Chapter 2: Special Relativity

Using equations (2-20), show that

${{\mathit{y}}^{\mathbf{\text{'}}}}_{\mathbf{u}}\mathbf{=}\left(1-\frac{u_{x}v}{c^2}\right){\mathit{y}}_{\mathbf{v}}\mathbf{,}{\mathit{y}}_{\mathbf{u}}$

By applying the relativistic velocity transformation to the left side of equation (2 - 23) and using the algebraic identity derived in Exercise 67, verify equation (2 - 23).

What is the ratio of the relativistically correct expression for momentum to the classical expression? Under what condition does the deviation become significant?

In the twin paradox situation, a fellow student objects to the argument that Anna's acceleration is the root of the asymmetry. "All motion is relative! Anna is accelerating relativetoBob, but Bob is accelerating relative to Anna" Answer this objection.

What are the momentum, energy, and kinetic energy of a proton moving at 0.8c?

What would be the internal energy, kinetic energy, and total energy of a 1 kg block moving at 0.8c?

By how much (in picograms) does the mass of 1 mol of ice at $\mathbf{0}\mathbf{°}\mathbf{C}$differ from that of 1 mol of water at 0°C?

A spring has a force constant 18 N/m. If it is compressed 50 cm from its equilibrium length, how much mass will it have gained?

A typical household uses 500 kWh of energy in I month. How much mass is convened to produce this energy?

Determine the momentum of an electron moving (a) at speed $\mathbf{2}\mathbf{.}\mathbf{4}\mathbf{\times }{\mathbf{10}}^{\mathbf{4}}$m/s (about three times escape velocity) and (b) at speed $\mathbf{2}\mathbf{.}\mathbf{4}\mathbf{\times }{\mathbf{10}}^{\mathbf{8}}$m/s. (c) In each case by how much is the classical formula in error?