GREPhysics.NET: GR9677 #36

GR9677 #36

Problem

GREPhysics.NET Official Solution

This problem is still being typed.

Special Relativity $\Rightarrow$ }Conservation of Energy

The rest mass for each mass is 4kg. They collide head-on with identical speeds pointing in opposite directions. This implies that the composite mass is at rest. Thus, recalling that the total energy is given by $E=\gamma mc^2$ and that the rest mass is given by $E=mc^2$ , one has
$2\gamma mc^2 = Mc^2$ , where M is the composite mass.

The particle travels at $v=3c/5$ , which yields $\gamma = 5/4$ . Plug this in to get $M=10/4 \times 4 = 10kg$ .

Alternate Solutions

There are no Alternate Solutions for this problem. Be the first to post one!

Comments

CaspianXI
2009-03-22 16:24:17

The two lumps' energies will be "converted" into mass when they collide and stop because we're given that no energy is radiated. Hence, the final mass must be greater than 8 kg. So, we can immediately eliminate options (A), (B), and (C).

So, if you can't figure it out, you can guess and have a 50% chance of getting it right.

Reply to this comment

lowder.chris
2007-10-03 21:31:57

Relativity gives me a headache. :)

bbaker03
2007-10-16 18:38:25

sorry im looking at the solution and getting confused. are you using the equation $\gamma$ = $\1/sqrt{1-v^2/c^2}$

grae313
2007-10-31 12:44:17

yes, bbaker03, if you plug in $v = 3c/5$ to the equation you wrote for gamma, you get $\gamma = 5/4$

bbaker03
2007-11-01 10:24:11

Thanks a lot for your help this site is saving my life on this test. Can't thank you all enough.

Reply to this comment

Post A Comment!

You are replying to:

Relativity gives me a headache. :)

Bare Basic LaTeX Rosetta Stone
LaTeX syntax supported through dollar sign wrappers $, ex., $\alpha^2_0$ produces $\alpha^2_0$ .
type this...	to get...
$\int_0^\infty$	$\int_0^\infty$
$\partial$	$\partial$
$\Rightarrow$	$\Rightarrow$
$\ddot{x},\dot{x}$	$\ddot{x},\dot{x}$
$\sqrt{z}$	$\sqrt{z}$
$\langle my \rangle$	$\langle my \rangle$
$\left( abacadabra \right)_{me}$	$\left( abacadabra \right)_{me}$
$\vec{E}$	$\vec{E}$
$\frac{a}{b}$	$\frac{a}{b}$

The Sidebar Chatbox...
Scroll to see it, or resize your browser to ignore it...

All-Solutions List | Latest Comments | Unanswered Questions (Cries for Help!) |::| About

This site is not affiliated with ETS, nor is it officially endorsed (yet) by ETS. This site is the work of an individual named Yosun Chang. The solutions, sans user comments and ETS questions, are © 2005 by Yosun Chang except where noted. All rights reserved. / The comments appending particular solutions are due to the respective users. / Educational Testing Service, ETS, the ETS logo, Graduate Record Examinations, and GRE are registered trademarks of Educational Testing Service. The examination questions are © 1997 and © 2001 by ETS.

Bare Basic LaTeX Rosetta Stone