Question

An aeroplane is flying at a velocity of $900km{h}^{-1}$ 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? [ $g=10m{s}^{-2}$ ]

Answer 1

Answer: 3125

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

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