Hello Lucas,
thanks for coming back to us with your findings. It is great to hear
that you can make good use of the book 'even in Switzerland'. ;-)
I checked the worked example 75 and you are right. There is an error
with the sin and the cos. Unfortunately there is another subsequent
error, which renders the whole solution wrong (numerically). We will
change the book accordingly.
For now here is how it is supposed to be:
[Remark: All the text stays the same (except for the last sentence),
just the equations change.]
First change: Step 3
F_E = T * cos (60 degrees) F_g = T * sin (60 degrees)
This is the error you spotted.
Explanation: T is the 60 degree projection on F_E, therefore it has to
be the cos. On F_g instead T is the 30 degree (90 degrees - 60
degrees) projection, which leaves us with cos (30 degrees) = sin (60
degrees).
Second problem: Step 3, second equation:
This equation is mathematically correct, but the result is wrong. It
should be T=115.5 N (not 1155 N).
Subsequently, step 3, third equation (the cos (60 degrees) was and is
correct here, the typo happened earlier as mentioned above):
Putting the correct result for T from the last equation here gives us:
F_E = 115.5 N * cos (60 degrees) = 57.75 N.
Finally, step 4:
|Q_x| is numerically wrong, due to the error introduced earlier. The
correct value is:
|Q_x| = sqrt( F_E * r^2 / k) = sqrt ( (57.75 N) * (0.5 m)^2) / ( 8.99
* 10^9 N * m^2 / C^2) )
= 5.67 * 10^(-5) C
"This the charge on X is -5.67 * 10^(-5) C."
Thanks again for finding this inconsistency. Please let me know if
everything is clear to you now.
What physics test are you learning for? Where in Switzerland are you?
You can also contact me in German (not in French, yet ;-) ) if this is
easier for you.
Greetings from Geneva,
Markus
address@hidden
Lucas Vogelsang wrote:
Hi,
I have found your book via Wikibooks. I am currently learning for a
physicstest and think that this book is quite helpfull for me, even
though I am from Switzerland.
However one thing confused me:
The worked example 75 seems to be wrong.
It first says:
F_{E} = T*sin(60) and F_{g} = T*sin(60)
next time they refer to F_{E} as F_{E} = T* cos(60) = ...
So what is correct?
I have found this in a pdf. It is on the pdf page 230 or the page 222
according to the documents page numbers.
regards,
Lucas
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