SPECIAL RELATIVITY - PROBLEMS 2
TOPICS | RELATIVITY
[PROBLEMS1] [USEFUL EQUATIONS]

These problems are concerned with the properties of Inertial Mass and the variance of this with the speed of a body. This leads to the result that infinite energy would be required to accelerate a body of non-zero rest mass to the speed of light.

Q1) We have shown that INERTIAL MASS is given by

where mo is the rest mass of a body.

(i) Plot a graph of m(v) / (mo) , (y - axis) against
(v / c) , (x - axis)

(ii) Comment on the physical significance of this.

Q2) Calculate the REST ENERGIES (Eo) for an electron and proton, giving your answer in mega - electron volts (MeV)

Q3) If Kinetic Energy (K) is now REDEFINED as the difference between
total energy (E) and rest energy (Eo) , then show that Relativistic Kinetic Energy is given by

 (a)

(b) If v<<c that this formula reduces to the familiar Newtonian formula

K = 1/2 mov2


Q4) Show that, for the relativistic case , the speed of the particle is given by

the formula
 


Q5) If we now use moc2 as a unit in which to measure the extra energy K that is added to a particle by means of an acceleration process, complete this table :( The quantity moc2 takes the value 1 in all cases)
 


 Q6)Using the table and your result from Q2 , plot a graph of v2 (y-axis)

against K (in (MeV) ) for an electron.

Q7) Explain clearly why particles with Non Zero rest mass (mo # 0) cannot reach the speed of light.
 

Q8) Add to your graph the curve for Newtonian Kinetic Energy ( 1/2 mov2) and explain clearly why this is not valid for elementary particles in Eg Cosmic Rays.


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