Relativistic Energy and Momentum Learning Goal: To learn to calculate energy and

Question

Relativistic Energy and Momentum

Learning Goal:

To learn to calculate energy and momentum for relativistic particles and to find relations among a particle's energy, momentum, and mass.

The first postulate of relativity states that all laws of physics are the same in every inertial frame of reference. Consequently, fundamental laws such as the conservation of momentum and the conservation of energy must also be valid in every inertial frame of reference. This required the introduction of new definitions of momentum and energy.

Consider a particle whose mass at rest is m. When the particle moves with velocity v? , its relativistic momentum p?  and energy E are given by

p? =mv? 1?v2c2?

and

E=mc21?v2c2?.

Moreover, the relativistic kinetic energy of the particle is given by K=E?mc2. The quantity mc2 is called rest energy and represents the energy of the particle associated with

A meteorite of mass 1500kg moves with a speed of 0.700c . Find the magnitude of its momentum p.

Express your answer in kilograms times meters per second to three significant figures.

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Part B

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Part C

What is the total energy E of the meteorite?

Express your answer in joules to three significant figures.

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Part D

What would the energy of the meteorite be if it were at rest?

Express your answer in joules to three significant figures.

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Part E

What is the relativistic kinetic energy K of the meteorite when it travels at 0.700c ?

Express your answer in joules.

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Part F

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Explanation / Answer

a) p = gamma m v = 1500*0.7*3.0E8/sqrt(1- 0.7^2)= 4.41E11

c) E = gamma mc^2 = 1500*3.0E8^2/sqrt(1- 0.7^2)= 1.89E20 J

d) E = mc^2 = 1500*3.0E8^2= 1.35E20

e) KE = E- mc^2 = 1.89E20 -1.35E20 = 0.54E20 = 5.40E19 J

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