Electric Potential Difference and COE

[physgrl]

Homework Statement

10. If an electron is released from infinity, how fast will it be traveling after falling to within 10-8m of a charge q of 4.8*10-19?

a. 1.32*104m/sec

b. 8.7*104m/sec

*c. 2.76*105m/sec

d. 4.01*105m/sec

Homework Equations

ΔU=ΔVq

V=kq/r

conservation of energy:
1/2mv²=Vq

The Attempt at a Solution

1/2mv²=Vq
1/2mv²=kq_electronq/r
v=√(2*kq_electronq/r*m)
v=√(2*9x10⁹*1.602x10^-19*4.8x10^-19/(10^-8*(9.11x10^-31))
v=3.89x10⁵

I get an answer not available in the options, the correct answer is supposed to be letter C
what did I do wrong?

 

[technician]

You need to calculate the electric potential at a distance of 10^-8m of the charge of 4.8x10^-19C.
The unit of potential is J/C
I got the same answer as you! (3.9x10^5) so don't know what is wrong with the question/answer
I would say d is the best answer

 

[physgrl]

i did that V=kq/r and plugged into get velocity and included the charge of the electron to get potential energy

 

[gneill]

Your calculated result would appear to be correct. Perhaps someone changed values in the problem statement but didn't change the answer key as well.

 

[physgrl]

ok thanks!

 

[technician]

To me it is a bit daft to quote the distance as "to within 10^-8m" because that could mean anything between 1x10^-9 and 1x10^-8m which makes a nonsense of quoting answers to 2 or 3 sig figs... UNLESS there is a subtle link with sig figs that they are testing... I don't know

 

[physgrl]

what do u mean a subtle link with sig figs?

 

[technician]

Well... to within 10^-8m probably means that you took the distance to be 1 x 10^-8m
That is what I did and seems perfectly logical but then 0.9 x 10^-8 would also be a logical number to use and you would get a different answer (greater speed). These differences are due to significant figures rather than the physical process.
If there is this variability in the data then it seems silly to me to give answers with 2 and 3 sig figs.
The answer really should be given to "within an order of magnitude" (power of 10)
It would be interesting to hear the explanation of the correct answer but basically I think what you (we!) have all done is correct.
This is a minor point. !don't let it distract you

 

[physgrl]

ohhh i see what u mean...yeah so there are many answers because there are many possible distances but we have no way of choosing just one ;)

 

[technician]

That is more or less it, their answer d corresponds to a distance just less than 1 x 10^-8m... so using 1 x 10^-8m gives the minimum speed (3.89)... which rounds up to 4.0
but there option is 4.01... looks wrong or sloppy from a sig figs point of view.
It is just a detail !

 

[physgrl]

ok :)

 

[technician]

More on this problem physgrl !
I took their "correct answer" of 2.76x10^5 m/s and worked back to find the corresponding distance from the charge and I got 1.99x10^-8m
This puts a different slant on the wording of the question. If by "to within 10^-8m" they mean between 1 and 2x10^-8m ...which could be seen as a fair interpretation then answer c is OK.
I would say this is a bad question, it seems to be testing your knowledge of electric fields, forces and potential but it comes down to understanding a vague statement... "to within 10^-8m..."
You know what you are doing regarding the "physics" of this question but seem to have been caught out/confused by the wording... just like the rest of us.
It is easy to analyse if you know the answer THEY REQUIRE

 

[physgrl]

hmm...so they probably expected us to check through the answers and find "a correct answer" rather than "the correct answer" like say "which of the following could be...?"

 

[physgrl]

which makes sense because 4.01x10^5 is closer to 10^-8 but it is in the 10^-7 range...and the others are x10 smaller

 

[technician]

I would not say that ! I think it lies in the understanding of a phrase such as "to within 10^-8" which in this question, I think, means less than 2x10^-8.
I must admit it does make sense but it is not "physics"... it is very subtle use of language... not wrong but not obviously understandable.
It is a shame that they did not just state a distance. It sounds like "lazy question writing" to me.
The person knew what answer they wanted but did not know how to phrase the question.

 

[physgrl]

lololol yeah

 

[technician]

one thing to be sure of... you know how to do the physics... and that is the important thing
So this question has 2 correct answers
ours and theirs

 

[physgrl]

ok thanks :)