1.8 Relativistic Mechanics

Irodov Problems 1.340 to 1.388.

49problems
110figures
Difficulty2.7avgDifficulty: 2 rated 1, 20 rated 2, 20 rated 3, 7 rated 4, 0 rated 5; mean 2.7.
Uniqueness3.1avgUniqueness: 2 rated 1, 9 rated 2, 20 rated 3, 17 rated 4, 1 rated 5; mean 3.1.

No.	Title	Difficulty	Uniqueness	Methods
1.340	Small Contraction, Not Small Speed	Difficulty 1 of 5	Uniqueness 1 of 5	length contraction · approximation expansion · limiting cases
1.341	Each Side Shrinks by Its Angle	Difficulty 3 of 5	Uniqueness 3 of 5	length contraction · vector decomposition · limiting cases
1.342	Only One Leg of the Rod Shrinks	Difficulty 2 of 5	Uniqueness 3 of 5	length contraction · vector decomposition · lorentz transformation
1.343	Only the Height Is Contracted	Difficulty 3 of 5	Uniqueness 3 of 5	length contraction · vector decomposition · limiting cases
1.344	How Fast to Lose Two Percent	Difficulty 1 of 5	Uniqueness 1 of 5	time dilation · frames of reference · limiting cases
1.345	Two Timings Fix One Proper Length	Difficulty 2 of 5	Uniqueness 3 of 5	length contraction · time dilation · frames of reference
1.346	The Lifetime Ratio Is Gamma	Difficulty 2 of 5	Uniqueness 2 of 5	time dilation · invariant interval · frames of reference
1.347	The Muon Sees a Shorter Distance	Difficulty 2 of 5	Uniqueness 3 of 5	time dilation · length contraction · frames of reference
1.348	One Clock Times a Contracted Gap	Difficulty 2 of 5	Uniqueness 2 of 5	length contraction · time dilation · frames of reference
1.349	Two Simultaneities, Two Lengths, One Rod	Difficulty 3 of 5	Uniqueness 4 of 5	length contraction · lorentz transformation · frames of reference
1.350	Two Rods, One Clock, One Gap	Difficulty 4 of 5	Uniqueness 4 of 5	length contraction · relative motion · frames of reference
1.351	Simultaneous for Them, Not for Us	Difficulty 3 of 5	Uniqueness 3 of 5	lorentz transformation · length contraction · frames of reference
1.352	Two Marks Made at Two Different Times	Difficulty 3 of 5	Uniqueness 4 of 5	length contraction · frames of reference · lorentz transformation
1.353	Each Rod Sees the Other Lag	Difficulty 3 of 5	Uniqueness 4 of 5	time dilation · length contraction · lorentz transformation · frames of reference
1.354	Same Moment, Two Different Answers	Difficulty 3 of 5	Uniqueness 4 of 5	lorentz transformation · frames of reference · length contraction
1.355	The Point Where Both Clocks Agree	Difficulty 3 of 5	Uniqueness 4 of 5	lorentz transformation · frames of reference · limiting cases
1.356	No Boost Outruns a Cause	Difficulty 3 of 5	Uniqueness 4 of 5	lorentz transformation · frames of reference · invariant interval
1.357	The Interval Answers Both Questions	Difficulty 3 of 5	Uniqueness 4 of 5	invariant interval · lorentz transformation · frames of reference
1.358	The Transverse Component Changes Too	Difficulty 2 of 5	Uniqueness 2 of 5	lorentz transformation · frames of reference · vector decomposition
1.359	The Gap Closes Faster Than Anything Moves	Difficulty 2 of 5	Uniqueness 4 of 5	relative motion · frames of reference · lorentz transformation
1.360	Compose the Speeds, Then Contract	Difficulty 3 of 5	Uniqueness 3 of 5	length contraction · lorentz transformation · relative motion
1.361	Pythagoras Loses a Relativistic Term	Difficulty 2 of 5	Uniqueness 3 of 5	lorentz transformation · relative motion · vector decomposition
1.362	Two Gammas Multiply Across the Boost	Difficulty 3 of 5	Uniqueness 3 of 5	lorentz transformation · time dilation · frames of reference
1.363	The Angle a Boost Bends	Difficulty 2 of 5	Uniqueness 2 of 5	lorentz transformation · frames of reference · vector decomposition · relative motion
