Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total...

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Chapter 37 Special Relativity (Momentum and Energy)

Transcript of Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total...

Page 1: Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very.

Chapter 37Special Relativity

(Momentum and Energy)

Page 2: Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very.

Relativistic Momentum

Page 3: Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very.

Relativistic EnergyAn object of mass m moving at velocity v has a total energy given by:

Recall that γ≥1 and c is a very very big number, this means that in general E is a huge number.

Page 4: Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very.

Rest EnergyThe relativistic energy given earlier E=γmc2 has a strange implication:• When an object is at rest (v =0), this gives γ =1.

However the energy is still non-zero.• This means an object with mass always carries non-

zero amount of “intrinsic” energy even when not in motion. This energy is call the rest energy.

Einstein’s most famous equation.We sometimes write E0 instead of E to emphasize it is the energy at rest although it is actually just a special case of E.

Page 5: Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very.

An exploding chickenCalculate the total energy released if a 1kg chicken is converted into energy completely.

Page 6: Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very.

Common unit: eV for Energy

J is the SI unit for energy, however in particle physics (where relativity is used most frequently) we often use another more convenient unit, the electron volts (eV), because the energy in particle physics is often very small.

Page 7: Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very.

Common unit: eV/c for Momentum

Page 8: Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very.

Energy of a speedy proton 1

Find the rest energy of a proton in electron volts.

Page 9: Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very.

Energy of a speedy proton 2

The total energy of a proton is three times its rest energy. What is the speed of the proton?

Page 10: Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very.

Electron mass in MeVGiven the mass of the electron is 0.511MeV, find its mass in kg.

Page 11: Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very.

Relativistic Kinetic energy

The KE is the difference between the total energy and the rest energy. Another way is to write it as:

E =E0 +KE

Page 12: Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very.

Newtonian limit of KE

Please remember that the above result is only true at very low speed.

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Energy of a speedy proton 3

The total energy of a proton is three times its rest energy. What is the KE of the proton?

Page 14: Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very.

Energy Summary

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Momentum and Energy

This equation is often useful in computing either energy or momentum of an object when the velocity is not given explicitly.

Page 16: Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very.

Energy of a speedy proton 4

The total energy of a proton is three times its rest energy. What is the momentum of the proton?

Page 17: Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very.

Velocity From p and E

Page 18: Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very.

Doppler Effect

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General Relativity

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Testing General Relativity

General relativity predicts that a light ray passing near the Sun should be deflected in the curved space-time created by the Sun’s mass

The prediction was confirmed by astronomers during a total solar eclipse

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Precession of Mercury

Newtonian theory (after taking into account things such as the gravitational forces from the other planets, the non-spherical shape of the sun…) differs from observation by 43 arc second (43’’ = 0.012°) per century.This tiny difference is perfectly explained in the general theory of relativity.

Page 22: Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very.

Black Holes If the concentration of

mass becomes very great, a black hole may form

In a black hole, the curvature of space-time is so great that, within a certain distance from its center, all light and matter become trapped

Page 23: Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very.

Expansion of Universe

The cosmological constant

“The greatest blunder of my life.”Einstein

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Experimental Tests of Relativity

• Muon decay• Clocks flying around the world• Clocks on a tower• GPS• The bending of starlight• Gravitational radiation of binary stars• Particle accelerators• Compton effect… and many many more

Page 25: Relativistic Momentum Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very.
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