Re: [力學]

作者: hydrasmith31   2014-04-20 02:28:55
※ 引述《simcity2013 (ONLY THE STRONG SURVIVE)》之銘言:
: [單元] 剛體動力學
: [來源] 劉宗儒精要
: [題目]
: A bullet of mass 4.0g and velocity 330m/s passes
: through a wheel at rest on a rough floor.The wheel is a
: solid disk of mass 2.0kg and radius 20cm.The bullet passes
: through the wheel at a perpendicular distance of 19cm from
: the center,and the bullet's final velocity is 220m/s.If the
: wheel rolls without slipping,find the wheel's angular velocity.
: [想法]
一、系統中有外力(摩擦力)作用,因此線動量不守恆
二、取輪子與地面的接觸點,由於摩擦力通過此點不造成力矩,所以系統
對地面接觸點而言角動量守恆
三、子彈質量m、相對地面距離r,初速度v、末速度v'、輪子質量M、半徑R,角速度w
可列式如下
mvr = (3/2)MR^2(w) + mv'r
四、將數值帶入
(0.004)(330)(0.39) = (3/2)(2)(0.04)(w) + (0.004)(220)(0.39)
可以解得w = 1.43 (rad/s)

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