So what about mass? 1. What happens to time from the frame of reference of a stationary observer on Earth as objects approach c? 2. What notation is given to this time? 3. What happens to the length of an object as it approaches c; a. From the frame of reference of a stationary observer? b. From the frame of reference of the moving object? 4. Mass also changes, as per the formula shown below. Does this mean the mass increases or decreases? Explain your answer:

MASS AND ENERGY 1. Be able to describe and calculate how mass changes at speeds approaching c 2. To know why c is a limiting factor and that nothing can travel faster than this 3. To know how relativistic effects need to be taken into account with Einstein's Equation e = mc 2

The speed of light – limiting factor It is impossible for objects to travel faster than c – why do you think this is? As v approaches c, the mass m gets bigger and bigger. The closer it gets, the more it tends to infinity. Further acceleration requires a force approaching infinity. So it is impossible for the speed of light to be reached, let alone exceeded by an object of non zero rest mass. Sketch how you think this graph will look: Speed Relativistic mass c m0m0

Thinking about energy A particle at rest has rest energy E 0 = m 0 c 2 If the same particle is moving at constant velocity v, the relativistic mass, m is given by: So we can write an expression for the total energy using: Total energy = Rest energy + kinetic energy

What’s wrong with this worked example? Calculate the speed of an electron which has been accelerated from rest through a p.d of 2.0 × 10 6 V. eV = ½ mv 2 v 2 = 2  1.6  C  2.0  10 6 V 9.11  kg = 7.02  m 2 /s 2 v = 8.38  10 8 m/s

Rest mass = 1.67  × 9.0  = 1.50  J Total energy of the proton is given by: v 2 /c 2 = = – =  = Total energy = 1.50  J  = 4.80  J Kinetic energy = 4.80  J  J = 3.30  J Voltage = 3.30  J  1.6  C = 2.06  10 9 V