35. Special Relativity

How did Einstein reconcile the idea that motion is relative with the observation that the speed of light $c$ is constant in all inertial frames?

You are a passenger on a spaceship. As the speed of the spaceship increases and approaches the speed of light, which of the following effects would you observe according to special relativity?

Suppose there is an astronaut who is traveling at a significant fraction of the speed of light $c$ relative to Earth. According to special relativity, which of the following effects would the astronaut experience compared to an observer at rest on Earth?

Which of the following statements is true concerning special relativity?

A newspaper delivery boy is riding his bicycle down the street at 5.0 m/s. He can throw a paper at a speed of 8.0 m/s. What is the paper's speed relative to the ground if he throws the paper (a) forward, (b) backward, and (c) to the side?

A baseball pitcher can throw a ball with a speed of 40 m/s. He is in the back of a pickup truck that is driving away from you. He throws the ball in your direction, and it floats toward you at a lazy 10 m/s. What is the speed of the truck?

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?

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?

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).