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Looking at: Linear Momentum and Mass in Special Relativity

Linear momentum transformation. In this section we will prove, that it is not possible to transform the linear momentum p of a particle moving close to the speed of light by making a substitution of the following kind:. Stationary frame. Moving frame. i.e. by applying the Lorentz velocity tr

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Looking at: Linear Momentum and Mass in Special Relativity

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    1. Looking at: Linear Momentum and Mass in Special Relativity PHYS 353-LGB

    2. Linear momentum transformation In this section we will prove, that it is not possible to transform the linear momentum p of a particle moving close to the speed of light by making a substitution of the following kind: PHYS 353-LGB

    3. Proof: To show that p=mv?mv’, does not hold true, we will apply it in the following example and see the result: Assume an elastic collision between two identical masses 1, 2 and write the law of conservation of linear momentum both with respect to a stationary and a moving observer. What do we notice? PHYS 353-LGB

    4. PHYS 353-LGB

    5. PHYS 353-LGB

    6. This fundamental law of physics- conservation of linear momentum- seems to be violated by using the transformation , leading to That is in disagreement with the postulate of special relativity that fundamental laws of physics must be independent of the choice of inertial frames. PHYS 353-LGB

    7. PHYS 353-LGB

    8. Rest mass and relativistic mass The concept of mass is fundamental in physics.  Its definition goes back to Galileo and Newton, who defined mass as that property of a body that governs its acceleration when acted on by a force.  In Special relativity, the above definition of mass still holds for a body at rest, and so is also called rest mass.  When a body though is moving, we find that its force–acceleration relationship is no longer constant, but depends on two quantities: its speed, and the angle between its direction of motion and the applied force.  If we relate the force to the resulting acceleration along each of the three mutually perpendicular spatial axes, we find that in each of the three expressions a factor of ? m appears, where the gamma factor ? = (1–v2/c2)–1/2  is a common quantity in special relativity, and m is the body's rest mass.  The new quantity ? m is traditionally called the body's relativistic mass PHYS 353-Leda G. Bousiakou 8

    9. Proof: PHYS 353-Leda G. Bousiakou 9

    10. PHYS 353-Leda G. Bousiakou 10

    11. Mass Dilation PHYS 353-Leda G. Bousiakou 11

    12. PHYS 353-Leda G. Bousiakou 12

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