Special relativity problems — More details below

[billllib]

[Note from mentor: this was originally posted in a non-homework forum, so it lacks the homework template.]

Summary:: Special relativity problems. More details below

The formula for speed for special relativity is

V = (u-v) / (1-u*v) / (c^2)
Here the book http://www.people.fas.harvard.edu/~djmorin/Relativity Chap 1.pdf

pg 40
B)

I need to figure out the speed of D?

I don't even know how to do this in Galilean physics if D is not given.

The only thing I know about relative velocity is from this video.



Could someone start off explaining the problem in Galilean physics?
page 41

 

[PeroK]

So, the problem is:

A train (A) of (proper) length $L$ is overtaking another train (B) of (proper) length $L$. The speeds of these trains are $v_A, v_B$, say.

A person (D) walks along train B, starting when the front of train A reaches the rear of train B, and getting to the front of train B just at the rear of train A passes. I.e. D walks along train B in the time it takes A to overtake B. How fast does D have to walk?

1) We want to solve this problem in classical physics.

2) We want to upgrade the solution for SR.

3) We want to calculate the time of the overtaking from the perspective of A, B and D.

Any ideas about 1?

 

[billllib]

I created an image. Scene 2 I know is wrong but I don't know why the vectors are wrong?
I think to get D reference frame in gallian physics I go A = 4c/5. B = 3c/5.

The formula for galilian physics is V = u - v. Since the arrows are A----> <----V.

D = (A ) - (- B) --> A + B. Is this correct for classical physics? I think I solve the rest if this correct.End of summary of private message.

To solve the problem I go V = u+v / 1- uv / c^2.
Plugging in the variables I would go D = A+B / 1- AB / c^2.
Is this correct? In the private message I sent a picture describing vectors . I didn't get the velocity vectors correct. Could you explain what I got wrong in scene 2 of the pictures I sent ?

 

[PeroK]

Assuming you want $D$ to move along the length of $B$ in the time it takes $A$ to overtake $B$, then in Galilean terms the velocity of $D$ is the average of $A$ and $B$:

$v_D = \frac{v+u}{2}$

And, in $D$'s reference frame, $A$ and $B$ move with equal and opposite velocities of magnitude $\frac{v-u}{2}$.

You can check this by using the Galilean velocity addition. Using primes for velocities in $D$'s frame we have:

$v'_A = v_A - v_D = v - \frac{v+u}{2} = \frac{v-u}{2}$

and

$v'_B = v_B - v_D = u - \frac{v+u}{2} = \frac{u-v}{2} = -v'_A$

The relativistic calculations are much harder, but are clearly explained by Morin.

 

[billllib]

Quick question, do you have a link or an online resource that explains the question in Galilean physics? What is the name of this specific calculation in Galilean physics?

 

[PeroK]

Quick question, do you have a link or an online resource that explains the question in Galilean physics? What is the name of this specific calculation in Galilean physics?

What don't you understand about post #4?

Any introductory kinematics text will cover these sorts of problems. You could try the Khan Academy. Or, here:

https://www.examsolutions.net/a-level-maths/edexcel/mechanics-a-level-tutorials/#kinematics1

 

[billllib]

What don't you understand about post #4?

Any introductory kinematics text will cover these sorts of problems. You could try the Khan Academy. Or, here:

https://www.examsolutions.net/a-level-maths/edexcel/mechanics-a-level-tutorials/#kinematics1

I get it, just curious the name