Frames of reference for speed?

jartsa

Oh yes, relative velocity formula, it's in Wikipedia too, and it's the right formula for our current task, while the velocity addition formula is not so good.

http://en.wikipedia.org/wiki/Relativ...ativity_theory

jartsa

That was not my point, and I don't think I made errors worth mentioning. Here's what I thought, quite simple isn't it?

Car1 ---> <---Car2
v=30 m/s v=-30 m/s



If the signs of the inputs of a formula, or the result, must be adjusted using intuition, then it's not so good formula. That's just my opinion. But here's a problem: what do you answer when a student asks "what exactly do I plug into this formula"?

robphy

I would tend to agree.
I tell often tell my students... How you would write a computer program [lacking physical intuition] to get the correct answer?
One could use a universal formula using signed-components.. or else use special cases depending on whether the ships are approaching or receding.

Nugatory

They don't have to be adjusted by intuition, it's just that developing that intuition is both less work and more valuable than memorizing the sign convention rules. The formula represents a model of a physical situation, and you should never be so focused on the model that you lose sight of the actual physical situation. If you do, you aren't understanding physics, you're just crunching numbers by rote, and eventually a computer will replace you.

Ask the student what might be plugged in, try to get him to justify each possible choice as he makes them. Sometimes, it's right to answer a question with a question.

ghwellsjr

You did make errors worth mentioning. When the OP asked if he should plug the two speeds into the Velocity Addition formula that I linked to, you said in post #9:
You stated that the correct answer was obviously 0 and if he plugged the numbers into the formula I gave him, he would get a different answer. Your answer was an error worth mentioning.

And then you added post #11:
Now you are suggesting that the correct formula was the relative velocity formula and restated that opinion in post #18:
But when discussing the relativistic velocity addition formula, you quoted from the wikipedia article concerning the ship and the fly which is exactly the scenario that the OP asked about but with approaching speeds rather than receding speeds. I pointed out your error in post #16 but you reject it. You want to change the OP's question from one similar to the shore, ship and fly orientation where the OP is the shore, the ship is the road and the fly is the other car, to one from the viewpoint on the ship and the OP is the shore traveling away in one direction while the other car is the fly traveling away in the other direction. Of course, the relative velocity formula will also work if you change the sign of one of the speeds but that is totally unnecessary to bring up in the OP's scenario.
Looks like another error because you've just set 30 m/s = - 30 m/s.
Every formula should include an explanation of what the variables mean as did the wikipedia article on velocity addition that I pointed him to. And the OP had no problem with it until after you told him that he was doing it incorrectly when he wasn't.

ghwellsjr

The OP already knew that he had to add the two speeds, he just didn't know that it took a special formula to add them. His intuition was correct, he didn't need any explanation on what he already understood and he especially didn't need any incorrect explanation.

But I certainly wouldn't have changed the explanation from one in which the speeds involved were large fractions of the speed of light where the correct sum was significantly different from the incorrect sum to one in which there was no significant difference between doing it the wrong way or doing it the correct way. That was the point he was asking about. Instead, we're off on this tangent that has nothing to do with his question or with the correct answer.

jartsa

Now I will correctly add the velocities of two cars driving on a road at velocities -0.5 c and 0.5 c, relative to the road. I will use the relativistic velocity addition formula.

car1 --> <-- car2
v1=0.5c v2=-0.5c

We need an observer and an object whose velocity is observed by the observer. Car1 will be an observer and the road will be the observed object, because we know the velocity of the road relative to car1, it's -0.5 c.


Then we need another observer and another object whose velocity is observed by the observer. The road will be the observer and car2 will be the observed object, because we know the velocity of car2 relative to the road, it's -0.5 c.



Car1 will observe the velocity of car2 to be:

[v +u]/[1+ vu/c2] =


(The velocity of the road according to car1 + The velocity of car2 according to the road) /

(1+(The velocity of the road according to car1 * The velocity of car2 according to the road) / c2)

= (-0.5c + -0.5c)/(1+ (-0.5c*-0.5c) / c2) = -0.8c

jartsa

When I just plugged the velocities of the cars into the relativistic velocity addition formula, I made the error of just mechanically plugging the numbers in.

Now I have corrected that error in post 24.

Wikipedia: A shore observes a ship, which observes a fly.
Me in post 24: A car observes a road, which observes another car.

Post 24 is correct, isn't it?

ghwellsjr

Yes, and that's exactly what I said in post #16 when I agreed with you that it is important to pay attention to signs.