5.9 Relativistic energy  (Page 7/16)

The Big Bang that began the universe is estimated to have released $10^{68}\text{J}$ of energy. How many stars could half this energy create, assuming the average star’s mass is $4.00\times {10}^{30}\text{kg}$ ?

A supernova explosion of a $2.00\times {10}^{31}\text{kg}$ star produces $1.00\times {10}^{44}\text{J}$ of energy. (a) How many kilograms of mass are converted to energy in the explosion? (b) What is the ratio $\text{Δ}m\text{/}m$ of mass destroyed to the original mass of the star?

(a) Using data from Potential Energy of a System , calculate the mass converted to energy by the fission of 1.00 kg of uranium. (b) What is the ratio of mass destroyed to the original mass, $\text{Δ}m\text{/}m?$

(a) Using data from Potential Energy of a System , calculate the amount of mass converted to energy by the fusion of 1.00 kg of hydrogen. (b) What is the ratio of mass destroyed to the original mass, $\text{Δ}m\text{/}m$ ? (c) How does this compare with $\text{Δ}m\text{/}m$ for the fission of 1.00 kg of uranium?

There is approximately $10^{34}\text{J}$ of energy available from fusion of hydrogen in the world’s oceans. (a) If $10^{33}\text{J}$ of this energy were utilized, what would be the decrease in mass of the oceans? (b) How great a volume of water does this correspond to? (c) Comment on whether this is a significant fraction of the total mass of the oceans.

A muon has a rest mass energy of 105.7 MeV, and it decays into an electron and a massless particle. (a) If all the lost mass is converted into the electron’s kinetic energy, find $\gamma$ for the electron. (b) What is the electron’s velocity?

A $\pi$ -meson is a particle that decays into a muon and a massless particle. The $\pi$ -meson has a rest mass energy of 139.6 MeV, and the muon has a rest mass energy of 105.7 MeV. Suppose the $\pi$ -meson is at rest and all of the missing mass goes into the muon’s kinetic energy. How fast will the muon move?

(a) Calculate the relativistic kinetic energy of a 1000-kg car moving at 30.0 m/s if the speed of light were only 45.0 m/s. (b) Find the ratio of the relativistic kinetic energy to classical.

Alpha decay is nuclear decay in which a helium nucleus is emitted. If the helium nucleus has a mass of $6.80\times {10}^{\mathrm{-27}}\text{kg}$ and is given 5.00 MeV of kinetic energy, what is its velocity?

(a) Beta decay is nuclear decay in which an electron is emitted. If the electron is given 0.750 MeV of kinetic energy, what is its velocity? (b) Comment on how the high velocity is consistent with the kinetic energy as it compares to the rest mass energy of the electron.

(a) At what relative velocity is $\gamma =1.50?$ (b) At what relative velocity is $\gamma =100?$

(a) At what relative velocity is $\gamma =2.00?$ (b) At what relative velocity is $\gamma =10.0?$

Unreasonable Results (a) Find the value of $\gamma$ required for the following situation. An earthbound observer measures 23.9 h to have passed while signals from a high-velocity space probe indicate that 24.0 h have passed on board. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?