Question.
An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h. Compare its centripetal acceleration with the acceleration due to gravity.
An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h. Compare its centripetal acceleration with the acceleration due to gravity.
solution:
Radius of the loop, $r=1 \mathrm{~km}=1000 \mathrm{~m}$
Speed of the aircraft, $v=900 \mathrm{~km} / \mathrm{h}=900 \times \frac{5}{18}=250 \mathrm{~m} / \mathrm{s}$
Centripetal acceleration, $a_{\mathrm{c}}=\frac{v^{2}}{r}$
$=\frac{(250)^{2}}{1000}=62.5 \mathrm{~m} / \mathrm{s}^{2}$
Acceleration due to gravity, $g=9.8 \mathrm{~m} / \mathrm{s}^{2}$
$\frac{a_{\mathrm{c}}}{\mathrm{g}}=\frac{62.5}{9.8}=6.38$
$a_{\mathrm{c}}=6.38 \mathrm{~g}$
Radius of the loop, $r=1 \mathrm{~km}=1000 \mathrm{~m}$
Speed of the aircraft, $v=900 \mathrm{~km} / \mathrm{h}=900 \times \frac{5}{18}=250 \mathrm{~m} / \mathrm{s}$
Centripetal acceleration, $a_{\mathrm{c}}=\frac{v^{2}}{r}$
$=\frac{(250)^{2}}{1000}=62.5 \mathrm{~m} / \mathrm{s}^{2}$
Acceleration due to gravity, $g=9.8 \mathrm{~m} / \mathrm{s}^{2}$
$\frac{a_{\mathrm{c}}}{\mathrm{g}}=\frac{62.5}{9.8}=6.38$
$a_{\mathrm{c}}=6.38 \mathrm{~g}$