Lesson 5.4 - Mass and Energy

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SO FAR

Effect of Relativistic speed on a time interval:


Effect of Relativistic speed on a length interval:


AND ALSO!

Effect of Relativistic speed on a Mass:


As an object's speed increases, its mass when viewed from a moving frame of reference increases by the factor of \( \gamma \)


RECALL:

Law of Convervation of Mass:

Question: So where does this additional mass come from?

Note that this is the relativistic mass, not rest mass, \(m_o\).

As we increase the speed of an object, we are giving it kinetic energy that is no longer distinguishable from the object's mass.



EXAMPLE PROBLEM #1

A neutron has a measured mass of \(1.71 \times 10^{-27} kg\). Determine its speed.

SOLUTION:

MASS/ENERGY EQUIVALENCE

Due to the famous equation \(E=mc^2\) we have a precise way of expressing the relationship between rest mass and energy. This is why most subatomic particle masses are listed in \(MeV/c^2\) instead of \(kg\).


ELECTRON POSITRON ANNIHILATION

After a \( \beta ^+ \) event a positron is produced. After a very short time it interacts with an electron and they annihilate each other (matter-antimatter annihilation).

To conserve mass-energy, two 511keV gamma rays are produced travelling in opposite directions to conserve momentum.


EXAMPLE PROBLEM #2

The Large Hadron Collider accelerates protons to 6.8 TeV. How fast are they travelling?

SOLUTION:



最后修改: 2025年06月28日 星期六 19:36