ANSWER:
(a) 112.58 m/s
(b) 16463.98 N
STEP-BY-STEP EXPLANATION:
Given:
Frequency (F) = 35.5 Hz
Mass (m) = 0.656 kg
Radius (r) = 50.5 cm = 0.505 m
(a) To determine the speed with which the mass moves, we must first calculate the angular speed, like this:
[tex]\begin{gathered} \omega=2\pi f \\ \\ \omega=(2)(3.14)(35.5) \\ \\ \omega=222.94\text{ rad/s} \end{gathered}[/tex]Now we can calculate the speed, with the help of the radius:
[tex]\begin{gathered} v=\omega r \\ \\ v=(222.94)(0.505) \\ \\ v=112.58\text{ m/s} \end{gathered}[/tex](b) The centripetal force is calculated using the following formula:
[tex]\begin{gathered} F_c=\frac{mv^2}{r} \\ \text{ } \\ \text{ we replacing} \\ \\ F_c=\frac{0.656\cdot(112.58)^2}{0.505} \\ \\ F_c=16463.98\text{ N} \\ \end{gathered}[/tex]