Length Contraction

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Time Dilation
For small velocities at which the relativity factor is very close to 1, then the time dilation can be expanded in a binomial expansion to get the approximate expression: See also Gravitational time dilation

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Relativistic MassThe increase in effective mass with speed is given by the expressionIt follows from the Lorentz transformation when collisions are described from a fixed and moving reference frame, where it arises as a result of conservation of momentum. The increase in relativistic effective mass makes the speed of light c the speed limit of the universe. This increased effective mass is evident in cyclotrons and other accelerators where the speed approaches c. Exploring the calculation above will show that you have to reach 14% of the speed of light, or about 42 million m/s before you change the mass by 1%.

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Relativistic Mass ExampleAt the electron accelerator in Cambridge, Mass., the final acceleration stage has the following characteristics:
This increase in velocity requires a 186x increase in energy, yet only saves one second off a two hour journey. Problems with variable mass concept 
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Problems with variable massEven though circumstances like that described at the Cambridge accelerator are conveniently described by assuming an increasing mass, that is not the only way to describe these experiments, and there are problems with the concept of variable relativistic mass. Einstein's point of view is described in the following quote:
Upon being introduced to special relativity for the first time, it is easier to contemplate concepts like the speed of light as the speed limit of the universe by envisioning the mass as increasing to infinity at velocity c. However, when one has become familiar with the concepts of relativistic momentum and relativistic energy, there is no real need for the variable mass concept. 
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