<p>Two air-track gliders of equal mass are initially moving in the same directio

Question

<p>Two air-track gliders of equal mass are initially moving in the same direction along a straight line. The rearmost glider has an initial speed of 4.6 m/s and the forward glider has a speed of 1.7 m/s. The collision is elastic.&#160;<br /><a name="13">What is the speed of the first glider (rearmost) after the collision?&#160;</a></p>
<p><a name="15">What is the speed of the second glider (forward)?&#160;</a></p>
<p>please show how you solve it</p>

Explanation / Answer

Solve the hard way:

m(v1i + v2i) = m(v1f + v2f)

(1/2)m(v1i2 + v2i2) = (1/2)m(v1f2 + v2f2)

the mass drops out so you are left with two simultaneous equations in two variables, v1f and v2f.

If you do all the work to substitue and plug in you will get the solutions v1f = 1.7 m/s and v2f = 4.6 m/s, but there is an easier way to do it.

Solve the easy way:

In the reference frame of the second block, in which it is fixed initially, v2 is zero to start and v1 is 2.9 m/s, its approach velocity. Since their masses are equal, when the collision happens, the first block becomes motionless and transfers all of its momentum to the second block, which is now moving at 2.9 m/s.

Take that and put it back in the observer's reference frame and you get the above results.

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