Question

A pilot of mass 80 kg in a jet aircraft while executing a loop the loop with a constant speed of 250m/s . If the radius of circle is 6000m ,compute the force exerted by sent on a pilot. at a) Top of loop

b)bottom of loop.

Answer 1

(a)

$$F_{top}+mg=\dfrac{mv^2}{r},$$ $$F_{top}=\dfrac{mv^2}{r}-mg,$$ $$F_{top}=\dfrac{80\ kg\cdot(250\ \dfrac{m}{s})^2}{6000\ m}-80\ kg\cdot10\ \dfrac{m}{s^2}=33\ N.$$

(b)

$$F_{bottom}-mg=\dfrac{mv^2}{r},$$ $$F_{bottom}=\dfrac{mv^2}{r}+mg,$$ $$F_{bottom}=\dfrac{80\ kg\cdot(250\ \dfrac{m}{s})^2}{6000\ m}+80\ kg\cdot10\ \dfrac{m}{s^2}=1633\ N.$$