00:01
In this problem, we want to know when gamma is just represented on a calculator.
00:09
This is actually, if you're talking about able to have eight digits, one, two, three, four, five, six, seven, eight digit calculator.
00:17
The first time you can see it.
00:22
And gamma is one over the square root, one minus v square, over a c square.
00:33
Now, this number is very close to one.
00:38
I mean, look at what you got to have.
00:39
5 -0 is then a 1.
00:40
So this v squared over c -square term is going to be very small.
00:44
Let's talk about this.
00:46
When v is 0, gamma is 1.
00:48
When v starts to rise, non -0, this term, this whole denominator drops below 1, and so we're starting to get values greater than 1 for gamma.
00:58
So we are now got a very small value beyond 1 for gamma at this point.
01:05
Now, don't interpret this to mean that v is small.
01:09
V over c that is small, but not necessarily v, as we'll see.
01:16
I'll show you what the v is in a second.
01:18
So let's rewrite this.
01:19
A square root is the same as half power, and when you bring that half power to the numerator becomes minus a half.
01:27
So it becomes minus 1 over v squared over c squared to minus 1 half.
01:36
Now, the binomial expansion, we take the power and we multiply that by the second term.
01:45
So this is going to become one minus one -half v -squared over c -squared.
01:54
So this becomes one plus one -half fee -squared over c -square.
02:00
So now let's solve for v -square -over -c -c -squared first.
02:04
Or do the one -half first and then we can take care of the rest...