A physics teacher: Division

This is the second part of a series of post on finding uncertainty in derived quantities. You can find the index here and the part on addition and subtraction here.

Now very often when you performed an experiment you meet quantities that need to be processed to obtain a derived quantity such as g, the acceleration due to gravity, or any other derived quantities.

You have already seen the first part on addition and subtraction and now you will see how to do it for multiplication and division.

If in an experiment is performed and the following quantities are measured with their uncertainties.

A = 10.2+-0.2 cm

B = 5.4 +-0.4 cm

Now if you need to process these quantities to find AB and A/B with their uncertainties how would you do it?

Uncertainty in multiplication

How would you determine the value of AB and its uncertainty?

You will have to calculate the value of AB first.

AB = 10.2 *5.4 = 55.o8 =55 (2 sf )

To determine the uncertainty in AB you will have to use the equation below.

Rearranging the equation will give you

Hence AB = 55+-5 cm²

Remember the uncertainty in A and B are to 1 sf hence the uncertainty in AB must be given to 1 sf.

Uncertainty in division

You are now going to determine the value of A/B and its uncertainty.

You will have to determine the value of A/B first.

A/B = 10.2 /5.4 =1.888 = 1.9

To determine the uncertainty of A/B you will determine the equation below

Rearranging the equation will give you

Remember the uncertainty in A/B is given to 1 sf since the uncertainties in A and B are given to 1 sf.

Hence A/B = 1.9 +-0.2

With these two formula you can thus determine the uncertainty in any derived quantities that involves multiplication and division.

Now you can move to the next part where the method to determine uncertainty of derived quantities where powers, square root, etc are involved.

Thursday, November 26, 2009

Measurement, errors and uncertainties

Calculation

Calculation in Physics

Performing addition and subtraction

Performing multiplication and division

Performing Calculation with lg and ln

Uncertainties and errors

Uncertainty and How to process it

How to determine uncertainty in a derived quantity when addition or subtraction is performed?

How to determine uncertainty in derived quantity when multiplication or division is performed.

How to determine uncertainty in a derived quantity when powers, root,etc are involved.

Monday, October 5, 2009

How to determine uncertainty in derived quantity when multiplication or division is performed

This is the second part of a series of post on finding uncertainty in derived quantities. You can find the index here and the part on addition and subtraction here.

Now very often when you performed an experiment you meet quantities that need to be processed to obtain a derived quantity such as g, the acceleration due to gravity, or any other derived quantities.

You have already seen the first part on addition and subtraction and now you will see how to do it for multiplication and division.

If in an experiment is performed and the following quantities are measured with their uncertainties.

A = 10.2+-0.2 cm

B = 5.4 +-0.4 cm

Now if you need to process these quantities to find AB and A/B with their uncertainties how would you do it?

Uncertainty in multiplication

How would you determine the value of AB and its uncertainty?

You will have to calculate the value of AB first.

AB = 10.2 *5.4 = 55.o8 =55 (2 sf )

To determine the uncertainty in AB you will have to use the equation below.

Rearranging the equation will give you

Hence AB = 55+-5 cm²

Remember the uncertainty in A and B are to 1 sf hence the uncertainty in AB must be given to 1 sf.

Uncertainty in division

You are now going to determine the value of A/B and its uncertainty.

You will have to determine the value of A/B first.

A/B = 10.2 /5.4 =1.888 = 1.9

To determine the uncertainty of A/B you will determine the equation below

Rearranging the equation will give you

Remember the uncertainty in A/B is given to 1 sf since the uncertainties in A and B are given to 1 sf.

Hence A/B = 1.9 +-0.2

With these two formula you can thus determine the uncertainty in any derived quantities that involves multiplication and division.

Now you can move to the next part where the method to determine uncertainty of derived quantities where powers, square root, etc are involved.

Saturday, October 3, 2009

Uncertainty and how to process it!

In physics all quantity that is measured come with its uncertainty. This is because the instrument, the experiment or the person performing the measurement is subjected to some limitations.

For example

Someone that is measuring a length with a metre rule cannot measure the length to a precision that is better than one mm. So a length that is measured with a metre rule will have an uncertainty of +-o.1 c m.
The limitation can either be due to the experiment itself, the apparatus, or the experimenter. Someone measuring the height of rebound will measure it with an uncertainty of +- 0.5 cm. Someone estimating the mass of an object can measure it with an uncertainty of +-0.5 kg. A voltmeter will give a reading with a percentage uncertainty of 1%.

[As you may have guess from 2 above not all measurements that are performed will have these uncertainty. These are for example only.]

As you can see all quantities that are measured will have uncertainties. And as a result any other quantities that are derived from the measured quantities will have their uncertainties.

We are going to see how to determine the uncertainty when the following operations are performed.

Addition and subtraction
multiplication and division
power, square root, square, etc
Other operations using the extreme-value method (under construction)

To know how to determine the uncertainty when addition and subtraction is performed see the next part of this series.

Tuesday, September 1, 2009

How to perform mutiplication and division?

Division and multiplication is often encountered in physics and it is very important that you know how to give the answer in the appropriate form.

Let us have a look at how division and multiplication is performed.

Multiplication

Let us see an example of a multiplication and see how to give the answer in the appropriate form.

23.2 * 3.1 = 71.92 = 72

Can you guess why the answer is 72?

Firstly you have to look at the number of significant figures in the two number used.

23.2 3 significant figures

3.1 2 significant figures

One of the numbers (3.1) has the smallest number of significant figures (2) as a result the answer must be given to 2 significant figures. Hence the answer is given as 72.

Let us have a look at a second example.

22.34 * 123 = 2747.82 = 2750

123 has 3 significant figures and 22.34 has 4 significant figures so the answer is given to 3 significant figures.

Have you guessed the law yet? If yes write it down. If not keep thinking. We will see it at the end of the post.

Division

In a way division is somewhat related to multiplication. Let us have a look at an example and see how the answer is given.

14.2 / 2.333 = 6.08658 = 6.09

As you can see it is similar to multiplication. The two number used has 3 and 4 significant figures respectively. And as a result the answer is given to 3 significant figures.

Let us have a look at a second example.

1.33 / 3.0 = 0.44333

Can you guess how to write the answer in the correct form?

Yes you have guessed right. It is 0.44. Since the two numbers used are at 3 and 2 significant figures respectively, then the answer is given to 2 significant figures.

So have you guessed the rule that govern the multiplication and division? Here it is!!

When a multiplication or a division is performed, the answer is given to the same number of significant figures as the number used with the smallest number of significant figures.

It is now time to do some exercises.