Relativistic Energy and Momentum: Part A: A meteorite of mass 1500kg moves with

Question

Relativistic Energy and Momentum:

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

Part B: Compare your answer to Part A with what you would have found had you used the classical expression for momentum p=mv. How do the relativistic and the classical momenta compare?

Part C: What is the total energy E of the meteorite?

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

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

Part F: Compare your answer to Part E with what you would have found if you had used the classical expression for kinetic energy: K=12mv2. How do the relativistic and classical expressions for kinetic energy compare?

HERE'S THE ANSWER!!!!

Explanation / Answer

Solution: Part A: According to the special theory of relativity,

Momentum p = mv = m0v/(1-v2/c2)1/2 where symbols have their usual meaning.

Calculating, p = 4.41 x 1011 kg-m/s.

Part B: considering classical p = mv, the momentum becomes p = 3.15 x 1011 kg-m/s.

Relativistic momentum is more compared to the classical momentum.

Part C: Relativistic total energy can be expressed as E = m0c2/(1-v2/c2)1/2, with symbols having their usual meaning. So, E = 1.89 x 1020 J.

Part D: if the meteorite be at rest, its energy will be E = m0c2 = 1.35 x 1020 J.

Part E: Relativistic energy can be expressed as E2 = m02c4 + p2c2, with symbols having their usual meaning. So, E = 2.71 x 1040 J.

Part F: Considering classical formula, kinetic energy will turn out to be Ek = 3.3 x 1019 J.

Evidently, relativistic kinetic energy is much more colossal than the classical counterpart.

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