phys問題題題2 - Ans.fyi 參考答案

phys問題題題2

2011-02-10 5:02 am

a u-tube contains liquid of density p. the total length of the liquid column is l. if the tube is shaken for a short while,determine the period of osc
可5可以幫手解答下呢題d step點解要咁計????
同埋個cross-sectional area of the tube其實係咩型狀???可能仲有問題@@thx

更新1:

你個Pressure difference點計?@@

回答 (1)

天同

2011-02-10 5:29 am

✔ 最佳答案

Let the liquid level on each arm of the U-tube be displaced by an amount x , upward or downward, from the equilibrium position.

Pressure difference = (2x)pg, where g is the acceleration due to gravity
Restoring force = (2x)pgA, where a is the cross-sectional area of the U-tube
hence, [l.A.p]a = - (2x)pgA
where [l.A] is the volume of the liquid, and thus [l.A]p is the mass of liquid

a = - (2x)g/l = -(2g/l)x
i.e. the motion is simple harmonic with angular frequency square w^2 = 2g/l
Hence, period = 2.pi.square-root[l/2g]

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