Question

A 45.2-kg person is on a barrel ride at an amusement park. She stands on a platform with her back to the barrel wall. The 3.74-meter diameter barrel spins rapidly in a circle, making a revolution every 1.65 seconds. Determine the net force (in N) acting on her. Use g = 9.8 m/s/s.

Answer 1

Answer:

• 1,230N

Explanation:

1. Name of the variables:

   $f:frequency\\\\ \omega:angular\text{ }speed\\\\ a_c:centripetal\text{ }acceleration\\\\ F_c:centripetal\text{ }force\\ \\ m:mass\\ \\ d:diameter\\ \\ r:radius\\ \\ g:gravitational\text{ }acceleration$

2. Formulae:

         $f=\dfrac{number\text{ }of\text{ }revolutions}{time}$

          $\omega=2\pi f$

          $a_c=\omega^2 r$

           $F_c=m\times a_c$

3. Solution (calculations)

       $f=\dfrac{1}{1.65s}=0.\overline{60}s^{-1}$

       $\omega=2\pi\times0.\overline{60}\approx 3.808rad/s$

      $a_c=(3.808rad/s)^2\times (3.74/2m)=27.12m/s^2$

      $F_c=45.2kg\times27.12m/s^2=1,225.67N\approx 1,230N$