Question

A molecule in a gas container hits a horizontal wall with speed 200 \(m\,s^{-1}\) and angle 30° with the normal, and rebounds with the same speed. Is momentum conserved in the collision ? Is the collision elastic or inelastic ?

Answer 1

Given Data

• Speed: \(v = 200\) m/s (before & after)
• Angle with normal: \(30^\circ\)
• Perfect reflection (specular collision)

Before: \(v_x = v \cos 30^\circ\), \(v_y = v \sin 30^\circ\)
WALL
After: \(v_x' = -v \cos 30^\circ\), \(v_y' = v \sin 30^\circ\)

Momentum Analysis

System: molecule + wall (Earth)

$$p_{x,\text{initial}} = m v \cos 30^\circ$$ $$p_{x,\text{final}} = m (-v \cos 30^\circ) + \Delta p_\text{wall}$$ $$\Delta p_\text{wall} = 2 m v \cos 30^\circ$$

Momentum:

YES, conserved (wall absorbs momentum change)

Kinetic Energy Analysis

$$KE_\text{initial} = \frac{1}{2} m v^2$$ $$KE_\text{final} = \frac{1}{2} m v^2$$ $$KE_\text{initial} = KE_\text{final}$$

Collision Type:

ELASTIC (speed unchanged)

Component Breakdown

Component	Before	After	Change
Normal (\(v_x\))	\(+v\cos30^\circ\)	\(-v\cos30^\circ\)	Reverses ✓
Tangential (\(v_y\))	\(+v\sin30^\circ\)	\(+v\sin30^\circ\)	Unchanged ✓
Speed	\(200\) m/s	\(200\) m/s	Same ✓

Physical Insight

• Ideal gas model assumes elastic molecule-wall collisions
• Normal momentum reverses (like 1D elastic collision)
• Tangential momentum unchanged (no friction)
• Pressure = rate of momentum transfer to walls