Help with maths

[barx1963 (Malcolm)]

I am, regretfully, mathematically challenged! I am trying to correct this but still come up against fairly simple things that stump me. I am currently reading "Why does E=MC2" By Brian Cox and Jeff Forshaw. I get most of the concepts, the maths stumps me. The authors state that the maths isn’t necessary to understand the book, but I am a bit compulsive and find anything I don’t fully comprehend a challenge.
The bit I am having trouble with is solving (cT)2=12+(vT)2 for T2. The result given is T2=1/(c2-v2) . I have tried to work out the steps but after so many years with no algebra, it’s a struggle!

[RobF (Rob)]

Originally Posted by barx1963

I am, regretfully, mathematically challenged! I am trying to correct this but still come up against fairly simple things that stump me. I am currently reading "Why does E=MC2" By Brian Cox and Jeff Forshaw. I get most of the concepts, the maths stumps me. The authors state that the maths isn’t necessary to understand the book, but I am a bit compulsive and find anything I don’t fully comprehend a challenge.
The bit I am having trouble with is solving (cT)2=12+(vT)2 for T2. The result given is T2=1/(c2-v2) . I have tried to work out the steps but after so many years with no algebra, it’s a struggle!

Did you mean to write the following perhaps Malcolm?

(cT)2=1+(vT)2

That would solve as:

c^2 + T^2 = 1 + v^2 * T^2
T^2(c^2 - v^2) = 1
T^2 = 1/(c^2-v^2)

I'm not familiar with the equations or application, but that might be the direction you're thinking?

[ballaratdragons (Ken)]

Originally Posted by barx1963

I am, regretfully, mathematically challenged! I am trying to correct this but still come up against fairly simple things that stump me. . . .

. . . The bit I am having trouble with is solving (cT)2=12+(vT)2 for T2. The result given is T2=1/(c2-v2) .

Is that mathematics???

Looks like a string of jibberish letters and numbers, or something that you just made up.
I've never seen anything like that before!

I have trouble with basic + - x and divide.

[ballaratdragons (Ken)]

Holy Cow, I just read Rob's reply

So it must be maths!
None that I've ever seen though.

I'm out of here coz I can't help

[barx1963 (Malcolm)]

Sorry. Where it has 2 that is supposed to be "squared" when I posted it the formatting for superscript apopears to have disappeared!

[Allan_L (Allan)]

Originally Posted by RobF

Did you mean to write the following perhaps Malcolm?

(cT)2=1+(vT)2

That would solve as:

c^2 + T^2 = 1 + v^2 * T^2
T^2(c^2 - v^2) = 1
T^2 = 1/(c^2-v^2)

I'm not familiar with the equations or application, but that might be the direction you're thinking?

But
(cT) squared is not c squared plus T squared !
I think it is c squared TIMES T squared.

Even though, I think you have corrected it in reaching the next line.

[sheeny (Al)]

Originally Posted by RobF

Did you mean to write the following perhaps Malcolm?

(cT)2=1+(vT)2

That would solve as:

c^2 + T^2 = 1 + v^2 * T^2
T^2(c^2 - v^2) = 1
T^2 = 1/(c^2-v^2)

I'm not familiar with the equations or application, but that might be the direction you're thinking?

Al.

[wasyoungonce (Brendan)]

or ...to be a PITA

T^2 = 1/(c + v)^2. Difference of 2 squares (c+v)(c-v)

[RobF (Rob)]

Originally Posted by Allan_L

But
(cT) squared is not c squared plus T squared !
I think it is c squared TIMES T squared.

Even though, I think you have corrected it in reaching the next line.

Oops - quite right Allan - didn't mean for a plus to be in there

[GeoffW1 (Geoff)]

Originally Posted by wasyoungonce

or ...to be a PITA

T^2 = 1/(c + v)^2. Difference of 2 squares (c+v)(c-v)

Hi,

That would still be

T^2 = 1/(c^2 - v^2)

= 1/[(c+v)(c-v)]

as RobF suggested

but 1/(c+v)^2 = 1/(c^2 + 2cv + v^2) , which is different

All this looks like the transformation for relativistic time dilation, but not quite the same, as there seems to be a factor c^2 missing.

This book by Prof Cox could be required reading, especially for those doing long time exposures where time dilation could be a factor I'm going to order it now.

Are there photos of PBC?

Cheers

[Kevnool (Kev)]

Humans have 1014 cells at a diameter of 0.01 mm each. If they were placed in a line, how many times around the Earth would they go? The radius of the Earth is 6.38 x 106 m.

Answer: 1014 x 0.01 x 10-6 m = 1 x 106m

Circumference = 2 x 3.14 x 6.38 x 106 = 4.0 x 107 m; No. of times = 40.

[GeoffW1 (Geoff)]

Originally Posted by Kevnool

Humans have 1014 cells at a diameter of 0.01 mm each. If they were placed in a line, how many times around the Earth would they go? The radius of the Earth is 6.38 x 106 m.

Answer: 1014 x 0.01 x 10-6 m = 1 x 106m

Circumference = 2 x 3.14 x 6.38 x 106 = 4.0 x 107 m; No. of times = 40.

Hi,

10^14 cells at 0.01 mm each, lined up, gives a line of

10^14*0.01/1000 m = 10^9 m

Earth's radius is 6.38 x 10^6 m, so

Circumference = 2*PI*6.38 x 10^6 = 40086680 m or so at the equator

then to find how many circumferences in this line of cells,

10^9/40086680 = 25 times or so.

Whether 25 or 40 I would not like to be smeared along the equator

Cheers

[shelltree (Shelley)]

I wish I could understand this I'm going to download the pdf of Algebra for Dummies I. Volume II was too complex And to be honest I'll probably have enough trouble with Volume I

[mswhin63 (Malcolm)]

have a go at this website –http://www.brightstorm.com/ I found it quite useful to revise my maths physics and chemistry.

Text information or assistance is nice and quite informative but these video tutorials are quite good.

The only negative about this site is it doesn't seem to follow any particular order in relation to low learning level to higher learning level so you need to go through and have a go and find out which is the best way.

[wasyoungonce (Brendan)]

Ahh yes my mistake here....a difference of 2 squares should be written a^2 - b^2. The 2 perfect squares are (a+b)^2; and (a-b)^2 but a difference of 2 squares ((a+b)(a-b)) cannot be written as (a+b)^2.

Anyway as said (a^2 - b^2) would be factorised as (a+b)(a-b) = a^2 -ab +ab - b^2 = (a^2 - b^2)

Thus I wrote it as a perfect square format which it isn't.

edit fixed sign typos

[barx1963 (Malcolm)]

Thanks for the help guys! Got the gist of it now.
Yes it is a formula for relativistic time dilation. The explanation for how time dilation works is excellent and makes perfect sense, so if anyone out there is baffled by the idea, I would heartily recommend this book.

Malcolm