# Collisions problem (How should I approach it)

by Hindi
Tags: collisions
 P: 9 Hi all, I came across a problem on collisions on one of my professors old exams. The problem is: http://home.comcast.net/~msharma15/problem_2.jpg The way I am trying to approach it is by applying the conservation of linear momentum and energy, but the problem is that I still get left with 3 unknowns. Here is what I know: Before the collision, only block A has kinetic energy. After the collision, the K.E. of system is (1/2 K.E. initial). block A has -1/2MV^2 and block B has 1/2MV^2. The final collision is what confuses me. Should I just work with K.E.i (only block A moving) with conservation of linear momentum? Any help would be greatly appreciated. Thanks!
 P: 364 by cons of p, $$m_1v_{1i}=m_1v_{1f}-m_2v_{2f}$$ where v_2f is reckoned as negative By the energy conditions, $$m_1v_{1i}^2=\frac {1}{2}(m_1v_{1f}^2+m_2v_{2f}^2)$$ which gives two equations with two unknowns.
 P: 9 Thanks for the reply StephenPrivitera. I am just wondering why you made m_2v_2f negative in the first equation?? Should it be the other way around?
Mentor
P: 40,907

## Collisions problem (How should I approach it)

The equations should be:
$$m_1v_{1i}=-m_1v_{1f}+m_2v_{2f}$$
$$\frac {1}{4}m_1v_{1i}^2=\frac {1}{2}(m_1v_{1f}^2+m_2v_{2f}^2)$$
(where the speeds are all positive)

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