bei48482_FM

Integrating by parts ( x dyxy y dx),

KE m



0

 mc^2  1 ^2 c^2



0

mc^2

Kinetic energy KE mc^2 mc^2 (1)mc^2 (1.20)

This result states that the kinetic energy of an object is equal to the difference between

mc^2 and mc^2. Equation (1.20) may be written

Total energy Emc^2 mc^2 KE (1.21)

If we interpret mc^2 as the total energyEof the object, we see that when it is at rest

and KE 0, it nevertheless possesses the energy mc^2. Accordingly mc^2 is called the

rest energyE 0 of something whose mass is m. We therefore have

EE 0 KE

where

Rest energy E 0 mc^2 (1.22)

If the object is moving, its total energy is

Total energy Emc^2  (1.23)

Example 1.6

A stationary body explodes into two fragments each of mass 1.0 kg that move apart at speeds

of 0.6crelative to the original body. Find the mass of the original body.

Solution

The rest energy of the original body must equal the sum of the total energies of the fragments. Hence

E 0 mc^2 m 1 c^2 m 2 c^2 

and

m2.5 kg

Since mass and energy are not independent entities, their separate conservation prin-

ciples are properly a single one—the principle of conservation of mass energy. Mass

canbe created or destroyed, but when this happens, an equivalent amount of energy

simultaneously vanishes or comes into being, and vice versa. Mass and energy are dif-

ferent aspects of the same thing.

(2)(1.0 kg)



 1 (0.60)^2

E^0

c^2

m 2 c^2



 1  22 c^2

m 1 c^2



 1  12 c^2

mc^2



 1 ^2 c^2

mc^2



 1 ^2 c^2

m^2



 1 ^2 c^2

d



 1 ^2 c^2

m^2



 1 ^2 c^2

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