(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A block of mass m_{1}= 1.6 kg is initially moving to the right with a speed of 4 ms^{-1}on a frictionless horizontal track and collides with a spring attached to a second block of mass m_{2}= 2.1 kg initially moving to the left at a speed of 2.5 ms^{-1}. The spring constant is 600 NM^{-1}.

a. Find the velocities of the two blocks after the collision.

2. Relevant equations

(1) m_{1}v_{1i}+m_{2}v_{2i}= m_{1}v_{1f}+m_{2}v_{2f}

(2) v_{1i}- v_{2i}= -(v_{1f}- v_{2f})

3. The attempt at a solution

So this is a problem in the book that is worked out for me, but I cannot seem to figure out the reasoning behind the way they combined and manipulated the equations. They first begin by subbing in the known values into EQ (1) which I agree with. They then state to use EQ (2) due to the collision being ellastic, which I don't totally understand this relationship. They sub known values into EQ (2) giving the following:

6.5 ms^{-1}= -v_{1f}= v_{2f}

The book then states that I must multiply the EQ I gave right above by 1.6 kg which gives me the following which I will label as EQ (3): This is what I don't understand, why would I multiply EQ (2) by 1.6kg?

10.4kgms^{-1}= (-1.6kg)v_{1f}+ (1.6kg)v_{2f}

The book goes on to state that I now must add EQ (1) and EQ (3) which apparently allows me to solve for v_{2f}, but I don't see where the thought process determines that I add these two EQ. Thanks in advance for the assistance, I am hoping this is a relatively simple algebraic procedure that I am missing.

Joe

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# Homework Help: Two body collision with a spring

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