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Do You Wanna Go Faster?? May 13, 2010

Posted by regan222 in Educational Ranting.
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Albert Einstein

Ok, hands up all of you who have heard of Einstein’s Theory of Special Relativity.  If you had been in my physics class for the past few days you would know exactly what I am talking about.  Well, maybe you wouldn’t know exactly what I was talking about but you would at least know something about it.  My question to those of you who were NOT in class this week is: Have you ever heard of Einstein’s Theory of Special Relativity?

“What’s so special about Relativity?”, you ask (and you are right to do so).  Well, according to Einstein’s theory, space and time are two sides to the same coin. Does that mean anything to you?  It should. 

Vectors and Scalars

A bit of background first.  There are two kinds of quantities that we consider at this basic level of physics.  We measure things in terms of Scalar quantities and Vector quantities.  A scalar has exactly one aspect or dimension.  Speed is a good example of a scalar.  We look at the speedometer in our car and it tells us only how fast we are going.  A vector, on the other hand, has two dimensions or aspects.  Vectors are made up of a quantity but there must also be direction.  Velocity is a vector.  I can say I am going 70 mph on the freeway and I am giving you my speed.  If I say I am going 70 mph east or 70 mph toward Dallas or 70 mph on a heading of 120 degrees then I am giving you a vector quantity.  Vectors are defined as magnitude (amount) and direction.

Guess What?!?! you can add and subtract vectors just like numbers.  You can also break vectors apart into their components.  By way of a simple example; if I am sitting on a bus and the bus is going 70 mph then I am also going 70 mph because I am connected to the bus.  Does that make sense?  If not then you need to get out more.  If the bus is moving and I am attached to the bus, then I am moving.

Lets say I am sitting in the back of the bus and I get up to ask the driver a question.  I know you are not supposed to go forward of the white line or talk to the driver but I need to know if this is my stop.  I walk to the front of the bus.  I can walk on level ground about 3 mph.  I know because I have measured it.  If I get up from my seat and go forward to talk to the driver, how fast am I walking?  (Hint: 3 mph).  If you sat beside me on a bus with a radar gun and clocked my speed walking to the front I would register at 3 mph.  Is that how fast I am going?  (Hint: yes, radar guns don’t lie).

Now, lets say you have a radar gun but you are NOT sitting on the bus with me.  You are sitting on the side of the road and watching me go by as I get up and walk to the front of the bus.  You carefully aim the radar gun at me and hit the trigger.  How fast am I going?  (Hint: The radar gun will show that I am going 73 mph.)  From your perspective sitting still we add the vector quantity of my going 3 mph the same direction as the bus with the buses’ speed of 70 mph and that gives my correct velocity of 73 mph the same direction as the bus.  Is the radar gun wrong this time?  Nope it is also correct.  “Mr White”, you ask,”How is it possible for two radar guns measuring the same object at the same time to show such different readings (73 mph or just 3 mph) and for both to be right??  Well Skippy I am glad you asked.  It is all a matter of perspective.

Whose View are You:

There are two perspectives (or frames of reference) to any event.  The first viewpoint is yours, whoever you may be.  The second viewpoint is that of an outside observer.  When you were sitting on the bus with me earlier you shared my perspective.  To you (and your radar gun)  I moved only 3 mph.  When you were sitting along side the road, you had the outside observer’s perspective.  For some reason, your radar gun said I was moving 73 mph.  You could say it was all a trick of perspective but (because of the radar guns and their vastly different readings) it is not possible that this is a trick.  Also the inertia and momentum generated by the motion of me and the bus is real.  If you doubt this, get a bus and a driver.  While the driver is moving down the road at 70 mph, start walking from the back of the bus to the front.  Ask the driver to slam on the brakes while you are walking (the shorter and more violent the stop, the better).  Your perspective and the buses’ perspective will change.  You will find yourself accelerating from 3 mph (walking speed) to 73 mph even though you have not sped up your walking speed at all.  You will also find that striking the front windshield of a bus at 73 mph from the inside is a drastic change in perspective.  Any questions thus far???  If you would like a less violent way of demonstrating this, try walking and tossing a ball straight up and catching it.  Keep your eyes on the ball.  Does it go anywhere but straight up and down?  Not if you are doing it right.  Now, have someone mark the path of the ball as you walk by and toss it up and catch it.  THEY will find that the ball moves a considerable distance forward along the direction you are walking as well as going straight up and down.  Same principle only you don’t end up with multiple fractures.  You now have the first piece of information you need to understand the Theory of Special Relativity.  Due to the amount of information here I think I will make this a series and will continue this article tomorrow.  Tomorrow we will learn all about postulates.

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