My background is not physics but I am interested in it and still remember some of the basic stuff I learned in high school and early college years. Ok, please see the attached drawing and here is some background info: I have constructed a simple and typical experiment, where a stack of rotary wheels is assembled in way that each wheel rotates on and is supported by the one beneath it. It means the wheel on top rotates relative to the one below, therefore, its total/absolute speed would be equal to its own speed + the speed of the wheel below...akin to a person running on a train in the direction the train is moving, i.e. Vc= Va+Vb. These wheels could be assumed as electric motors connected in series mechanically, so the speeds add up! Therefore, by having enough number of wheels rotating at a constant speed (i.e. 5000 RPM), we could potentially reach speeds close to the speed of light without violating any rules I can think of? So do you think this experiment is flawed, or will fail to reach speed of light, why? Thanks.
The flaw is that you haven't tried to calculate the torque required to acceletate the system: you're ignoring the entire reason it is impossible. Presumably you posed the question because you know physics says light speed by an object is impossible. Do you know WHY physics says it is impossible?
Actually, no. Speeds don't add up the way you think. You must add them relativistically, according to the relativistic addition of velocities formula: [tex]V_{c} = \frac{V_{a} + V_{b}}{1 + (V_{a} V_{b})/c^2}[/tex] No matter how many speeds you add up, the total will never reach the speed of light (c). Note that if the speeds are low enough (Va, Vb << c, the speed of light), that reduces to the formula you had in mind: Vc= Va+Vb.
My assumption was that by starting from the top wheel and continuing down to lower wheels step by step, we would then need to bring the new mass from 0- 5000 RPM(whatever RPM) everytime...thereby the change in kinetic energy would be the difference in omega of a slightly bigger mass, but omega still from 0- 5000/whatever rpm: [tex] KE\ =\ \frac{1}{2}\,I\omega^2 [/tex] My misconception was that as we move down the axis step by step, we were to deal with a little more mass, so that the new kinetic energy required to go from 0-5000 rpm would be a little higher due to higher mass, ignoring each individual components on top spinning at different omegas. I now understand that as the omegas get bigger and bigger, more torque and energy would be required...approaching impossible! So I think my experiment reached a dead-end here.
Well, since I studied mechanical engineering (never finished it though), my point of view is inherently different from the physics point of view when it comes to designing machines and coming up with new ideas (never mind how dumb they could appear to a physicist). But I am still struggling to comprehend why (as you guys claim) mass gets bigger and bigger as we approach the speed of light??? and if I understand it correctly, that's the only barrier to approaching light speed. Can somebody please without mathematical formulas explain what happens to the mass of an object as its speed gets higher and higher?
Without getting into the whole discussion of "Mass" vs "Relativistic Mass". Let's put it this way: One of the properties of Mass is inertia. The greater the mass, the harder it is to change its velocity. This is why it takes more energy to get a bowling ball rolling vs a marble. One of the discoveries of Relativity is that what we call mass and energy are related, They are two aspects of the same thing. One of the properties they share is inertia. Thus when you add more energy to an object you also increase its inertia or its resistance to changes in its velocity, just like the object's mass had increased. Thus when you accelerate an object, it takes a certain amount of energy to do so. This energy is added to the kinetic energy of the object. If you wish to increase the speed of the object further, you need to add more energy. But the energy you already added has increased its inertia, so it takes an extra amount of energy to make up for that. So you see how it goes; it is a vicious cycle. You need to add energy to overcome inertia, but adding energy adds to the inertia. At first, it adds up slowly, so at normal everyday speeds, we don't notice it. But as the speeds increase the effect starts to compound until by the time to get near the speed of light, huge amounts of added energy will only increase the speed by smaller and smaller amounts, and the final velocity can get closer to, but never equal to the speed of light.
Thanks Janus for clarification, very informative for me. On a different but related note, in the case of free fall, what is the max speed an object can reach when it's stuck in the gravitational pull of a SUPER massive star or planet? For instance, a planet/star whose gravity would be a=1,000,000 G and constant over a relatively long distance from its surface. By our calculations, according to V=a*t --> t=c/a = 30s. So it would take only 30s for an object to reach C and possibly faster!!? What's now wrong with this scenario?
You are still relying on non-relativistic dynamics. Implicit in your equation is Newton's equation: F=ma. You have substituted mg for the force and canceled out the m's, so that you get a=g. This equation is wrong for substantial speeds. Instead, one must use F=dp/dt where p=gamma*mv. If you formulate your question like this (the math is not trivial), you will see that you will never reach the speed c. You will, in fact, accelerate slower and slower no matter how strong the force is. What you are saying is equivalent to the statement: "if I have constant of 9.8m/s^2 acceleration for all time, I will eventually go faster than c". That statement is absurd because you CANNOT have constant acceleration for all time. Also, for strong gravitational fields, one must switch to general relativity as well. So, that complicates matters even more.