F = kQq/R2 finding force problem

[xNick94]

Two charges Q1 amd Q2 jabe a force of 3.1x10^-8 N when the distance between them is 3m. Use the formula F = kQq/R2 to determine the force when the distance (R) between charge Q1 and Q2 increased from 3m to 4.5m

The Attempt at a Solution

My attempt was that
F = 1/R^2
k= 9.0x10^9

F=(3/4.5)^2
F=0.44N

3.1x10^-8 / 0.44
=.7 x10^-8

The answer being F = .7 x10^-8 N


Is that correct?

 

[PeterO]

Two charges Q1 amd Q2 jabe a force of 3.1x10^-8 N when the distance between them is 3m. Use the formula F = kQq/R2 to determine the force when the distance (R) between charge Q1 and Q2 increased from 3m to 4.5m

The Attempt at a Solution

My attempt was that
F = 1/R^2
k= 9.0x10^9

F=(3/4.5)^2
F=0.44N

3.1x10^-8 / 0.44
=.7 x10^-8

The answer being F = .7 x10^-8 N


Is that correct?

Up to (3/4.5)^2 I was fairly comfortable with.

From there on, not so much.
I think 0.44N was not such a great statement, but I know what you meant [it reads like a force value in Newtons]

Next I am not sure why you decided to divide by 0.44 - nor why you thought the answer was what you gave.

I don't think you should round of 4/9 to 0.44, and think more carefully about how to use that factor.

 

[xNick94]

Up to (3/4.5)^2 I was fairly comfortable with.

From there on, not so much.
I think 0.44N was not such a great statement, but I know what you meant [it reads like a force value in Newtons]

Next I am not sure why you decided to divide by 0.44 - nor why you thought the answer was what you gave.

I don't think you should round of 4/9 to 0.44, and think more carefully about how to use that factor.

Yes good idea, i'll stick with 4/9 instead of the decimal to preserve accuracy. Since F is proportional to 1/R^2. If R increases from 3 m to 4.5 m shouldn't the force decrease by a factor of (3/4.5)^2. And i thought decrease by a factor means divided by so i divide the original force by the force i got from the divide i did prior?

Edit: I just divided it the 4/9, it gives me 6.9x10^-8 ( i see why you suggested i'd use 4/9 )

 

[PeterO]

Yes good idea, i'll stick with 4/9 instead of the decimal to preserve accuracy. Since F is proportional to 1/R^2. If R increases from 3 m to 4.5 m shouldn't the force decrease by a factor of (3/4.5)^2. And i thought decrease by a factor means divided by so i divide the original force by the force i got from the divide i did prior?

Edit: I just divided it the 4/9, it gives me 6.9x10^-8 ( i see why you suggested i'd use 4/9 )

It is common for people to confuse what to do with the factors.

You calculated a factor of 4/9 [good], and wanted to find the reduced force. That is, you wanted to get a smaller value for the Force.

How do you use 4/9 to get a smaller value?

Note: Some people get a factor of 9/4 [perhaps in error]. what should they do with a factor of 9/4 in order to get a smaller value?

And don't forget to apply your factor to the original value given!

 

[xNick94]

It is common for people to confuse what to do with the factors.

You calculated a factor of 4/9 [good], and wanted to find the reduced force. That is, you wanted to get a smaller value for the Force.

How do you use 4/9 to get a smaller value?

Note: Some people get a factor of 9/4 [perhaps in error]. what should they do with a factor of 9/4 in order to get a smaller value?

And don't forget to apply your factor to the original value given!

Hmm so was my original divide procedure justified from my explanation?
3.1x10^-8 / (4/9) = 6.9x10^-8 ...the force increased so this has to be wrong since it has to decrease right?

 

[PeterO]

Hmm so was my original divide procedure justified from my explanation?
3.1x10^-8 / (4/9) = 6.9x10^-8 ...the force increased so this has to be wrong since it has to decrease right?

Yes - it is supposed to decrease.

I never bother too much which factor my students calculate [4/9 or 9/4], I just want them to think about how to effect the change needed.
If you want a smaller answer, and will be using a factor less than 1, you need to multiply.
If you want a smaller answer, and will be using a factor greater than 1, you need to divide.

Send me back your new answer then I will explain how I would have looked at/solved the problem.

 

[PeterO]

Hmm so was my original divide procedure justified from my explanation?
3.1x10^-8 / (4/9) = 6.9x10^-8 ...the force increased so this has to be wrong since it has to decrease right?

Did you sort out where you went wrong? Only a single, simple error!

 

[xNick94]

Sorry for the late reply, had to work and family friends were visiting.

If you want a smaller answer, and will be using a factor less than 1, you need to multiply.
If you want a smaller answer, and will be using a factor greater than 1, you need to divide.

Did you sort out where you went wrong? Only a single, simple error!

Would you then have to multiply it since 4/9 is under 1.
3.1x10^-8 x 4/9 = 1.3 x 10^-8

Would the force be just 1.3x10^-8 or would i have to subtract that from 3.1x10^-8?

 

[PeterO]

Sorry for the late reply, had to work and family friends were visiting.

Would you then have to multiply it since 4/9 is under 1.
3.1x10^-8 x 4/9 = 1.3 x 10^-8

Would the force be just 1.3x10^-8 or would i have to subtract that from 3.1x10^-8?

The multiplication is correct. Though you have merely "truncated" the answer rather than round it off - it should be 1.4 x 10^-8 when rounded to 2 figures.

Fortunately if you had subtracted 4/9 form 3.1 x 10^8 you would get approximately -4/9 and thus recognise it as wrong.

4/9 was a factor, and you either multiply or divide by factors.

Fractions are always a problem, because often work backwards: multiplying by them you get smaller, divide you get bigger.

The way I would have done it - which ultimately is numerically the same thing - is.

Since separation is changing from 3 to 4.5 - not an integer factor change - I would work on an interim separation of 1.5 m

This is half the first separation - meaning 4 x the force or 12.4 x 10^-8

I then change to 4.5.

This is 3 times the interim separation so it if F / 9 or 1.377778 x 10^-8

Rounding to 2 significant figure this is 1.4 x 10^-8

********** Be careful to always do calculations to as many figures as your calculator can handle - then at the end ROUND OFF, don't just chop off the last figures.**************