating by the limit acceleration we have the following equation:

$\frac{v^2}{r}=8g\implies r=\frac{v^2}{8g}=\frac{340^2}{8\cdot9.8}\approx 1474.5 \, m$