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?

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.]

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?

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?

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.

The Sun radiates energy at a rate of about $4 \times 10^{26} \mathrm{W}$. Estimate how long the Sun could last if it radiated constantly at this rate.

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?

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?

An electron $(m=9.11 \times 10^{-31} \mathrm{kg})$ enters a uniform magnetic field B = 1.8 T, and moves perpendicular to the field lines with a speed v = 0.92 c. What is the radius of curvature of its path?

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.

How many grams of matter would have to be totally destroyed to run a 100-W lightbulb for 1 year?