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Tuesday, November 9, 2010
Chapter 26, problems 1-6
Material to be covered in the Nov. 11 lecture.
Note the comments on a couple of the problems that I made in the WebAssign instructions.
7 comments:
Anonymous
said...
I am having problems with number 4. I am using Δt=Δtp*(1-x/2) where Δt=#hrs given and x=(v/c)^2, but my calculator says that (1-x/2)=1 so my answer is Δt=Δtp which is incorrect. What could I be doing wrong?
Your calculator doesn't work with exact numbers, but keeps about ten decimal digits of accuracy. I did a very similar problem in class on Thursday - look at slide #29.
If you look at my explanation, that's exactly what I did (I had a typo though, I wrote - instead of +). I took the equation straight from the notes and I still get λ=1.
Here are my numbers: Δt=1.7h=6120s, v=1200km/h=333.33m/s
This is exactly what I am doing on paper: Δtp=(6120s)/(1+(.5*333.33^2)/(c^2)).
I have put this exact calculation into my calculator several times, broke it down into several steps to ensure I didn't miss anything, and even tried a different calculator, but my answer is still Δt=Δtp. Is there a mistake in the way I am writing it on my paper?
What you describe is not what I did on that slide. Work with gamma-1, which is ((v/c)^2)/2. That will be the difference in time between the two clocks.
I just wanted to point out that there seems to be a typo in problem 4. The problem suggests that the approximation for (1-x)^1/2 is (1-x/2). According to slide 29 from the lecture given on 11/6 the approximation should be (1+x/2). With x being equal to (1-(v/c)^2)^1/2.
7 comments:
I am having problems with number 4. I am using Δt=Δtp*(1-x/2) where Δt=#hrs given and x=(v/c)^2, but my calculator says that (1-x/2)=1 so my answer is Δt=Δtp which is incorrect. What could I be doing wrong?
Your calculator doesn't work with exact numbers, but keeps about ten decimal digits of accuracy. I did a very similar problem in class on Thursday - look at slide #29.
If you look at my explanation, that's exactly what I did (I had a typo though, I wrote - instead of +). I took the equation straight from the notes and I still get λ=1.
Here are my numbers: Δt=1.7h=6120s,
v=1200km/h=333.33m/s
This is exactly what I am doing on paper: Δtp=(6120s)/(1+(.5*333.33^2)/(c^2)).
I have put this exact calculation into my calculator several times, broke it down into several steps to ensure I didn't miss anything, and even tried a different calculator, but my answer is still Δt=Δtp. Is there a mistake in the way I am writing it on my paper?
What you describe is not what I did on that slide. Work with gamma-1, which is ((v/c)^2)/2. That will be the difference in time between the two clocks.
Prof Stephens, I was having trouble as well with 4. The slides helped greatly. Thanks for the help.
I just wanted to point out that there seems to be a typo in problem 4. The problem suggests that the approximation for (1-x)^1/2 is (1-x/2). According to slide 29 from the lecture given on 11/6 the approximation should be (1+x/2). With x being equal to (1-(v/c)^2)^1/2.
No typo. For small x, sqrt(1-x) is approximately 1-x/2, and 1/sqrt(1-x) is approximately 1+x/2.
The useful approximation is for x=(v/c). Then, for small (v/c), the approximation gives gamma as a number slightly larger than unity.
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