Relativity, Light Speed & Model Limits — Practice · Grade 12 Science

Chapter: Modern Physics

What this practice covers

By the end of Relativity, Light Speed & Model Limits you should be able to:

8 questions, numeric and written answer, each with a worked explanation.

Vocabulary used: inertial frame, proper time, Lorentz factor.

Problem 1

Proper time 4 s andγ=2. Find dilated interval.
Hints

Write the relationship first; substitute with consistent units.

Answer and explanation

8 s

2×4=8.

Problem 2

Why does Newtonian mechanics work well for walking-speed motion?
Answer and explanation

v/c is very small, so relativistic corrections are negligible for ordinary precision.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 3

A proper interval is 12 s and γ=1.25. Find other-frame interval.
Hints

List the given quantities, select a relationship, and check units before substituting.

Answer and explanation

15 s

1.25×12=15.

Problem 4

Does a photon’s zero rest mass mean zero energy?
Answer and explanation

No. Its energy is hf and its momentum E/c.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 5

Find γ for v=0.80c. Show the reasoning, not just the conclusion.
Hints

Specify which events and clock define proper time.

Answer and explanation

1/√0.36=1/0.6≈1.67.

Problem 6

Why is classical mechanics often adequate for everyday speeds?
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

When v is much smaller than c, relativistic corrections are extremely small within ordinary measurement precision.

Problem 7

Length contraction uses simultaneous endpoint positions in one frameLength contraction uses simultaneous endpoint positions in one frameRest length L₀=10 mAt0.60c: L=L₀/γ=8 mMoving-frame endpoints must be measured simultaneously.
Original rest/moving length schematic for parallel motion, not a literal visual photograph.
Interpret the supplied visual. Why is an ordinary photograph not automatically a direct length-contraction measurement?
Answer and explanation

Its image combines light emitted at different times and travel paths; simultaneous endpoint coordinates need separate reconstruction.

Proper length L₀ is measured in the object’s rest frame. An inertial frame where it moves parallel to its length measures L=L₀/γ, using endpoint positions at the same time in that measuring frame. The apparent photograph is a different problem because light from different parts can arrive after different travel times. Only the motion-parallel component contracts in this simple comparison; the object is not described as mechanically crushed by motion.

Its image combines light emitted at different times and travel paths; simultaneous endpoint coordinates need separate reconstruction.

Response criteria

  • Interpret labels, structures, axes, units and directions correctly.
  • Explain the physical or environmental relationship or mechanism.
  • Respect stated assumptions and distinguish observation from inference.

Problem 8

A process has proper duration 3.0 μs and moves at 0.80c relative to a lab. Find γ and lab duration; a rest 10 m object moving parallel at that speed has what lab length?
Answer and explanation

γ=1/√0.36=5/3. Lab duration=5.0 μs; length=10/(5/3)=6.0 m, with simultaneous endpoints in the lab.

γ=1/√0.36=5/3.

Lab duration=5.0 μs; length=10/(5/3)=6.0 m, with simultaneous endpoints in the lab.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

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