Relativistic Addition of Electron Velocities

In summary, two electrons are moving in separate accelerators with speeds of 0.822c and 0.424c respectively. Using the formula V_{a/c} = \frac{V_{a/b} + V_{b/c}}{1 + (V_{a/b} V_{b/c})/c^2}, it was determined that the speed of the second electron relative to the lab is 0.583c.
  • #1
Cheezay
26
0

Homework Statement


An electron moves to the right in a laboratory accelerator with a speed of 0.822c. A second electron in a different accelerator moves to the left with a speed of 0.424c relative to the first electron. Calculate the speed of the second electron (in c) relative to the lab. Do not enter unit.


Homework Equations


[tex]
V_{a/c} = \frac{V_{a/b} + V_{b/c}}{1 + (V_{a/b} V_{b/c})/c^2}
[/tex]


The Attempt at a Solution


Relativity is difficult for me to get a handle on. The way I am setting this up, is I'm using the velocity .822c for Va/b and -.424c(since it this one goes left) for Vb/c, and Vac would be the velocity of the second electron relative to the lab, however I'm not getting the right answer. I'm guessing that I don't have the velocities substituted in the proper places in the formula, any help?
 
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  • #2
Cheezay said:
… I'm using the velocity .822c for Va/b and -.424c(since it this one goes left) for Vb/c, and Vac would be the velocity of the second electron relative to the lab …

Hi Cheezay! :smile:

You're using a for the 1st electron, and b for the lab, then b for the second electron and c for the 1st electron :frown: …

fiddle around with it, to get it consistent, and remember that Va/b = -Vb/a :smile:
 
  • #3
Ok. So considering that a = electron 1, b = electron 2, and c = lab... I now have Va/c= .822c, and because Va/b=-Vb/a.. i use -.424c for the speed of electron 2 relative to the lab. Now i solve for Vb/c. I'm fairly confident i have my equation set up correctly now, which means I'm making an algebraic error now... any help?

Using V as a variable, in place of Vb/c

.822c=[-.424c + V]/[1-(.424c x V)/(c^2)] c's cancel...

.822c=[-.424c + V]/[1-(.424 x V)/c] i move the whole term...

.822c[1-(.424 x V)/c]=-.424c + V distribute .822c (c's cancel again)

.822c - .348528 -.822V = -.424c +V

-.348528 - .822V = -1.246c + V

-.348528 - V = -1.51582c + V

-2V = -1.16729c so V= .583c which isn't correct


Any more help would be greatly appreciated! I have been on this problem for 3 days now!
 
  • #4
Hi Cheezay! :smile:
Cheezay said:
Ok. So considering that a = electron 1, b = electron 2, and c = lab... I now have Va/c= .822c, and because Va/b=-Vb/a.. i use -.424c for the speed of electron 2 relative to the lab.

(you mean relative to electron 1 :wink:)
Using V as a variable, in place of Vb/c

.822c=[-.424c + V]/[1-(.424c x V)/(c^2)] ...

However did you get an unknown on the RHS? :redface:

Choose a b and c (it might be easier if you call them 1 2 and L) so that the RHS contains your two knowns, and the unknown is on the LHS! :smile:
 
  • #5
Ok.. I've figured it out. Thanks for the help!
 

FAQ: Relativistic Addition of Electron Velocities

What is the concept of "Relativistic Addition of Electron Velocities"?

The concept of "Relativistic Addition of Electron Velocities" is based on Einstein's theory of relativity. It states that the velocity of an electron cannot be simply added to another velocity in a linear manner, as it would be in classical physics. Instead, the velocities must be combined using a formula that takes into account the effects of time dilation and length contraction at high speeds.

Why is the "Relativistic Addition of Electron Velocities" important?

The "Relativistic Addition of Electron Velocities" is important because it allows us to accurately calculate the velocity of an electron or other high-speed particle in relation to an observer. This is crucial in many fields of science, such as particle physics and astrophysics, where understanding the behavior of particles at high speeds is essential.

What is the formula for "Relativistic Addition of Electron Velocities"?

The formula for "Relativistic Addition of Electron Velocities" is V = (v1 + v2)/(1 + (v1*v2)/c^2), where V is the combined velocity, v1 and v2 are the individual velocities, and c is the speed of light. This formula takes into account the effects of time dilation and length contraction, which become significant at high speeds.

How does "Relativistic Addition of Electron Velocities" differ from classical physics?

In classical physics, velocities can simply be added together in a linear manner. However, in "Relativistic Addition of Electron Velocities", the velocities must be combined using a formula that takes into account the effects of time dilation and length contraction at high speeds. This is because at high speeds, the laws of classical physics break down and the principles of relativity take over.

What are some real-world applications of "Relativistic Addition of Electron Velocities"?

"Relativistic Addition of Electron Velocities" has important applications in fields such as particle accelerators, where electrons and other particles are accelerated to high speeds. It is also relevant in space travel, where understanding the behavior of particles at high speeds is crucial. Additionally, this concept is used in the development of technologies such as GPS systems, which rely on accurate calculations of velocity to function properly.

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