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.
(N/A) Radius of the loop,$r = 1 \; km = 1000 \; m$.
Speed of the aircraft,$v = 900 \; km/h = 900 \times \frac{5}{18} = 250 \; m/s$.
Centripetal acceleration,$a_c = \frac{v^2}{r}$.
$a_c = \frac{(250)^2}{1000} = \frac{62500}{1000} = 62.5 \; m/s^2$.
Acceleration due to gravity,$g = 9.8 \; m/s^2$.
Comparing the two,$\frac{a_c}{g} = \frac{62.5}{9.8} \approx 6.38$.
Therefore,the centripetal acceleration is $6.38$ times the acceleration due to gravity,i.e.,$a_c = 6.38 \; g$.
Speed of the aircraft,$v = 900 \; km/h = 900 \times \frac{5}{18} = 250 \; m/s$.
Centripetal acceleration,$a_c = \frac{v^2}{r}$.
$a_c = \frac{(250)^2}{1000} = \frac{62500}{1000} = 62.5 \; m/s^2$.
Acceleration due to gravity,$g = 9.8 \; m/s^2$.
Comparing the two,$\frac{a_c}{g} = \frac{62.5}{9.8} \approx 6.38$.
Therefore,the centripetal acceleration is $6.38$ times the acceleration due to gravity,i.e.,$a_c = 6.38 \; g$.
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