35. Special Relativity

The half-life of a muon at rest is 1.5 μs. Muons that have been accelerated to a very high speed and are then held in a circular storage ring have a half-life of 7.5 μs. What is the total energy of a muon in the storage ring? The mass of a muon is 207 times the mass of an electron.

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?

The sun radiates energy at the rate 3.8 x 10²⁶ W. The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is 2.0 x 10³⁰ kg. Fusion takes place in the core of a star, where the temperature and pressure are highest. A star like the sun can sustain fusion until it has transformed about 0.10% of its total mass into energy, then fusion ceases and the star slowly dies. Estimate the sun's lifetime, giving your answer in billions of years.

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?

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 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?

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

The quantity dE/dv, the rate of increase of energy with speed, is the amount of additional energy a moving object needs per 1 m/s increase in speed. A 25,000 kg rocket is traveling at 0.90c. How much additional energy is needed to increase its speed by 1 m/s?

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 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?

The sun radiates energy at the rate 3.8 x 10²⁶ W. The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is 2.0 x 10³⁰ kg. What percent is this of the sun's total mass?