动能守恒与动量守恒联立求解的问题
\u52a8\u91cf\u5b88\u6052\u548c\u52a8\u80fd\u5b88\u6052\u65b9\u7a0b\u8054\u7acb\u600e\u4e48\u89e3\uff1f\u8fd9\u4e2a\u7b80\u4fbf\u7b97\u6cd5\u53ef\u4ee5\u9002\u7528\u4e8e\u4efb\u4f55\u76f4\u7ebf\u4e0a\u7684\u5f39\u6027\u78b0\u649e
\u52a8\u91cf\u5b88\u6052\u65b9\u7a0b\uff1am1v1+m2v2=m1v1'+m2v2' \u2026(1)
\u80fd\u91cf\u5b88\u6052\u65b9\u7a0b\uff1a0.5m1vi^2+0.5m2v2^2=0.5m1v1'^2+0.5m2v2'^2 \u2026(2)
(1)\u5f0f\u79fb\u9879\u5f97\uff1am1(v1-v1')=m2(v2'-v2) \u2026(3)
(2)\u5f0f\u79fb\u9879\u5f97\uff1am1(v1-v1')(v1+v1')=m2(v2'-v2)(v2'+v2) \u2026(4)
\u7528(4)\u5f0f\u9664\u4ee5(3)\u5f0f\uff0c\u5f97v1+v1'=v2'+v2 \u2026(5)
\u8054\u7acb(1)(5)\u4e24\u4e2a\u4e00\u6b21\u7684\u5f0f\u5b50\u5c31\u597d\u7b97\u591a\u4e86~~~
\u95ee\u9898\u4e2d\uff0c\u7b2c\u4e00\u4e2a\u5f0f\u5b50\u4e2d2/1\u5e94\u8be5\u662f1/2\u5427\u3002\u9996\u5148\uff0c\u5c06\u542b\u6709m,M\u5404\u79fb\u5230\u4e00\u8fb9\uff0c\u52a8\u80fd\u5f0f\u4e3am(v0 v1)(v0-v1)=Mv22,\u52a8\u91cf\u5f0f\u4e3am(v0-v1)=Mv2.\u4e24\u5f0f\u76f8\u9664\uff0c\u5f97v0 v1=v2,\u518d\u8054\u5408\u52a8\u91cf\u5f0f\uff0c\u6c42\u5f97v1=(m-M/m M)v0,v2=(2m/m M)v0
m1v+m2v=m1v1+m2v2m1v^2+m2v^2=m1v1^2+m2v2^2
m1(v-v1)=m2(v2-v)
m1(v^2-v1^2)=m2(v2^2-v^2)
m1(v+v1)(v-v1)=m2(v2+v)(v2-v)
v+v1=v2-v
v2-v1=2v
条件不足,只能到这一步了,
v1=(m1-m2)v/(m1+m2),v2=2m1v/(m1+m2)。如果真是条件不足那你高考时就笑了
easy
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