Lesson Plan

Describe and calculate time dilation using Δt = γΔt₀

Compute the relativistic factor γ and explain when relativistic effects are significant

Describe and calculate length contraction using L = L₀/γ, distinguishing proper length L₀ from L

Explain relativistic momentum p = γmu and why a massive object cannot reach the speed of light

State and apply mass–energy equivalence, E = γmc² (total) and E₀ = mc² (rest energy)

Use mass–energy equivalence to calculate the energy released by a nuclear reaction from a mass defect

10.2

"Time dilation is the phenomenon of time passing more slowly for an observer who is moving relative to another observer." "The relationship between Δt and Δt₀ is given by Δt = γΔt₀, where γ is the relativistic factor given by γ = 1/√(1 − v²/c²)." "The shortening of distance experienced by an observer moving with respect to the points whose distance apart is measured is called length contraction. Proper length, L₀, is the distance between two points measured in the reference frame where the observer and the points are at rest." "Relativistic momentum, p, is classical momentum multiplied by the relativistic factor γ. p = γmu, where m is the rest mass of the object … and γ, as before, is the relativistic factor." "a particle or object of mass m moving at velocity u has relativistic energy given by E = γmc². … Then the rest energy, E₀, is simply E₀ = mc². This is the correct form of Einstein's famous equation." "In general, the nuclei of stable isotopes have less mass then their constituent subatomic particles. The energy equivalent of this difference is called the binding energy of the nucleus. … Expressed as mass, it is called the mass defect."