Unit 9 · Problem 1
ap2-u09-q01
10 points
Show problem
Two-dimensional collisions and a pressure reading
Two identical ideal-gas atoms each have mass 4.0 × 10⁻²⁶ kg. Atom A initially has velocity (300, 400) m/s in the (x,y) plane; atom B is initially at rest. After their elastic collision, A has velocity (300, 0) m/s. Later, A hits a smooth wall perpendicular to x and rebounds. Treat the wall as fixed.
Find B’s velocity after the atom–atom collision and check that the supplied outcome is elastic.
Find the impulse delivered to the wall by one atom A. If 5.0 × 10²² equivalent collisions occur per second over area 0.040 m², find average pressure.
A student says pressure is zero away from the container walls because no wall is present there. Evaluate the claim.
Part a 3 points
| Criterion | Points |
|---|---|
a1 Sets up momentum conservation separately in x and y for the isolated two-atom system. | 1 |
a2 Calculates B’s final velocity as (0, +400) m/s. | 1 |
a3 Checks that initial and final total kinetic energies both equal one half of m times (300² + 400²), confirming elasticity. | 1 |
Part b 4 points
| Criterion | Points |
|---|---|
b1 Uses reversal of A’s normal momentum to obtain a wall impulse of magnitude 2m(300 m/s), opposite the atom’s impulse. | 1 |
b2 Calculates the wall impulse as 2.4 × 10⁻²³ N·s in the +x direction. | 1 |
b3 Multiplies impulse per collision by 5.0 × 10²² collisions/s to obtain an average normal force of 1.2 N. | 1 |
b4 Calculates pressure from normal force divided by 0.040 m² as 30 Pa. | 1 |
Part c 3 points
| Criterion | Points |
|---|---|
c1 States that the claim is false and pressure is nonzero in the gas interior. | 1 |
c2 Explains that atoms transfer normal momentum to an imagined surface or sensor inside the gas. Do not award for
| 1 |
c3 Explains that equal opposing face forces can cancel the net force without making pressure on either face zero. | 1 |