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.

Respuesta :

We will have the following:

[tex]f=\frac{1}{2\pi}\sqrt[]{\frac{k}{m}}[/tex]

So:

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

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

[tex]m_t\approx50\cdot10^3-35\cdot10^3\Rightarrow m_t\approx15000[/tex][tex]\Rightarrow m_t\approx1.5\cdot10^4Kg[/tex]

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