Respuesta :
Given data
*The given mass of the child is m = 65 kg
*The given number of revolutions is 12.0
*The given time is t = 35.2 s
*The given radius of the barrel is r = 3.50 m
The frequency is calculated as
[tex]\begin{gathered} f_{}=\frac{12}{35.0} \\ =0.34\text{ Hz} \end{gathered}[/tex]The formula for the linear velocity is given as
[tex]\begin{gathered} v=\omega r \\ =(2\pi f)r \end{gathered}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} v=(2\times3.14\times0.34)(3.50) \\ =7.47\text{ m/s} \\ \approx7.50\text{ m/s} \end{gathered}[/tex]The formula for the centripetal force is given as
[tex]F_c=\frac{mv^2}{r}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} F_c=\frac{(65)(7.50)^2}{(3.50)} \\ =1045.6\text{ N} \\ =1050\text{ N} \end{gathered}[/tex]The formula for the centripetal acceleration is given as
[tex]a_c=\frac{v^2}{r}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} a_c=\frac{(7.50)^2}{3.50} \\ =16.1m/s^2 \end{gathered}[/tex]