11/29/2013
11.4 Mass-Energy Equivalence
 For Newtonian Work:
 Mass remains constant.
 Energy transferred to an object to increase EK results in an
increase in speed, v, only.
 Mass and energy are separate, and conserved separately.
 However early in the 20th century, scientists
discovered, through experiments performed, that
results for work and kinetic energy were not valid.
Relativistic Total Energy
 Using equations of special relativity, Einstein was
able to conclude that the increased mass
represented an increased energy.
 The total energy for an object, with rest mass m,
moving with speed v, is equal to:
Increase in Mass?
 Only once special relativity was applied, did the
experiments abide with the laws of physics.
 Recalling discussions on relativistic momentum in
section 11.3, at relativistic speeds, mass undergoes
dilation.
 As v approaches c, where does this increase in mass
come from?
Rest Energy
 When an object is at rest (v=0), its rest energy with
respect to the observer simplifies to:
 This is Einstein’s famous equation, meaning an
object’s rest mass and energy are equivalent.
 Rest mass is a form of energy that is convertible.
Relativistic Kinetic Energy
 When an object is in motion, its total energy is
larger than its rest energy.
 The relativistic kinetic energy of the object
becomes the difference between its total energy
and its rest energy.
Increase in Mass
 Due to relativity, kinetic energy can become very
large, but the object’s speed never reaches the
speed of light.
 As the speed of the object increases, the object
responds as if its mass increases.
1
11/29/2013
Mass Energy Equivalence
Mass Energy Equivalence
 Just as space and time shifted to a unified space-time
 Fission is the decomposition of large, unstable nuclei
theory; mass and energy shifts to a unified massenergy theory.
into smaller more stable nuclei.
 Fusion occurs when the nuclei of two atoms fuse
together to form a larger nucleus.
 We no longer have the conservation of mass and the
conservation of energy separately, but rather the
principle of conservation of mass-energy.
 Mass and energy are equivalent.
 The energy released by the fission of uranium in a
nuclear reactor results in a decrease in the rest mass
of the reactants.
 The Sun releases its energy via the fusion of
hydrogen and helium nuclei, where 𝐸 = 𝑚𝑐 2 .
Electron-Volt
 For subatomic particles with extremely small masses,
the SI units of joules are not convenient.
 Physicists use the electron-volt (eV) as the unit of
energy, where 1 𝑒𝑉 = 1.60 × 10−19 𝐽
 The electron-volt is defined as the work done on an
electron by 1 volt of electric potential.
2