- #1
bolzano95
- 89
- 7
Homework Statement
I have an escapement in a clock. It given shape is hoop with radius 5mm, mass 0.01g and has a frequency 5Hz. For how much does the frequency change if we warm the hoop for 20K?
[tex]α= 1.2 ⋅10^{-5} K^{-1}[/tex]
Homework Equations
[tex]
l=2πr\\Δl=lαΔT\\w=\sqrt{\frac{2D}{mr^2}}⇒D\\Δ\nu=\nu_1- \nu= \frac{(\sqrt{\frac{2D}{mR^2}}-\sqrt{\frac{2D}{mr^2}})}{2π}=-1.2⋅10^{-3} s^{-1}\\\frac{Δ\nu}{\nu}=-2.4⋅10^{-4} s^{-1}
[/tex]
The Attempt at a Solution
Well, official result is
[tex]
\frac{Δ\nu}{\nu}=-1.2⋅10^{-4} s^{-1}
[/tex]
but I got a solution
[tex]
\frac{Δ\nu}{\nu}=-2.4⋅10^{-4} s^{-1}
[/tex]
I am not sure if official solution is correct, because I couldn't find an error in my result. I would like to ask you to check this problem over. Let me know if I missed something!
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