How Close Must Two Stationary Electrons Be to Double Their Mass?

[whitehorsey]

1. How close would two stationary electrons have to be positioned so that their total mass is twice what it is when the electrons are very far apart?


2. p = (mv) / (squareroot(1-(v²/c²))
E = (mc²) / (squareroot(1-(v²/c²))
E = mc²
m = (rest mass) / (squareroot(1-(v²/c²))
L = (proper length)*(squareroot(1-(v²/c²))

3. m = 2(rest mass)
m = (rest mass) / (squareroot(1-(v²/c²))
v = 6.75 * 10¹⁶

I solved up to the velocity but I don't know how to calculate the distance.



1. A spacecraft approaching the Earth launches an exploration vehicle. After the launch, an observer on Earth sees the spacecraft approaching at a speed of 0.50c and the exploration vehicle approaching at a speed of 0.70c. What is the speed of the exploration vehicle relative to the spaceship?

2. u = (u' + v) / (1 + (u;v/ c²))
u' = (u - v) / ( 1- (uv/c²))

3. I attempted this problem by setting u' equal to each other (each u either represents the exploration vehicle or the spaceship). But, I got stuck. I didn't know which v was for which vehicle/spaceship.

 

[Andrew Mason]

1. How close would two stationary electrons have to be positioned so that their total mass is twice what it is when the electrons are very far apart?


2. p = (mv) / (squareroot(1-(v²/c²))
E = (mc²) / (squareroot(1-(v²/c²))
E = mc²
m = (rest mass) / (squareroot(1-(v²/c²))
L = (proper length)*(squareroot(1-(v²/c²))

3. m = 2(rest mass)
m = (rest mass) / (squareroot(1-(v²/c²))
v = 6.75 * 10¹⁶

I solved up to the velocity but I don't know how to calculate the distance.

The electrical potential energy has to equal 2m_e². What is the expression for that potential energy in terms of distance between the electrons?

1. A spacecraft approaching the Earth launches an exploration vehicle. After the launch, an observer on Earth sees the spacecraft approaching at a speed of 0.50c and the exploration vehicle approaching at a speed of 0.70c. What is the speed of the exploration vehicle relative to the spaceship?

Use http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel.html#c1"

AM