|MadSci Network: Physics|
Chris, This is a great question and good “outside-the-box” thinking. Let’s assume that the object you are referring to is moving back-and-forth in a straight line. It must stop and turn around at each end. It will therefore have zero velocity at the ends of it’s travel. Thus the average velocity would be: v = d/t v =(1.49E-4 m)/(1E-12 s) v = 1.49E8 m/s The speed of light is about 3E8 m/s so your object is traveling, on average, about half as fast as light. But of course to average 1.49E8 m/s it must be going faster since it is stopped on each end, but how fast and for how long? Assuming that the change in velocity from zero to the maximum is uniform, the average velocity would be the average of all of the velocities during the movement from one end of its course to the other. That can be real tricky to do and is usually done with calculus. But, since this is uniform, there is an easier way to do it. During half of its trip it starts at zero and ends at its maximum speed before having to start slowing down before stopping on the other end. What is its average speed during this part of the trip? Va = (vi + vf)/2 Vf = 2va – vi Vf = 2(1,49 E8 m/s) – 0 Vf = 2.98E8m/s The second half of its travel from maximum to zero ends up with the same result. (Try your algebra skills to prove it using 2.98E8 as vi and 0 as vf) Like you said that’s about 99% of the speed of light. That should be fast enough to have some relativistic effects, but will it? For a good look at relative time go to: http://patsy.hunter.cuny.edu/CORE/CORE4/LectureNotes/relativity/relativity4 .htm There should be some relative time dilation occurring under the circumstances. Can a material object be made to oscillate at such a high frequency? How do we usually make things vibrate? Atomic and molecular particles are usually made to vibrate by subjecting them to varying electromagnetic fields. Microwaves cook your food by “vibrating” water molecules. NMR and MRI instruments vibrate individual protons, so there are ways to “shake” particles. What frequency would be required and how much energy expended to keep an object going? Let’s use the smallest stable particle, a hydrogen atom and Nuclear Magnetic Resonance (NMR). The usual range for NMR is up to 440 MHz which is less than half of what you need. Even this can only be done with supercooled magnets. The energy required to continue the shaking is around 752 MWatts for each atom! (The calculations for this are tricky) Given just a few atoms you are well over a GigaWatt! You would dim the lights in New York if you tried it on a fair sized sample. An additional problem occurs with the relative change in mass. As our object approaches the speed of light its relative mass increases in proportion to the time dilation. Thus the force required to accelerate our object becomes even greater. I don’t think there is enough energy on the planet to do what you want! So…although your idea is really cool it has some inherent problems with a device which can shake your matter fast enough and have enough energy available to keep it going. Ah but only if we had a “Mister Fusion” device available we could get rid of some garbage and generate enough energy with the “Flux Capacitor”. I’ll bet you never thought such a simple question would have such a complex answer! Regards, E Stammel firstname.lastname@example.org
Try the links in the MadSci Library for more information on Physics.