Not a homework question, but I am trying to understand some stuff in Leibniz's 17th century "natural philosophy" which got me realizing that I don't have a clear grasp of my high school physics from 40 years ago.(adsbygoogle = window.adsbygoogle || []).push({});

Imagine a closed system consisting of 2 objects, and imagine a perfect elastic collision between them. The first object has a mass of 1 unit and is travelling at a velocity of 10 units (straight north). The second object weighs 2 units and is originally at rest. The first hits the second straight on and transfers all its motion to it. By the conservation of momentum, the second will travel at 5 units (same direction).

m1 * v1 = m2 * v2

1 * 10 = 2 * v2

v2 = 5

(I realize that velocity is a vector quantity, but if the direction is unchanged this can be ignored here, I think.)

Now, since the formula for Kinetic energy is one half mass times velocity squared, the kinetic energy of the system before the collision is (10 * 10) / 2 = 50 units, but the kinetic energy of the system after the collision is 2 * (5 * 5) / 2 = 25 units.

How is this consistent with the law of the conservation of energy? Has the energy been converted from kinetic energy to some other form? Or have I misunderstood something in my statement of the problem.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Two conservation laws but how are they compatible

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