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

• 1,230N

Step-by-step 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=\frac{number\text{ }of\text{ }revolutions}{time}`

`\omega=2\pi f`

`a_c=\omega^2 r`

`F_c=m* a_c`

3. Solution (calculations)

`f=(1)/(1.65s)=0.\overline{60}s^(-1)`

`\omega=2\pi*0.\overline{60}\approx 3.808rad/s`

`a_c=(3.808rad/s)^2* (3.74/2m)=27.12m/s^2`

`F_c=45.2kg*27.12m/s^2=1,225.67N\approx 1,230N`