When two moles of hydrogen and one mole of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elements decrease in this reaction? What % of the total original mass of the system does this mass change represent?

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

The Sun radiates energy at a rate of about $4\times1026$ W. (a) At what rate is the Sun's mass decreasing? (b) How long does it take for the Sun to lose a mass equal to that of Earth? (c) Estimate how long the Sun could last if it radiated constantly at this rate.

A certain galaxy has a Doppler shift given by $f_0-f=0.1015 f_0$. Estimate how fast it is moving away from us.

(II) A certain galaxy has a Doppler shift given by $f_0-f=0.697 f_0$, How fast is it moving away from us?

How much energy can be obtained from conversion of 1.0 gram of mass? How much mass could this energy raise to a height of $100$ m?

How much energy can be obtained from conversion of 1.0 gram of mass? How much mass could this energy raise to a height of 0.25 km above the Earth's surface?

(II) An unstable particle is at rest and suddenly decays into two fragments. No external forces act on the particle or its fragments. One of the fragments has a speed of $0.60 \mathrm{c}$ and a mass of $6.68 \times 10^{-27} \mathrm{~kg}$, while the other has a mass of $1.67 \times 10^{-27} \mathrm{~kg}$. What is the speed of the less massive fragment?

An unstable particle is at rest and suddenly decays into two fragments. No external forces act on the particle or its fragments. One of the fragments has a speed of $0.53 \mathrm{c}$ and a mass of $6.68 \times 10^{-27} \mathrm{~kg}$, while the other has a mass of $1.67 \times 10^{-27} \mathrm{~kg}$. What is the speed of the less massive fragment?

(II) $(a)$ A particle travels at $v=0.10 c$. By what percentage will a calculation of its momentum be wrong if you use the classical formula?

A particle travels at $v=0.10 c$. By what percentage will a calculation of its momentum be wrong if you use the classical formula?

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?

Two protons, each having a speed of $0.990 c$ in the laboratory, are moving toward each other. Determine the momentum of one proton as seen by the other proton.