Question
A molecule in a gas container hits a horizontal wall with speed $200 ms^{-1}$ and angle $30^{\circ}$ with the normal, and rebounds with the same speed. Is momentum conserved in the collision? Is the collision elastic or inelastic?
✓
Answer
Momentum is always conserved in all collisions, hence momentum will be conserved in the given situations
also. Therefore, the molecular speed is the same before and after the collision, hence the kinetic energy will also be conserved. Thus this collison is elastic. If the mass of gas molecule is m and mass of wall is M then total kinetic energy after elasticity is
$\begin{array}{l} E _2=\frac{1}{2} m(200)^2+\frac{1}{2} M \times(0)^2 \\ E _2=2 \times 10^4 m J\end{array}$
Kinetic energy of the molecule before the collison,
$
\begin{array}{l}
E_1=\frac{1}{2} m(200)^2=2 \times 10^4 m J \\
E_1=E_2
\end{array}
$
Hence, the collision is elastic.
also. Therefore, the molecular speed is the same before and after the collision, hence the kinetic energy will also be conserved. Thus this collison is elastic. If the mass of gas molecule is m and mass of wall is M then total kinetic energy after elasticity is
$\begin{array}{l} E _2=\frac{1}{2} m(200)^2+\frac{1}{2} M \times(0)^2 \\ E _2=2 \times 10^4 m J\end{array}$
Kinetic energy of the molecule before the collison,
$
\begin{array}{l}
E_1=\frac{1}{2} m(200)^2=2 \times 10^4 m J \\
E_1=E_2
\end{array}
$
Hence, the collision is elastic.
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