CK-12-Physics - Intermediate

http://www.ck12.org Chapter 22. The Special Theory of Relativity

22.4 Mass-Energy Equivalence

Objectives

The student will:

• Understand the equivalence of mass and energy

Vocabulary

• Mass-Energy

Mass-Energy Equivalence

Using special relativity, force and momentum must also be altered with the multiplicative factor√^1
1 −vc^22

.

The relativistic equations for force and momentum are:

F=ma→F=

ma

√

1 −v

2

c^2

p=mv→p=

mv

√

1 −v

2

c^2

Using special relativity, Einstein was also able to show that mass and energy were not independent of each other, but
rather, equivalent. In fact, energy could be converted to mass, and vice versa.

We state without proof that Einstein derived the relationship between energy and mass asE= mc
√^2
1 −vc^22

.

The termmc^2 is called the rest energy of the object. Einstein reasoned that since mass and energy were equivalent,
a resting object of massmwould have an equivalent energymc^2. Thus, even when an object has no kinetic energy,
it still has energy by virtue of the fact that it has mass.

The total energyEof the object can be rewritten as:

E=mc^2 +KE

This equation states that the total energyEof an object is equal to the sum of the rest energy of the objectmc^2 and
the kinetic energy of the objectKE.

Notice that if theKEof the object is zero, the total energy of the object reduces toE=mc^2 , which is Einstein’s
iconic equation.