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Mechanics}Conservation of Momentum

From conservation of momentum, one has 2mv = 3mv' \Rightarrow v'=2/3 v.

The initial kinetic energy is 1/2 m v^2 = mv^2.

The final kinetic energy is 1/2 (3m) v'^2 = 3/2 m (2/3 v)^2.

The ratio of the final to initial kinetic energy is 2/3.

The kinetic energy lost in the collision is 1 minus that ratio. Thus, the answer is 1/3, as in choice (C).

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Comments
archard
2010-04-11 14:54:59
Another quick way is to remember that kinetic energy can be written as \frac{p^2}{2m}, and since momentum is conserved, the final:initial kinetic energy ratio is \frac{2(m1)}{2(m1+m2)} = \frac{2}{3}. Which means the fractional kinetic energy loss is \frac{1}{3}NEC
wittensdog
2009-10-08 16:29:07
Here's something that's surprisingly useful. When a moving body hits a second one at rest, and they stick, the fractional loss of kinetic energy is,

m2 / ( m1 + m2)

If you just memorize that, all sorts of problems involving sticky collisions become way faster, even ones where you have falling masses on pendulums and so forth.
NEC
herrphysik
2006-09-19 16:14:15
Small typo: You're missing a 2 in the left side of the initial KE equation.Typo Alert!

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