Question

An aeroplane is flying at a velocity of $900 \, km \, h^{- 1}$ loops a vertical circular loop. If the maximum force pressing the pilot against the seat is five times his weight, what would be the diameter (in $m$ ) of the loop? [ $g=10 \, m \, s^{- 2}$ ]

Answer 1

$v=900\text{km h}^{- 1}$
$= \text{900} \times \frac{5}{\text{18}}$
$=\text{250 }m \, s^{- 1}$

the maximum force is at the bottom of the vertical circle
$F_{\text{max}}=\frac{m v^{2}}{r}+mg=5mg$
$v^{2}=\text{4}\textit{gr}$
$r=\frac{v^{2}}{\text{4} \textit{g}}=\frac{\left(\text{250}\right)^{2}}{4 \left(\text{10}\right)}=\text{1562.5 }m$
$d=2r=3125 \, m$