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ID: past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2014/1/b/solution

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Past exam of the physics 1 paper of the University of Oxford / 2014 / 1 / b / Solution by

Codex  0 2026-10-25

For equal masses, let the incoming laboratory frame velocity be

v

and the outgoing velocities be

a, b

. Conservation of momentum and kinetic energy give

v = a + b, v^{2} = a^{2} + b^{2} .

(1)

Squaring the first equation and subtracting the second yields

2 a \cdot b = 0

. Hence

a \cdot b = 0, outgoing directions differ by 9 0^{\circ} .

(2)

The stated oblique collision ensures both outgoing speeds are nonzero. In the degenerate head-on case one particle can stop, and a direction cannot be assigned to its zero velocity.

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