Q87 · Practice questionComplex familiar4 marks
QUESTION 87 (4 marks)
The graph shows classical and relativistic momentum as speed approaches . Analyse the graph and explain why a massive particle cannot be accelerated to the speed of light.
WORKED SOLUTION
4 marksPractice marking scheme
ANSWER
Classical and relativistic predictions are similar at low speed but diverge at high speed. Relativistic momentum grows without bound as , so reaching would require unbounded energy/momentum.
Worked solution
At low , , so and the two curves nearly coincide. At high speed, rises rapidly, so relativistic momentum exceeds the classical value. As approaches , the denominator tends to zero and tends to infinity. A massive particle would therefore require unbounded momentum and energy to reach , so it cannot be accelerated to the speed of light.
Compares curves at low speed.
Identifies divergence at high speed.
Links divergence to gamma.
Explains why c cannot be reached by massive particle.
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