15.
(2022高一下·湛江期末)
如图所示,现有质量分别为m、
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Em%3C%2Fmi%3E%3C%2Fmath%3E)
的小球a和物块b静置于光滑的水平轨道上,水平轨道右端与光电装置相连,左端与一停在光滑水平面上长为l、质量为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmi%3Em%3C%2Fmi%3E%3C%2Fmath%3E)
的小车c上表面平齐,小球a和物块b中间夹有少量炸药,炸药突然爆炸,爆炸后,物块b沿水平轨道向左运动滑上小车c,且小车c与物块b之间的动摩擦因数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3E%CE%BC%3C%2Fmtext%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
, 小球a沿水平轨道向右运动,光电装置被触动,控制电路会使转筒立刻以某一角速度匀速连续转动起来。转筒的底面半径为l,轨道末端与转筒上部相平,与转筒的转轴距离为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmsqrt%3E%3Cmrow%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsqrt%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmi%3El%3C%2Fmi%3E%3C%2Fmath%3E)
, 与转简侧壁上的小孔的高度差为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3El%3C%2Fmi%3E%3C%2Fmath%3E)
, 开始时转筒静止,且小孔正对着轨道方向。若小球a正好能钻入转筒的小孔,(小孔比小球略大,小球视为质点,不计空气阻力,重力加速度为g)求:
![](//tikupic.21cnjy.com/2022/07/21/c1/b8/c1b8704fcfad05671f6797dc17e5d38d_279x292.png)