Re: [力学]

楼主: hydrasmith31   2014-04-20 02:28:55
※ 引述《simcity2013 (ONLY THE STRONG SURVIVE)》之铭言:
: [单元] 刚体动力学
: [来源] 刘宗儒精要
: [题目]
: 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、系统中有外力(摩擦力)作用,因此线动量不守恒
二、取轮子与地面的接触点,由于摩擦力通过此点不造成力矩,所以系统
对地面接触点而言角动量守恒
三、子弹质量m、相对地面距离r,初速度v、末速度v'、轮子质量M、半径R,角速度w
可列式如下
mvr = (3/2)MR^2(w) + mv'r
四、将数值带入
(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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