91Ó°ÊÓ

$\mathrm{Mass}=80\mathrm{kg},\mathrm{circle}\mathrm{of}\mathrm{radius}=10\mathrm{m},\mathrm{speed}=6.1\mathrm{m}/\mathrm{s}$

This problem is based on the concept of uniform circular motion. Uniform circular motion is a motion in which an object moves in a circular path with constant velocity. Also, it involves Newton’s second law of motion.

Formula:

The velocity in uniform circular motion is given by,

$\mathrm{v}=\frac{2\mathrm{Ï€¸é}}{\mathrm{T}}$

where, v is the velocity, R is the radius and T is the time period

According to Newton’s second law of motion

${\mathrm{F}}_{\mathrm{N}}-\mathrm{mg}={\mathrm{ma}}_{\mathrm{c}}$

where,${}^{{\mathrm{a}}_{\mathrm{c}}}$is an acceleration, g is an acceleration due to gravity, m is mass,${}^{{\mathrm{F}}_{\mathrm{N}}}$ is the normal force and R is the radius.

Using equation (i) the time can be written as,

$$\begin{gathered} \mathrm{T}=2\mathrm{Ï€¸é}/\mathrm{V} \\ -2\mathrm{Ï€}\left(10\mathrm{M}\right)/(6.1\mathrm{m}/\mathrm{s}) \\ =10\mathrm{s} \end{gathered}$$

Hence, the period of the motion is 10 s.

In this case, Normal force ${}^{{\mathrm{F}}_{\mathrm{N}}}$is directed upward, gravitational force mg is to downward and acceleration is also directed to the down. Thus, by using Newton’s 2nd law,

${\mathrm{F}}_{\mathrm{N}}-\mathrm{mg}={\mathrm{ma}}_{\mathrm{c}}$(Centripetal acceleration is due to the circular motion)

$$\begin{gathered} {\text{F}}_{\mathrm{N}}=\mathrm{m}(\mathrm{g}-{\mathrm{v}}^2/\mathrm{R}) \\ =486\mathrm{N} \\ ≈4.9×{10}^2\mathrm{N} \end{gathered}$$

Hence, the magnitude of the normal force on the addict from the seat when both go through the highest point of the circular path is${}^{4.9×{10}^{2}N}$.

Now, reverse both the normal force direction and the acceleration direction

Thus,

$$\begin{gathered} \mathrm{F}=\mathrm{m}(\mathrm{g}+{\mathrm{v}}^2/\mathrm{R}) \\ -1081\mathrm{N} \\ ≈1.1\mathrm{kN} \end{gathered}$$

Hence, the magnitude of the normal force on the addict from the seat when both go through the lowest point is${}^{1.1\mathrm{kN}}$