Question

In 1986, a 35 × 10^3 kg watch was demonstrated in Canada. Suppose this watch is placed on a huge trailer that rests on a lightweight platform, and that oscillations equal to 0.71 Hz are induced. Find the trailer’s mass if the platform acts like a spring scale with a spring constant equal to 1.0 × 10^6 N/m.

Answer 1

We will have the following:

`f=(1)/(2\pi)\sqrt[]{(k)/(m)}`

So:

`0.71=(1)/(2\pi)\sqrt[]{(1.0\cdot10^6)/(m)}\Rightarrow0.5041=(1)/(4\pi^2)((1.0\cdot10^6)/(m))`
`\Rightarrow m=(1.0\cdot10^6)/(4\pi^2(0.5041))\Rightarrow m=50248.55368`
`\Rightarrow m\approx50\cdot10^3Kg`

Now, to determine the mass of the trailer we subtract the mass of the watch:

`m_t\approx50\cdot10^3-35\cdot10^3\Rightarrow m_t\approx15000`
`\Rightarrow m_t\approx1.5\cdot10^4Kg`

So, the mass of the trailer is approximately 1.5*10^4 Kg.