91影视

Given that ring rotates once every 4.5 s.

And mass of rider is 55 kg

Diameter of ring = 16 m

First draw free body diagram and the equate forces

From the diagram we can get

$$\begin{gathered} T_{Top}=\frac{m{v}^2}{r}-mg........................\left(1\right) \\ {T}_{Bottom}=\frac{m{v}^2}{r}+mg........................\left(2\right) \end{gathered}$$

We can find v by using v=蝇 r

We have period as 4.5 s So

$蝇=\frac{2蟺}{T}$

And $v=\frac{2蟺r}{T}=\frac{(2脳3.14)\left(8m\right)}{4.5s}=11.17m/s$

Now substitute the given values in equation (1) and (2)

role="math" localid="1649077252870" $T_{Top}=\frac{\left(55kg\right){(11.17m/s)}^2}{8m}-\left(55kg\right)(9.8m/s^2)=318.24N=0.32N$

Similarly

$T_{Top}=\frac{\left(55kg\right){(11.17m/s)}^2}{8m}+\left(55kg\right)(9.8m/s^2)=1397.34N=1.4KN$

Given that ring rotates once every 4.5 s.

Mass of rider = 55 kg

Diameter of ring = 16 m

We have calculated velocity = 11.17 m/s

For longest rotation period prevent riders to fall means resultant force is zero

$$\begin{gathered} \frac{m{v}^2}{r}-mg=0 \\ v=\sqrt{rg} \end{gathered}$$

Substitute the values given we get

$v=\sqrt{\left(8m\right)(9.8m/s^2)}=8.86m/s$

We know

$T=\frac{2蟺r}{v}$

Substitute values we get

$T=\frac{(2脳\mathrm{蟺}脳8)}{8.86}=5.67s$