Pretend that the starship Enterprise in the previous problem is somehow traveling at $c$ with respect to the Earth, and it fires a drone forward at speed $c$ with respect to itself. Use the equation for the relativistic addition of velocities to show that the speed of the drone with respect to the Earth is still $c$.

Why are gravitational waves so difficult to detect?

A star 10 light-years away explodes and produces gravitational waves. How long will it take these waves to reach Earth?

Some heavy nuclei, containing even more protons than the uranium nucleus, undergo "spontaneous fission," splitting apart without absorbing a neutron. Why is spontaneous fission observed only in the heaviest nuclei?

What occurs in the surrounding space when a massive object undergoes a change in its motion?

The isotope of lithium used in a hydrogen bomb is Li-6, whose nucleus contains three protons and three neutrons. When a $\mathrm{Li}-6$ nucleus absorbs a neutron, a nucleus of the heaviest hydrogen isotope, tritium, is produced. What is the other product of this reaction? Which of these two products fuels the explosive reaction?

A starship passes Earth at $80 \%$ of the speed of light and sends a drone ship forward at half the speed of light relative to itself. Show that the drone travels at $93 \%$ of the speed of light relative to Earth.

A passenger on an interplanetary express bus traveling at v=0.99c takes a five-minute catnap, according to his watch. How long does the nap last from your vantage point on a fixed planet?

U- 235 releases an average of $2.5$ neutrons per fission, while Pu-239 releases an average of $2.7$ neutrons per fission. Which of these elements might you therefore expect to have the smaller critical mass?

Assume that all of the following nuclei undergo fission into a pair of equal or nearly equal mass fragments. Using the periodic table, rank from greatest to least the reduction in mass per nucleon for these nuclei after fission. a. Uranium b. Silver c. Gold d. Iron

How can we explain why electrons don't spiral into the attracting nucleus?

What did Benjamin Franklin postulate about electricity?

A typical wavelength of infrared radiation emitted by your body is $25 \mu \mathrm{m}\left(2.5 \times 10^{-5} \mathrm{~m}\right)$. What is the energy per photon of such radiation?

You decide to roll a 0.1-kg ball across the floor so slowly that it will have a small momentum and a large de Broglie wavelength. If you roll it at $0.001 \mathrm{~m} / \mathrm{s}$, what is its wavelength? How does this compare with the de Broglie wavelength of the high-speed electron in the previous problem?