Special Theory of Relativity - Lecture-9

Special Theory of Relativity

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Lorentz Transformation : Example 4 : Two - particles move in opposite direction with velocity 0.6c in the laboratory, -frame. Calculate the velocity of one - particle in the moving frame attached to the other - particle by applying relativistic transformation. Repeat the calculations by taking speed of  particles as 0.06c . Compare the result with that obtained from Example 2. Solution:    Here,  Example 5 :  A 2m long stick, when it is at rest, moves past an observer on the ground with a speed of 0.5c.                (a)  What is the length measured by the observer ?                (b)  If the same stick moves with the velocity of 0.05c what would be its length measured by the observer ? Solution:                                                               Thus if the velocity of the stick is very small compared to c, the result is close to that of classical theory. Example 6 :  A cubical shape of body with 1m length on each side when it is at rest, moves with a velocity 0.6c along x - direction. What is the shape and dimension of the body noted by an observer on ground. Solution:                                    It would be a parallelepiped shape with dimension  Example-7:  A proton of mass  kg moves with a velocity of  Calculate its relativistic and non-relativistic momentum. Sol: Relativistic momentum,                                      Example 8 :  Calculate the momentum and kinetic energy of - particle moving with a velocity of                (a)  0.01 c                (b)  0.1 c  and                (c)  0.4 c  Solution:     -particle is bassically a He ion with mass number A=4.                                                                                     Two - particles moving in opposite direction