# Relativity: Mass with respect to velocity

1. Mar 23, 2013

### ek=1/2mv^2

1. The problem statement, all variables and given/known data
In the theory of relativity, mass of a particle is

m= m$_{0}$/ $\sqrt{1-v^{2}/c^{2}}$

m is the mass when the particle moves at v relative to the observer, and m$_{0}$ is the rest mass.

Sketch the graph of m with respect to v.

2. Relevant equations
E = mc$^{2}$

3. The attempt at a solution
No idea where to start :(

Last edited by a moderator: Mar 23, 2013
2. Mar 23, 2013

### Curious3141

Don't you know how to sketch a curve? Think of what the vertical intercept is, and whether there's an asymptote.

3. Mar 23, 2013

### LCKurtz

Would you know where to start if the problem was to graph$$y = \frac 1 {\sqrt{1-\frac{x^2} 9}}$$?

4. Mar 25, 2013

### ek=1/2mv^2

Theory of special relativity graph

1. The problem statement, all variables and given/known data

In the theory of special relativity, mass of a particle is

$m = \frac{m_{0}}{\sqrt{1-v^{2}/c^{2}}}$

m is the mass when the particle moves at v relative to the observer, and m0 is the rest mass.

Sketch the graph of m with respect to v.

2. Relevant equations

$m = \frac{m_{0}}{\sqrt{1-v^{2}/c^{2}}}$

3. The attempt at a solution

In order to sketch the graph, I had to first (before finding the derivative and second derivative):

- Define the domain
- Find the x and y intercepts
- Find where there would be asymptotes (both vertical and horizontal)
- Check for symmetry

DOMAIN

When the x-axis is the velocity of a particle, the domain is 0 $\leq x$$\leq c$

INTERCEPTS

$f(x) = y = m$

$x = v$

therefore,

$f(x) = \frac{m_{0}}{\sqrt{1-x^{2}/c^{2}}}$
I didn't find any x-intercepts

Found a y-intercept at $y = m_{0}$

ASYMPTOTES
since domain has been restricted to be between 0 and C, there is no horizontal asymptote.

Vertical asymptote:
Took the just the denominator and made it = to zero, got v=c. Since v is x. It is $x = c$, the vertical asymptote.

SYMMETRY

There is Even symmetry, $f(x) = f(-x)$

Ok, so now the 1st and 2nd derivatives

1st derivative

$m^{\prime} = \frac{-mv}{c^{2}-v^{2}}$

x-intercept at 0, therefore there is an interval of increase between 0 and c.

2nd derivative

$m^{\prime \prime} = \frac{-(m + v) + 2m^{\prime}v}{c^{2} - v^{2}}$

Here is when i am really stuck, how do we find the zeros for the second derivative?

BTW, pic of question and answer is attached. (number 53)

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Last edited by a moderator: Mar 26, 2013
5. Mar 26, 2013

### Simon Bridge

You have an equation for m and m' to substitute in, m''=0, so solve for v.
Shortcut - what would m''=0 tell you?
What would that mean for relativity?
Is that reasonable physically?

http://www.weburbia.com/physics/mass.html

6. Mar 28, 2013

### ek=1/2mv^2

Thanks, that helped alot. Have a great day.