1.364	A Rod Tilted by Disagreeing Clocks	Difficulty 4 of 5	Uniqueness 4 of 5	lorentz transformation · length contraction · frames of reference
1.365	The Clock Transforms Too	Difficulty 4 of 5	Uniqueness 3 of 5	lorentz transformation · frames of reference · calculus of motion
1.366	A Year at Ten Gravities	Difficulty 4 of 5	Uniqueness 3 of 5	relativistic dynamics · differential equation · frames of reference · approximation expansion
1.367	The Crew Ages Only Logarithmically	Difficulty 3 of 5	Uniqueness 4 of 5	time dilation · relativistic dynamics · calculus of motion
1.368	Inertia from the Square Root's Edge	Difficulty 2 of 5	Uniqueness 2 of 5	relativistic dynamics · approximation expansion
1.369	Rest Mass over a Shrinking Box	Difficulty 2 of 5	Uniqueness 3 of 5	length contraction · relativistic dynamics
1.370	Half a Percent Short of Light	Difficulty 2 of 5	Uniqueness 2 of 5	relativistic dynamics · invariant interval · approximation expansion
1.371	The Excess Factor Is Just Gamma	Difficulty 2 of 5	Uniqueness 2 of 5	relativistic dynamics · limiting cases
1.372	The Same Two Tenths of c Cost Three Times More	Difficulty 2 of 5	Uniqueness 3 of 5	work energy · relativistic dynamics · approximation expansion
1.373	Where Motion Doubles a Particle's Energy	Difficulty 2 of 5	Uniqueness 2 of 5	relativistic dynamics · limiting cases
1.374	How Slow Is Slow Enough	Difficulty 3 of 5	Uniqueness 4 of 5	relativistic dynamics · approximation expansion · limiting cases
1.375	Momentum from Kinetic Energy Alone	Difficulty 2 of 5	Uniqueness 3 of 5	relativistic dynamics · invariant interval · limiting cases
1.376	Momentum and Energy per Unit Time	Difficulty 2 of 5	Uniqueness 2 of 5	momentum flux · relativistic dynamics · limiting cases
1.377	Both Frames Agree on the Pressure	Difficulty 4 of 5	Uniqueness 4 of 5	momentum flux · length contraction · frames of reference · relativistic dynamics
1.378	Momentum Grows Forever, Speed Saturates	Difficulty 2 of 5	Uniqueness 3 of 5	relativistic dynamics · impulse · calculus of motion · limiting cases
1.379	Hyperbolic Motion Hides a Constant Force	Difficulty 3 of 5	Uniqueness 3 of 5	relativistic dynamics · calculus of motion · limiting cases
1.380	Two Inertias, One Rest Mass	Difficulty 3 of 5	Uniqueness 4 of 5	relativistic dynamics · vector decomposition · limiting cases
1.381	Energy and Momentum Are One Vector	Difficulty 3 of 5	Uniqueness 4 of 5	lorentz transformation · four vectors · relativistic dynamics · invariant interval
1.382	Chasing a Photon Lowers Its Energy	Difficulty 2 of 5	Uniqueness 3 of 5	lorentz transformation · relativistic doppler · four vectors
1.383	Every Frame Agrees on Rest Mass	Difficulty 2 of 5	Uniqueness 3 of 5	relativistic dynamics · invariant interval · four vectors
1.384	The Frame Where Momentum Vanishes	Difficulty 3 of 5	Uniqueness 3 of 5	relativistic dynamics · invariant interval · frames of reference · collisions
1.385	Sticking Together Creates New Rest Mass	Difficulty 3 of 5	Uniqueness 3 of 5	relativistic dynamics · four vectors · collisions · momentum conservation
1.386	The Price of a Stationary Target	Difficulty 3 of 5	Uniqueness 4 of 5	relativistic dynamics · invariant interval · frames of reference · collisions
1.387	When the Other Two Move Together	Difficulty 4 of 5	Uniqueness 4 of 5	relativistic dynamics · invariant interval · optimization · momentum conservation
1.388	The Rocket Adds Rapidity Not Speed	Difficulty 4 of 5	Uniqueness 5 of 5	variable mass · relativistic dynamics · lorentz transformation · differential equation