Physical Solid State Physics

Question

Physical Solid State Physics

I am doing a program that includes the physics of elastic balls. I developed all the math for collisions with walls and fixed objects, but I can’t understand what happens when two moving balls collide. I have mass and speed (more precisely, the speed x and y, but the speed of each ball and their direction will do) and would like formulas for them. Remember - this is a perfect elastic collision - so there are no spinning balls, etc.

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collision 2d physics

J843136028 Feb 04 '16 at 20:36

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1 answer

cromod · Answer 1 · 2016-02-04T22:11:10+0000

This wikipedia article article contains a formula for calculating velocities after a collision between two particles:

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There are many reasons to use this formula:

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$m_1\mathbf{v'_1}+m_2\mathbf{v'_2}=m_1\mathbf{v_1}+m_2\mathbf{v_2}$

:

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, :

$\left\{\begin{matrix} \left \langle \mathbf{v'_1}|\mathbf{t} \right \rangle=\left \langle \mathbf{v_1}|\mathbf{t} \right \rangle \\ \left \langle \mathbf{v'_2}|\mathbf{t} \right \rangle=\left \langle \mathbf{v_2}|\mathbf{t} \right \rangle \end{matrix}\right.$

Proof

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$\left\{\begin{matrix} m_1 {\left \langle \mathbf{v'_1}|\mathbf{n} \right \rangle}+m_2 {\left \langle \mathbf{v'_2}|\mathbf{n} \right \rangle} =m_1 {\left \langle \mathbf{v_1}|\mathbf{n} \right \rangle}+m_2 {\left \langle \mathbf{v_2}|\mathbf{n} \right \rangle} \\ m_1 {\left \langle \mathbf{v'_1}|\mathbf{n} \right \rangle}^{2}+m_2 {\left \langle \mathbf{v'_2}|\mathbf{n} \right \rangle}^{2}=m_1 {\left \langle \mathbf{v_1}|\mathbf{n} \right \rangle}^{2}+m_2 {\left \langle \mathbf{v_2}|\mathbf{n} \right \rangle}^{2} \end{matrix}\right.$

, :

$m_1 {\left \langle \mathbf{v'_1}|\mathbf{n} \right \rangle}^{2}-m_1 {\left \langle \mathbf{v_1}|\mathbf{n} \right \rangle}^{2}=m_2 {\left \langle \mathbf{v_2}|\mathbf{n} \right \rangle}^{2}-m_2 {\left \langle \mathbf{v'_2}|\mathbf{n} \right \rangle}^{2}$

$\Rightarrow {\left \langle \mathbf{v'_1}|\mathbf{n} \right \rangle}+{\left \langle \mathbf{v_1}|\mathbf{n} \right \rangle}={\left \langle \mathbf{v_2}|\mathbf{n} \right \rangle}+{\left \langle \mathbf{v'_2}|\mathbf{n} \right \rangle}$

v'1:

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, wikipedia v'1:

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v'2 .

Physical Solid State Physics

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