In reply to David Roberson's message of Thu, 27 Nov 2014 23:47:17 -0500: Hi Dave, [snip]
The "v" in the formula Ek = 1/2 mv^2 actually applies to the change in velocity, not velocity in any absolute sense. For the sake of convenience, we normally choose a frame of reference in which the initial velocity is zero which makes the calculation simpler. For observer 1, the change is 1/2 * m * (2-0)^2 = 1/2 * m * (2)^2. For observer 2, the change is 1/2 * m * (1 - -1)^2 = 1/2 * m * (2)^2. I.e. they both see the same change in kinetic energy. Note 1: I have not included the dimensions here to keep the formula as simple as possible in ASCII text. Note 2: Depending on the initial direction of motion, you may choose to write the equation for observer 2 as 1/2 * m * (-1 - 1)^2 = 1/2 * m * (-2)^2, however this still gives the same result for the kinetic energy change. > > Robin, I just came up with a thought experiment that lends support to the > idea that a reactionless drive is not likely to exist. Take 2 different > observers, one that is moving beside the ship at the same velocity as it has > prior to activating the drive. The second one is moving at a velocity that > allows him to observe the ship decelerate first until it reaches a velocity > of zero relative to him and then to accelerate in the reverse direction until > it reaches the exact same original velocity in the opposite direction. > >The first observer sees the velocity of the ship go from for this example 0 >meters per second to 2 meters per second. He determines that the ship now has >2*2*Mass/2 units of kinetic energy. The amount of internal mass that the ship >burns up to achieve this acceleration is extremely small and can almost be >neglected. > >The second observer sees the ship moving at the same speed before and then >after the application of the drive. The only difference he measures is that >the direction of the motion of the ship is reversed by the drive. So he sees >the ship begin the motion moving 1 meter per second relative to him initially >and then after the drive shuts down the ship is moving 1 meter per second in >the opposite direction. This observer determines that the kinetic energy of >the ship has not changed measurably due to the application of the drive. > >At this low velocity the second observer determines that the mass converted >into drive power is essentially the same as that determined by the first >observer. Both guys have a very hard time figuring out exactly how much mass >is converted, and they agree that any difference is hidden in the noise. > >In this experiment we have two independent observers seeing the same ship >being subject to the same drive. The amount of kinetic energy being deposited >to the ship by essentially the same loss of internal mass varies remarkably >according to each. This does not add up. > >As I have mentioned before, with a normal drive this case can be handled >without a problem. The exhaust material supplies the kinetic energy and >momentum needed to balance the equation. > >Apparently every observer moving at a different initial velocity relative to >the driven ship arrives at a significantly different calculation regarding the >ships energy balance after the application of the drive. How could something >this radical be possible? Let me say it again, there is no problem of this >sort to deal with when a standard drive is applied. > >Dave > Regards, Robin van Spaandonk http://rvanspaa.freehostia.com/project.html
