Physics Lesson 20.2.2 - Mass - Energy Equivalence

Please provide a rating, it takes seconds and helps us to keep this resource free for all to use

Welcome to our Physics lesson on Mass - Energy Equivalence, this is the second lesson of our suite of physics lessons covering the topic of Nuclear Forces, Defect of Mass and Binding Energy, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Mass - Energy Equivalence

Consider an object of mass m moving linearly at a very high uniform speed, very close to the speed of light. Obviously, we denote this speed by c. Since the speed is uniform, there is a constant force F acting on the object during its motion. As a result, an energy E and momentum p are induced in the object, where

and

Here, d represents the distance travelled by the object during the process. We have used the scalar versions of formulae as we assumed the motion as linear.

Giving that the momentum gained during the process is equal to the impulse of object, we have

where t is the duration of moving process. Thus, rearranging the last formula for F and substituting it in the first formula, we obtain

Thus, we obtain

This is the famous equation of mass-energy equivalence, introduced by Einstein. It implies that, despite the total mass of a system may change, the total energy and momentum remain constant. For example, if an electron and a proton collide with each other, this process destroys the mass of both particles but generates a large amount of energy in the form of photons. Now, you understand where does the m₀ · c² term discussed in article 18.6 when dealing with relativistic energy comes from. To avoid confusion we denoted this energy by ε instead of E and explained that it represents the stored energy in the object when it is at rest (we called it rest energy).

As you know, there are other forms of energy than just the rest energy and the kinetic energy. There is heat energy, chemical energy, binding energies of atoms and nuclei, etc. It turns out that all forms of energy are reflected in the total mass of the body. So although we have justified E = mc² in terms of the kinetic energy, the mass-energy equivalence is quite a bit more general.

Example 1

How much energy a 200 g apple at rest would release if it was totally destroyed (not existed anymore)?

Solution 1

Clues:

m = 200 g = 0.2 kg
c = 300 000 km/s = 3 × 10⁸ m/s
E = ?

The problem implies that the entire mass of the apple converts to energy. From the formula of mass-energy equivalence

we obtain after substitutions:

This value is enormous; it is 30 times greater than the energy released during the atomic bombing of Hiroshima (6 × 10¹⁴ J). However, it is not easy to convert mass into energy; this process requires very special appliances and the cost of this operation is extremely high.

You have reached the end of Physics lesson 20.2.2 Mass - Energy Equivalence. There are 3 lessons in this physics tutorial covering Nuclear Forces, Defect of Mass and Binding Energy, you can access all the lessons from this tutorial below.

More Nuclear Forces, Defect of Mass and Binding Energy Lessons and Learning Resources

Whats next?

Enjoy the "Mass - Energy Equivalence" physics lesson? People who liked the "Nuclear Forces, Defect of Mass and Binding Energy lesson found the following resources useful:

1. Energy Equivalence Feedback. Helps other - Leave a rating for this energy equivalence (see below)
2. Nuclear Physics Physics tutorial: Nuclear Forces, Defect of Mass and Binding Energy. Read the Nuclear Forces, Defect of Mass and Binding Energy physics tutorial and build your physics knowledge of Nuclear Physics
3. Nuclear Physics Revision Notes: Nuclear Forces, Defect of Mass and Binding Energy. Print the notes so you can revise the key points covered in the physics tutorial for Nuclear Forces, Defect of Mass and Binding Energy
4. Nuclear Physics Practice Questions: Nuclear Forces, Defect of Mass and Binding Energy. Test and improve your knowledge of Nuclear Forces, Defect of Mass and Binding Energy with example questins and answers
5. Check your calculations for Nuclear Physics questions with our excellent Nuclear Physics calculators which contain full equations and calculations clearly displayed line by line. See the Nuclear Physics Calculators by iCalculator™ below.
6. Continuing learning nuclear physics - read our next physics tutorial: Radioactivity and Half-Life

Help others Learning Physics just like you

Please provide a rating, it takes seconds and helps us to keep this resource free for all to use

We hope you found this Physics lesson "Nuclear Forces, Defect of Mass and Binding Energy" useful. If you did it would be great if you could spare the time to rate this physics lesson (simply click on the number of stars that match your assessment of this physics learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of physics and other disciplines.

Nuclear Physics Calculators by iCalculator™