Question

An aircraft executes a horizontal loop of radius $1.00\text{km}$ with a steady speed of $900\text{km/h}$. Compare its centripetal acceleration with the acceleration due to gravity.

Answer 1

Step 1: Convert $\text{km/h}$ into $\text{m/s}$.

Given, radius of the circular path, $r=1\text{km}=1000m$.
Speed of the aircraft, $v=900\text{km/h}$
$v=900\times \frac{1000}{3600}m/s=250m/s$

Step 2: Find the centripetal acceleration.
As the centripetal acceleration is given by, $a_c=\frac{v^2}{r}$
Substituting the value of v and r, we get
$a_c=\frac{250\times 250}{1000}$
$a_c=62.5m{s}^{-2}$

We know that acceleration due to gravity, $g=9.8{\text{ms}}^{-2}$.

Now, $\frac{a_c}{g}=\frac{62.5}{9.8}=6.38\approx 6.4\Rightarrow a_c=6.4g$.