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A molecule in a gas container hits the wall with speed $200 \mathrm{~m} / \mathrm{s}$ at an angle $30^{\circ}$ with the normal and rebound with the same speed. Is momentum conserved in the collision? Is collision elastic or inelastic?
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Verified Answer
Momentum is conserved in all types of collisions.
Let $m \rightarrow$ mass of the molecule, $\mathrm{M} \rightarrow$ mass of the wall $\therefore$ K.E. after collision $=\frac{1}{2} \mathrm{~m}(200)^2+\frac{1}{2} \mathrm{M}(0)^2=2 \times 10^4$ mJ.
K.E. before collision $=\frac{1}{2} \mathrm{~m} \times(200)^2=2 \times 10^4 \mathrm{~mJ}$
$=\mathrm{K}$.E. after collison.
$\because$ K.E. before collison $=\mathrm{K}$. E. after collision
$\therefore$ The collision is elastic.
Let $m \rightarrow$ mass of the molecule, $\mathrm{M} \rightarrow$ mass of the wall $\therefore$ K.E. after collision $=\frac{1}{2} \mathrm{~m}(200)^2+\frac{1}{2} \mathrm{M}(0)^2=2 \times 10^4$ mJ.
K.E. before collision $=\frac{1}{2} \mathrm{~m} \times(200)^2=2 \times 10^4 \mathrm{~mJ}$
$=\mathrm{K}$.E. after collison.
$\because$ K.E. before collison $=\mathrm{K}$. E. after collision
$\therefore$ The collision is elastic.
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