本题目来源于试卷: 2012美国US F=MA物理竞赛，类别为 美国F=MA物理竞赛
[单选题]
A particle at rest expl x0k** f2 bf:2ydrc xsotfe7h.r/a bx : 8f;hxfdk53 sqs(gui:odes into three particles of equal mass in the absence of external forces. Two particles emerge at a right angs/5q :;3b(8 ifhxkadguf: xsrle to each other with equal speed $v$. What is the speed of the third particle?
A. $v$
B. $\sqrt{2}v$
C. $2v$
D. $2\sqrt{2}v$
E. The third particle can have a range of different speeds.
参考答案: B
本题详细解析:
The initial momentum of the system is zero. By conservation of momentum, the toto 3ddxlftr3vcq02 r to4(xuv)+u;nu 7al final momentum must also be zero. Let the two particles travel along the x and y axr3cd;3 +0d)fxnu(ol2v7rq4otvt x uu es. Their momenta are $\vec{p}_1 = mv \hat{i}$ and $\vec{p}_2 = mv \hat{j}$. The momentum of the third particle $\vec{p}_3$ must be $\vec{p}_3 = -(\vec{p}_1 + \vec{p}_2) = -mv \hat{i} - mv \hat{j}$. The magnitude of this momentum is $|\vec{p}_3| = \sqrt{(-mv)^2 + (-mv)^2} = \sqrt{m^2v^2 + m^2v^2} = \sqrt{2m^2v^2} = mv\sqrt{2}$. Since $p_3 = mv_3$, the speed of the third particle is $v_3 = \sqrt{2}v$.
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