Question

A way to test the tensile strength of a wire is to place a mass at the end of it and spin the mass with uniform circular motion. The speed at which the wire breaks is a measure of its strength. The maximum frequency of rotation before a certain wire breaks is 35.5 Hz. The wire is 50.5 cm long and has a mass of 0.656 kg. (a) Determine the speed with which the mass moves. (b) Calculate the centripetal force acting on the wire

Answer 1

(a) 112.58 m/s

(b) 16463.98 N

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:

`\begin{gathered} \omega=2\pi f \\ \\ \omega=(2)(3.14)(35.5) \\ \\ \omega=222.94\text{ rad/s} \end{gathered}`

Now we can calculate the speed, with the help of the radius:

`\begin{gathered} v=\omega r \\ \\ v=(222.94)(0.505) \\ \\ v=112.58\text{ m/s} \end{gathered}`

(b) The centripetal force is calculated using the following formula:

`\begin{gathered} F_c=(mv^2)/(r) \\ \text{ } \\ \text{ we replacing} \\ \\ F_c=(0.656\cdot(112.58)^2)/(0.505) \\ \\ F_c=16463.98\text{ N} \\ \end{gathered}`