The time dilation effect is sometimes expressed as "moving clocks run slowly." Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then does it deal with?

At what speed do the relativistic formulas for length and time intervals differ from classical values by $1.00$ percent? (This is a reasonable way to estimate when to do relativistic calculations rather than classical.)

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?

Suppose you decide to travel to a star 90 lightyears away. How fast would you have to travel so the distance would be only $25$ light-years?

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

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 rest mass.

A farm boy studying physics believes that he can fit a 15.0-m-long pole into a $12.0$-m-long barn if he runs fast enough (carrying the pole). Can he do it? Explain in detail. How does this fit with the idea that when he is running the barn looks even shorter than $12.0$ m?

A healthy astronaut's heart rate is $60$ beats$/ \mathrm{min}$. Flight doctors on Earth can monitor an astronaut's vital signs remotely while in flight. How fast would an astronaut be flying away from Earth if the doctor measured her having a heart rate of $25$ beats$/ \mathrm{min}$ ?

According to the special theory of relativity, the factor $\gamma$ that determines the length contraction and the time dilation is given by $\gamma=1 / \sqrt{1-v^2 / c^2}$. Determine the numerical values of $\gamma$ for an object moving at speed $v=0.01 c, 0.05 c, 0.10 c, 0.20 c, 0.30 c, 0.40 c, 0.50 c, 0.60 c,$ $0.70 c, 0.80 c, 0.90 c, 0.95 c,$ and $0.99 c$. Make a graph of $\gamma$ versus $v$.

Two protons, each having a speed of 0.935c in the laboratory, are moving toward each other. Determine (a) the momentum of each proton in the laboratory, (b) the total momentum of the two protons in the laboratory, and (c) the momentum of one proton as seen by the other proton.

The nearest star to Earth is Proxima Centauri, $4.3$ lightyears away. A spacecraft travels from Earth to reach the star in $4.9$ years, as measured by travelers on the spacecraft. How long does the trip take according to Earth observers?

What is the percentage increase in the mass of a car traveling 110 km/h as compared to at rest?

A negative muon traveling at 33 % the speed of light collides head on with a positive muon traveling at 50% the speed of light. The two muons (each of rest mass $105.7 \mathrm{MeV} / \mathrm{c}^{2})$ annihilate, and produce how much electromagnetic energy?

What minimum amount of electromagnetic energy is needed to produce an electron and a positron together? A positron is a particle with the same rest mass as an electron, but has the opposite charge.