An unknown particle is measured to have a negative charge and a speed of $2.24 \times 10^8 \mathrm{~m} / \mathrm{s}$. Its momentum is determined to be $3.07 \times 10^{-22} \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$. Identify the particle by finding its mass.

The Sun radiates energy at a rate of about $4 \times 10^{26} \mathrm{~W}$. How long does it take for the Sun to lose a mass equal to that of Earth?

The Sun radiates energy at a rate of about $4 \times 10^{26} \mathrm{~W}$. At what rate is the Sun's mass decreasing?

If E is the total energy of a particle with zero potential energy, show that dE/dp=v, where p and v are the momentum and velocity of the particle, respectively.

If $E$ is the total energy of a particle with zero potential energy, show that $d E / d p=v$, where $p$ and $v$ are the momentum and velocity of the particle, respectively.

What minimum amount of electromagnetic energy is needed to produce an electron and a positron together? A positron is a particle with the same mass as an electron, but has the opposite charge. (Note that electric charge is conserved in this process.)

A young-looking woman astronaut has just arrived home from a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to him as her son. How might this be possible ?

As a rough rule, anything traveling faster than about $0.1 c$ is called relativistic - that is, special relativity is a significant effect. Determine the speed of an electron in a hydrogen atom (radius $0.53 \times 10^{-10} \mathrm{~m}$ ) and state whether or not it is relativistic. (Treat the electron as though it were in a circular orbit around the proton.)

How many grams of matter would have to be totally destroyed to run a $15~\mathrm{W}$ lightbulb for $1.0$ year?

$(a)$ What is the speed $v$ of an electron whose kinetic energy is $14,000$ times its rest energy? You can state the answer as the difference $c-v$. Such speeds have been reached in the Stanford Linear Accelerator, SLAC. $(b)$ If the electrons travel in the lab through a tube $3.0 \mathrm{~km}$ long (as at SLAC), how long is this tube in the electrons' reference frame? [Hint: Use the binomial expansion.]

What is the speed $v$ of an electron whose kinetic energy is $14,000$ times its rest energy? You can state the answer as the difference $c-v$. Such speeds have been reached in the Stanford Linear Accelerator, SLAC.

What is the speed v of an electron whose kinetic energy is 14,000 times its rest energy? You can state the answer as the difference $c-v$. Such speeds are reached in the Stanford Linear Accelerator, SLAC.

Rocket A passes Earth at a speed of 0.65 c. At the same time, rocket B passes Earth moving 0.85 c relative to Earth in the same direction. How fast is B moving relative to A when it passes A?

A spacecraft (reference frame S') moves past Earth (reference frame S) at velocity $\overrightarrow{\mathbf{v}}$, which points along the x and x' axes. The spacecraft emits a light beam (speed c) along its y' axis as shown in the given figure. Compare these relativistic results to what you would have obtained classically (Galilean transformations).