<< Chapter < Page Chapter >> Page >

A photon decays into an electron-positron pair. What is the kinetic energy of the electron if its speed is 0.992 c size 12{c} {} ?

Answer

KE rel = ( γ 1 ) mc 2 = 1 1 v 2 c 2 1 mc 2 = 1 1 ( 0.992 c ) 2 c 2 1 ( 9.11 × 10 31 kg ) ( 3.00 × 10 8 m/s ) 2 = 5.67 × 10 13 J
Got questions? Get instant answers now!

Test prep for ap courses

A mass of 50 g is completely converted into energy. What is the energy that will be obtained when such a conversion takes place?

Got questions? Get instant answers now!

Show that relativistic kinetic energy becomes the same as classical kinetic energy when v = c .

Relativistic kinetic energy is given as KE rel = ( γ 1 ) m c 2

where γ = 1 1 v 2 c 2

Classical kinetic energy is given as KE class = 1 2 m v 2

At low velocities v = 0 , a binomial expansion and subsequent approximation of γ gives:

γ = 1 + 1 v 2 2 c 2 or γ 1 = 1 v 2 2 c 2

Substituting γ 1 in the expression for KE rel gives

KE rel = [ 1 v 2 2 c 2 ] m c 2 = 1 2 m v 2 = KE class

Hence, relativistic kinetic energy becomes classical kinetic energy when v c .

Got questions? Get instant answers now!

The relativistic energy of a particle in terms of momentum is given by:

  1. E = p 2 c 2 + m 0 2 c 4
  2. E = p 2 c 2 + m 0 4 c 4
  3. E = p 2 c 2 + m 0 2 c 2
  4. E = p 2 c 4 + m 0 2 c 2
Got questions? Get instant answers now!

Section summary

  • Relativistic energy is conserved as long as we define it to include the possibility of mass changing to energy.
  • Total Energy is defined as: E = γmc 2 , where γ = 1 1 v 2 c 2 .
  • Rest energy is E 0 = mc 2 , meaning that mass is a form of energy. If energy is stored in an object, its mass increases. Mass can be destroyed to release energy.
  • We do not ordinarily notice the increase or decrease in mass of an object because the change in mass is so small for a large increase in energy.
  • The relativistic work-energy theorem is W net = E E 0 = γ mc 2 mc 2 = γ 1 mc 2 .
  • Relativistically, W net = KE rel , where KE rel is the relativistic kinetic energy.
  • Relativistic kinetic energy is KE rel = γ 1 mc 2 , where γ = 1 1 v 2 c 2 . At low velocities, relativistic kinetic energy reduces to classical kinetic energy.
  • No object with mass can attain the speed of light because an infinite amount of work and an infinite amount of energy input is required to accelerate a mass to the speed of light.
  • The equation E 2 = ( pc ) 2 + ( mc 2 ) 2 relates the relativistic total energy E and the relativistic momentum p . At extremely high velocities, the rest energy mc 2 becomes negligible, and E = pc .

Conceptual questions

How are the classical laws of conservation of energy and conservation of mass modified by modern relativity?

Got questions? Get instant answers now!

What happens to the mass of water in a pot when it cools, assuming no molecules escape or are added? Is this observable in practice? Explain.

Got questions? Get instant answers now!

Consider a thought experiment. You place an expanded balloon of air on weighing scales outside in the early morning. The balloon stays on the scales and you are able to measure changes in its mass. Does the mass of the balloon change as the day progresses? Discuss the difficulties in carrying out this experiment.

Got questions? Get instant answers now!

The mass of the fuel in a nuclear reactor decreases by an observable amount as it puts out energy. Is the same true for the coal and oxygen combined in a conventional power plant? If so, is this observable in practice for the coal and oxygen? Explain.

Got questions? Get instant answers now!

We know that the velocity of an object with mass has an upper limit of c size 12{c} {} . Is there an upper limit on its momentum? Its energy? Explain.

Got questions? Get instant answers now!

Questions & Answers

what is angular velocity
Obaapa Reply
Why does earth exert only a tiny downward pull?
Mya Reply
hello
Islam
Why is light bright?
Abraham Reply
what is radioactive element
Attah Reply
an 8.0 capacitor is connected by to the terminals of 60Hz whoes rms voltage is 150v. a.find the capacity reactance and rms to the circuit
Aisha Reply
thanks so much. i undersooth well
Valdes Reply
what is physics
Nwafor Reply
is the study of matter in relation to energy
Kintu
a submersible pump is dropped a borehole and hits the level of water at the bottom of the borehole 5 seconds later.determine the level of water in the borehole
Obrian Reply
what is power?
aron Reply
power P = Work done per second W/ t. It means the more power, the stronger machine
Sphere
e.g. heart Uses 2 W per beat.
Rohit
A spherica, concave shaving mirror has a radius of curvature of 32 cm .what is the magnification of a persons face. when it is 12cm to the left of the vertex of the mirror
Alona Reply
did you solve?
Shii
1.75cm
Ridwan
my name is Abu m.konnek I am a student of a electrical engineer and I want you to help me
Abu
the magnification k = f/(f-d) with focus f = R/2 =16 cm; d =12 cm k = 16/4 =4
Sphere
what do we call velocity
Kings
A weather vane is some sort of directional arrow parallel to the ground that may rotate freely in a horizontal plane. A typical weather vane has a large cross-sectional area perpendicular to the direction the arrow is pointing, like a “One Way” street sign. The purpose of the weather vane is to indicate the direction of the wind. As wind blows pa
Kavita Reply
hi
Godfred
what about the wind vane
Godfred
If a prism is fully imersed in water then the ray of light will normally dispersed or their is any difference?
Anurag Reply
the same behavior thru the prism out or in water bud abbot
Ju
If this will experimented with a hollow(vaccum) prism in water then what will be result ?
Anurag
What was the previous far point of a patient who had laser correction that reduced the power of her eye by 7.00 D, producing a normal distant vision power of 50.0 D for her?
Jaydie Reply
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
A young woman with normal distant vision has a 10.0% ability to accommodate (that is, increase) the power of her eyes. What is the closest object she can see clearly?
Jaydie
29/20 ? maybes
Ju
In what ways does physics affect the society both positively or negatively
Princewill Reply
how can I read physics...am finding it difficult to understand...pls help
rerry Reply
try to read several books on phy don't just rely one. some authors explain better than other.
Ju
And don't forget to check out YouTube videos on the subject. Videos offer a different visual way to learn easier.
Ju
hope that helps
Ju
Practice Key Terms 3

Get the best College physics for ap... course in your pocket!





Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics for ap® courses' conversation and receive update notifications?

Ask