Chapter Questions
Looking at the javelin thrower in Figure 53.1 , would the effect of special relativity as observed by a bystander result in a speed for the javelin slower than Galilean relativity would predict, or faster? Explain.
What is the Lorentz factor for a spaceship traveling at $0.5 \mathrm{c}$ ?
Assuming that the Lorentz factor becomes significant if it affects measured lengths and times at the $10 \%$ level (a Lorentz factor value of 1.1 ), how fast must the observed speed of an object be to reach this threshold?
What speed would give a Lorentz factor of about 1 million $\left(10^{6}\right) ?$
The Earth is traveling at about $30 \mathrm{km} / \mathrm{sec}$ as it orbits the Sun.a. How much more slowly does time run on the Earth than in the Sun's rest frame?b. Why will the time be measured as slower on the Earth than in the Sun's rest frame? (Why is it not "just relative"?)
Suppose a 1 -gram paperclip struck a spaceship at $99 \%$ of the speed of light. Special relativity indicates that the paperclip's energy goes from $\gamma \times m c^{2}$ and drops down to its "rest mass energy" of $m c^{2}$ once it stops moving.a. How much energy is released in the collision?b. How much energy is this in kilotons of TNT?
How fast must a spacecraft travel to reach the center of our Galaxy $(26,000 \text { ly away) in } 100$ years "ship time"?