Water surface!

Classical Mechanics Level 4

We have a long cylinder with radius of 10cm ,filled with water , if the whole system is rotating with an angular velocity of 10 π \pi rad/s, find h the difference between the highest and the lowest point of the curve of the water surface! take g=10 N/kg.

Report your answer in meters.

this problem is reborn by Osama Karkout!


The answer is 0.4934.

Jafar Badour by jafar badour , 23, Russia

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1 solution

Jafar Badour
Oct 7, 2015

m g s i n θ = m ω 2 r c o s θ mgsin\theta =m\omega^2 rcos\theta |

g t a n θ = ω 2 r gtan\theta =\omega^2 r |

g d h d r = ω 2 r g\frac{dh}{dr}=\omega^2 r |

h = ω 2 r 2 2 g + C 1 h=\frac{\omega^2 r^2}{2g} +C_1 |

the high deference is Δ h \Delta h equals: |

h = ( 10 π ) 2 ∗ 0. 1 2 20 − ω 2 0 2 20 = 0.4934 h=\frac{(10\pi)^2 *0.1^2}{20} -\frac{\omega^2 0^2}{20} =0.4934 |

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