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What I know:

Wen an inelastic collision takes place the momentum of the two objects before the collision: m1 * v1 + m2 * v2 is equal to the momentum of the objects after the collision: (m1 + m2) * u

But the energy in the system gets a bit lower because some energy gets lost in warmth.

Here comes the question:

If something is warmed up, the particles in it are just getting faster, right? Faster particle means higher momentum, so where does the increase in momentum for the particles in the object warmed up in this case come from? If the momentum came from the colliding objects, the momentum in the system would not stay the same, pretty much like the energy. But it does. This really blows my mind.

Maybe I'm just being dumb but this vector vs scalar think and other mathematical approaches are totally logical to me. The thing I described in the question still blows my mind anyway.

(Sorry for my bad English, I'm a foreign speaker)

Qmechanic
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Sebastian
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1 Answers1

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As you already said, the total momentum in the (fully) inelastic collision stays constant $$L=m_1\vec v_1+m_2\vec v_2=(m_1+m_2)\vec u$$ The kinetic energy reduces by $$\Delta E_{kin}=E_1-E_2=\frac{m_1\vec v_1^2+m_2\vec v_2^2}{2}-\frac{(m_1+m_2)\vec u^2}{2}=\frac{m_1\vec v_1^2+m_2\vec v_2^2}{2}-\frac{(m_1\vec v_1+m_2\vec v_2)^2}{2(m_1+m_2)}$$ The energy difference is found in the internal energy rise of the colliding bodies. If this internal energy rise is purely thermal it consists of an increase in the energy of the molecules and a increase of the mean momentum of the molecules. Because they move randomly in all directions their total momentum relative to the center of mass is zero. In the end you have both conservation of the total energy and of the total momentum.

freecharly
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