1. Relativity of Mass
According to Newtonian mechanics the mass of a body is unaffected with change in velocity.
But space and time change……..
Therefore “mass” of a body is no longer be unaffected

2. When v is small as compared to c, v2/c2 <<<1
Relativity of Mass
When v is small as compared to c, v2/c2 <<<1
 m = m0 i.e. at velocities much smaller than c the mass of the moving object is same as the mass at rest.
When v is comparable to c, the 1- v2/c2 < 1 , m > m0  mass of the moving object is greater than at rest.
When v c, v2/c2 1 , so m =  or imaginary. This is non sense concept.

3. Relation between Mass and Energy
Limiting Case: When v << c
Limiting Case: When v  c
K.E. tends to infinity.  to accelerate the particle to the speed of light infinite amount of work would be needed to be done .

4. o
o o o

5. Relativity of Mass
Mass at rest.
Relativistic mass
Proof: do it yourself
Note:
Length contraction,
Time Dilation
Rest mass is least
Numerical: A stationary body explodes in to two fragments each of mass 1 kg that move apart at speeds of 0.6c relative to the original body. Find the mass of the original body.
Ans: 2.5 kg

6. Examples of mass-energy equivalence
Pair Production: when a photon of energy equal to or greater than 1.02 MeV passes close to an atomic nucleus, it disappears and a pair of electron and positron is created i.e.
 (Gamma Photon) =e- (electron) + e+ (positron)
Positron is a particle of same mass as electron but equal and opposite charge.
(2) Pair Annihilation: when an electron and positron come close together, they annihilate each other and equal amount of energy is produced in the form of a pair of - ray photons.
e- (electron) + e+ (positron) =  + 

7. Examples of mass-energy equivalence
Pair Production: when a photon of energy equal to or greater than 1.02 MeV passes close to an atomic nucleus, it disappears and a pair of electron and positron is created i.e.
 (Gamma Photon) =e- (electron) + e+ (positron)
Positron is a particle of same mass as electron but equal and opposite charge.
(2) Pair Annihilation: when an electron and positron come close together, they annihilate each other and equal amount of energy is produced in the form of a apir of - ray photons.
e- (electron) + e+ (positron) =  + 

8. Relation between Total energy (E) and momentum(p)

9. Relation between Kinetic energy (K) and momentum (p)
If v<<c, that is , p<<moc2 , then
Neglecting higher order terms of binomial expansion, we get
 Limiting value of Relativistic Kinetic Energy

10. Limiting value of Relativistic kinetic energy
Relativistic kinetic energy is
Expanding by Binomial theorem
If v<<c i.e. v/c<<1 So
This is expression for kinetic energy in non relativistic case.

11. Mass less Particle? 1) When m0=o and v<c, E=0, p=0
2) When m0=o and v=c, E=0/0, p=0/0 indeterminate form, hence must have E and p.

12. Answer : is Photon. Mass less Particle?
A particle which has zero rest mass

13. Units of energy, mass and momentum
Energy; eV, keV, MeV, GeV
Mass; MeV/c2,
Momentum: MeV/c
Rest mass Energy of
Electron: m0c2=0.51MeV
Proton: m0c2=938 MeV
Neutron: m0c2=931 MeV
Photon: m0c2=0 as massless particle

14. Ex : Find the mass and speed of 2MeV electron.
m=3.55  10-30kg
v=2.90  108 ms-1
Ex: Calculate the speed of an electron accelerated through a potential difference of 1.53106 volts.
Given c=3108 m/sec, mo=9.110-31Kg, and e= 1.610-19 Coulomb
v=0.968c
Ex: A body whose specific heat is 0.2kcal/kg-oC is heated through 100oC. Find the % increase in its mass.
% increase =9.3310-11 %

15. Summary Special theory of relativity Basic Postulates
Galilean transformation equations: v << c
Lorentz transformation equations: v ≈ c
Length contraction:
Time dilation:
Addition of velocities
Rest mass is least
Energy –mass relationship
Mass-less particle.

16. Summary