# Special relativity - velocity additions/energy

## Homework Statement

1. A spaceship travelling away from earth with a speed of 0.6c as measured by an observer on earth. The rocket sends back a light pulse back to earth every 10 minutes as measured by a clock in the spaceship.
How far does the spaceship travel between each light pulses as measured by: a) the observer on earth and b) someone on the spaceship?

2. An electron is moving at a constant velocity of 0.90c with respect to a lab observer X. Another observer Y is moving at a constant velocity of 0.50c with respect to X in a direction opposite to that of the electron in X's reference frame. What is the mass of the electron as measured be Y?

3. Protons are accelerated from rest through a potential difference of 8.0E8 V. Calculate as measured in the laboratory frame of reference after acceleration the proton's mass, velocity, momentum and total energy.

## Homework Equations

Lorentz transformation?

## The Attempt at a Solution

1. a) I first found time t passed on earth between pulses and simply used d = (t)(0.6c). But it didn't work. And I haven't a clue how to do the second part.

The other ones I don't have a single clue.

These equations might help:

$$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$$

$$w'=\frac{w-v}{1-wv/c^2}$$

If the observer in S sees an object moving along the x axis at velocity w, then the observer in the S' system, a frame of reference moving at velocity v in the x direction with respect to S, will see the object moving with velocity w'.

$$M = \frac{E}{c^2}\!$$

$$m_{\mathrm{rel}} = { m \over \sqrt{1-{v^2\over c^2}}}$$

$m_{\mathrm{rel}}$=relativistic mass.

Oh and for part one you might want to convert .6c into m/s so you are using the same units. Might make it easier.

Edit:

Oh and:

$$\ t' = t-vx/c^2$$

Last edited:
Doc Al
Mentor

## The Attempt at a Solution

1. a) I first found time t passed on earth between pulses and simply used d = (t)(0.6c). But it didn't work.
Why didn't it work? How did you find t?

Never mind, I figured it out.

But for the 2nd question, I'm confused. To find the mass, I first need to find the velocity of the electron relative to Y. How would I input the values into the equation? If Y is moving in opposite direction of the electron, then I should put its velocity as negative? And so U' = 0.9c - (-0.5c)/(1 - (-0.5c x 0.9c)/c^2)) = 1.4/1.45 = 0.97c
But the answer to the question says that the relative velocity is 0.73c....

As for the 3rd question, I really don't even know how to approach this. I was thinking that E = Vq = mc^2 but my answer was totally off. The answer is 3.1 x 10^-27 kg for mass.

Last edited:
Doc Al
Mentor
But for the 2nd question, I'm confused. To find the mass, I first need to find the velocity of the electron relative to Y. How would I input the values into the equation? If Y is moving in opposite direction of the electron, then I should put its velocity as negative? And so U' = 0.9c - (-0.5c)/(1 - (-0.5c x 0.9c)/c^2)) = 1.4/1.45 = 0.97c
But the answer to the question says that the relative velocity is 0.73c....
Your answer for the relative velocity is correct. An answer of 0.73c makes no sense, since you know the speed must be greater than 0.9c.

As for the 3rd question, I really don't even know how to approach this. I was thinking that E = Vq = mc^2 but my answer was totally off. The answer is 3.1 x 10^-27 kg for mass.
Vq represents an increase in the kinetic energy; it does not equal the total energy (or the rest energy).