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Unformatted text preview: Kinetic Energy and Mass for Slow Particles Recall that to get momentum to be conserved in all inertial frames, we had to assume an increase of mass with speed by the factor This necessarily implies that even a slow- moving object has a tiny mass increase if it is put in motion . How does this mass increase relate to the kinetic energy? Consider a mass m , moving at speed v , much less than the speed of light. Its kinetic energy E = m v , as discussed above. Its mass is which we can write as m 0 + dm, so dm is the tiny mass increase we know must occur. Its easy to calculate dm . For we can make the approximations So, for Again, the mass increase dm is related to the kinetic energy KE by KE = ( dm ) c 2 . Having looked at two simple cases, were ready to derive the general result, valid over the whole range of possible speeds. Kinetic Energy and Mass for Particles of Arbitrary Speed We have shown in the two sections above that (in the two limiting cases) when a force does work...
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