How much energy can be obtained from conversion of 1.0 gram of mass? How much mass could this energy raise to a height of 1.0 km above the Earth’s surface?

An electron moving to the right at 0.90c collides with a positron moving to the left at 0.90c. The two particles annihilate and produce two gamma-ray photons. What is the wavelength of the photons?

At what speed do the relativistic formulas for (a) length and (b) time intervals differ from classical values by 1.00%? (This is a reasonable way to estimate when to use relativistic calculations rather than classical.)

Reference frame S' moves at speed v = 0.88c in the +x direction with respect to reference frame S. The origins of S and S' overlap at t = t' = 0. An object is stationary in S' at position x' = 100m. What is the position of the object in S when the clock in S reads 1.00 μs according to the Galilean?

Two identical particles of mass m approach each other at equal and opposite speeds, v. The collision is completely inelastic and results in a single particle at rest. What is the mass of the new particle? How much energy was lost in the collision? How much kinetic energy was lost in this collision?

The evolution of stars, as discussed in Section 44–2, can lead to a white dwarf, a neutron star, or even a black hole, depending on the mass. (a) Referring to Sections 44–2 and 44–4, give the radius of (i) a white dwarf of 1 solar mass, (ii) a neutron star of 1.5 solar masses, and (iii) a black hole of 3 solar masses. (b) Express these three radii as ratios (r_i : r_ij : r_iii).

We cannot use Hubble’s law to measure the distances to nearby galaxies, because their random motions are larger than the overall expansion. Indeed, the closest galaxy to us, the Andromeda Galaxy, 2.5 million light-years away, is approaching us at a speed of about 130km/s. (a) What is the shift in wavelength of the 656-nm line of hydrogen emitted from the Andromeda Galaxy, as seen by us? (b) Is this a redshift or a blueshift? (c) Ignoring the expansion, how soon will it and the Milky Way Galaxy collide?

Calculate the speed of a proton (m = 1.67 x 10^-27 kg) whose kinetic energy is exactly half its total energy.

Suppose a spacecraft of mass 17,000 kg was accelerated to 0.22c.

(a) How much kinetic energy would it have?

(b) If you used the classical formula for kinetic energy, by what percentage would you be in error?