# Help with length contraction and relativistic momentum please

• shamille
In summary, the conversation discusses a problem involving a woman's relativistic momentum, given her height and mass. The observer measures her momentum to be 2.30x10^10 kg·m/s and the goal is to find her height. The conversation also mentions the equations for relativistic length and momentum, and the process of solving for v using algebra.

## Homework Statement

A woman is 2.0 m tall and has a mass of 60 kg. She moves past an observer with the direction of the motion parallel to her height. The observer measures her relativistic momentum to have a magnitude of 2.30x1010 kg·m/s. What does the observer measure for her height?

## Homework Equations

L=Lo √1 - (v2/c2)
p=mv/√1 - (v2/c2)

## The Attempt at a Solution

I'm pretty sure that these are what the variables are
Lo= 2.0m proper length
p=2.3x1010
m=60kg
we want to solve for L

my problem is I don't know what v is, if I did i could find it.

I saw that L/Lo = mv/p
so L= Lomv/p right?

but i have no idea how to get v. i haven't had math in a while! any ideas or can you help me? I've tried an online equation solver for didn't work...

You have p and m so you can solve the momentum equation for v.

well i got the answer as 1.24 but i had to use a function grapher and play around with the x and y mins and maxes to find what speed gives a momentum of 2.3E10! which was 0.79C

but i still want to know how to do this because there will be a test and i won't have the internet to help me

Cyosis said:
You have p and m so you can solve the momentum equation for v.

yes but this is relativistic momentum not p=mv but
p=mv/√(1 - (v2/c2))
and i couldn't solve it for v... is it because I'm crap at math?
can you walk me through how to solve for it? maybe it's more algebra than physics but...

shamille said:
yes but this is relativistic momentum not p=mv but
p=mv/√(1 - (v2/c2))

There are still only three variables of which you know two.You know how to solve quadratic equations I assume?

\begin{align} p=mv \gamma=\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}} \\ p\sqrt{1-\frac{v^2}{c^2}}=mv \\ p^2(1-\frac{v^2}{c^2})=m^2v^2 \end{align}

Can you solve it from here on?

yes! wow as soon as i wrote that last message i figured it out. I don't know where my head was before... and then I used a - instead of +... gahhh

i'm sorry!

but thank you so much

You're welcome.

## 1. What is length contraction?

Length contraction is a phenomenon in special relativity where the length of an object appears to decrease when it is moving at high speeds relative to an observer.

## 2. How does length contraction occur?

Length contraction occurs due to the relativity of simultaneity, which means that two events that appear simultaneous to one observer may not appear simultaneous to another observer in a different reference frame. This leads to a difference in the measurement of the length of an object.

## 3. How is length contraction calculated?

The formula for length contraction is L = L0 * √(1 - v2/c2), where L0 is the rest length of the object, v is the relative velocity between the object and the observer, and c is the speed of light.

## 4. What is relativistic momentum?

Relativistic momentum is the momentum of an object moving at high speeds, taking into account the effects of special relativity. It takes into consideration the increase in mass and decrease in velocity at high speeds.

## 5. How is relativistic momentum calculated?

The formula for relativistic momentum is p = m * v / √(1 - v2/c2), where p is the relativistic momentum, m is the rest mass of the object, v is the velocity of the object, and c is the speed of light.