91Ó°ÊÓ

The given data can be listed below as,

• The mass of the pilot is, $\mathrm{m}=50.0 \mathrm{kg}$.
• Velocity of the plain is, $\mathrm{v}=95.0 \mathrm{m}/\mathrm{s}$.

Force acting on the body due to which it moves on a circular path is known as centripetal force. It is always directed to the center of the circular path.

The path is circular, the expression for centripetal force can be expressed as,

$F=\frac{m{v}^2}{r}$

Here m is the mass of the pilot, v is the velocity of plane, and ris the radius of the circular path.

Substitute 50 kg for m, 95.0 m/s for v in the above equation.

$F=\frac{\left(50kg\right){\left(95.0m/s\right)}^2}{r}$

The expression for the force using Newton’s second law can be expressed as,

$F=ma$

Here m is the mass, and ais the acceleration.

Substitute $\frac{\left(50kg\right){\left(95.0m.s\right)}^2}{r}$ for F , $4.00 (9.8 m/s^2)$ for a , and 50 kg for m in the above equation.

$$\begin{gathered} \frac{\left(50\mathrm{kg}\right){\left(95.0\mathrm{m}.\mathrm{s}\right)}^2}{\mathrm{r}}=\left(50\mathrm{kg}\right)×4.00\left(9.8\mathrm{m}/{\mathrm{s}}^2\right) \\ \mathrm{r}=\frac{{\left(95.0\mathrm{m}/\mathrm{s}\right)}^2}{4.00\left(9.8\mathrm{m}/{\mathrm{s}}^2\right)} \\ =230.23\mathrm{m} \end{gathered}$$

Hence, required radius is, 230.23 m.

The expression for the weight at lowest point can be expressed as,

Substitute 50 kg for m , $9.8m/s^2$ for g ,and 95.0 m/s for v , 230.23 m for rin the above equation.

$$\begin{gathered} {\mathrm{N}}_{\mathrm{bottom}}=\left(50\mathrm{kg}\right)\left(9.8\mathrm{m}/{\mathrm{s}}^2\right)+\frac{\left(50\mathrm{kg}\right)\left(9.8\mathrm{m}/{\mathrm{s}}^2\right)}{230.23\mathrm{m}} \\ =2450\mathrm{N} \end{gathered}$$

Hence, the required weight is, 2450 N.