An astronaut on a spaceship traveling at 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats his lunch in 23 min. How long does the astronaut's lunch take to eat according to observers on Earth?

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 to him than 12.0 m?

An electron is accelerated so that its kinetic energy is greater than its rest energy $m_{0} c^{2}$ by a factor of 999. What is the speed of the electron in each case?

An electron is accelerated so that its kinetic energy is greater than its rest energy $m_{0} c^{2}$ by a factor of 5.00. What is the speed of the electron in each case?

The fictional starship Enterprise obtains its power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise is approximately $5 \times 10^{9} \mathrm{kg},$ how much mass must be converted into kinetic energy to accelerate it from rest to one-tenth the speed of light?

Show analytically that a particle with momentum p and energy E has a speed given by $v=\frac{p c^{2}}{E}=\frac{p c}{\sqrt{m_{0}^{2} c^{2}+p^{2}}}$

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

Two protons, each having a speed of 0.935c in the laboratory, are moving toward each other. Determine the total momentum of the two protons in the laboratory.

Two protons, each having a speed of 0.935c in the laboratory, are moving toward each other. Determine the momentum of each proton in the laboratory.

What is the percentage increase in the (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binomial expansion.]

In an Earth reference frame, a star is 82 light-years away. How fast would you have to travel so that to you the distance would be only 35 light-years?

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?

How much energy would be required to break a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the total binding energy of the $\frac{4}{2}$He nucleus.)

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.