91影视

Weight of seat$W_c=255鈥�\mathrm{N}$

Weight of person $W_p=255鈥�\mathrm{N}$

Seat swing at a rate of $n=28.0鈥�\mathrm{rpm}$

Radius of circular path$r=7.5鈥�\text{m}$.

The force applied to an item in curved motion that is pointed toward the axis of rotation or the centre of curvature is known as a centripetal force.

A fictitious force that moves in a circle and is directed away from the centre of the circle is called centrifugal force.

$F_c=\frac{m{v}^2}{r}鈥�鈥�\text{or}鈥�鈥�mr{蝇}^2$

Where, m is mass of body, v is velocity of body, r is radius of circular path and the$蝇$ is angular speed.

Let assume that tension in upper cable is $T_1$and the tension in the horizontal cable is $T_2$

Total weight of seat and person is

$\begin{array}{rcl}W& =& 255鈥�\text{N}+825鈥�\text{N}\\ & =& 1080\text{N}\end{array}$

Total mass of seat and person is

$\begin{array}{rcl}m& =& \frac{1080鈥�\text{N}}{9.8鈥�{\text{m/s}}^2}\\ & =& 110.204鈥�\text{kg}\end{array}$

Determine the angular speed of seat

$\begin{array}{rcl}蝇& =& \frac{2蟺n}{60}\\ & =& \frac{2蟺脳28.0鈥�\mathrm{rpm}}{60}\\ & =& 2.93鈥�\text{rad/s}\end{array}$

Equating the vertical forces

$T_1\sin {50}^0=mg$

Substituting all the values in above equation to get value oflocalid="1668424843713" $\begin{array}{rcl}& & T_1\end{array}$

localid="1668424837705" $\begin{array}{rcl}{T}_1& =& \frac{1080\text{N}}{\sin {50}^0}\\ & =& 1409.84鈥�\text{N}\end{array}$

Hence the tension in the upper cables islocalid="1668424848310" $1409.84鈥�\text{N}$

Now equating the horizontal forces

localid="1668424853079" $$\begin{gathered} F_c=T_2+T_1\cos {50}^0 \\ mr{蝇}^2=T_2+T_1\cos {50}^0 \end{gathered}$$

Substituting all the values in above equation to the value oflocalid="1668424865980" $T_2$

localid="1668424858614" $\begin{array}{rcl}110.204鈥�\text{kg}脳\text{7.5}鈥�\text{m}脳{\left(\text{2.93}鈥�\text{rad/s}\right)}^2& =& T_2+1409.84鈥�\text{N}脳\cos {50}^0\\ T_2& =& 7095.67鈥�\text{N}-906.22鈥�鈥�\text{N}\\ & =& 6189.45鈥�\text{N}\end{array}$

Hence the tension in the horizontal cables is localid="1668424875875" $6189.45鈥�\text{N}$.