Errors - Applied Physics - Lecture Slides, Slides of Applied Chemistry

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What is an error?

Some are due to

human error…

For example, by not using the equipment correctly

Let’s look at some examples.

Human error

Example 1

Professor Messer is trying to measure the length of a piece of wood:

Discuss what he is doing wrong.

How many mistakes can you find? Six?

Human error

Example 2

Reading a scale:

Discuss the best position to put your eye.

your eye

Human error

2 is best.

1 and 3 give the wrong readings. This is called a

parallax error.

your eye

It is due to the gap here, between the pointer and the scale. Should the gap be wide or narrow?

Anomalous results

Look at this graph:

Which result do you think may be anomalous?

A result like this should be taken again, to check it.

x

x

x x

x

x

ERRORS

If we are making physical measurements,

there is always error involved. The error is

notated by using the delta, Δ, symbol

followed by the variable representing the

quantity measured.

For example, if we are measuring volume,

the error in measuring the volume would be

symbolized Δ V.

Example:

Find the truncation error for at x= if the first 3

terms in the expansion are retained.

Sol: Error = True value – Approx value

e

x

x

+ +x+

x

x

= +x+

2 3 2

3 4 5 + !

_x

!_

_x

!_

x =

TYPE OF ERRORS

Type of errors

1. Gross error/human Errors
2. Random Errors
3. Systematic Errors
4. Constant Errors
5. Absolute Errors
6. Relative Errors
7. Percentage Errors

Static Errors

TYPES OF STATIC ERROR (cont)

2. Systematic Error

• due to shortcomings of the instrument ( such as defective or worn parts, ageing or effects of the environment on the instrument)  In general, systematic errors can be subdivided into static and dynamic errors.  Static – caused by limitations of the measuring device or the physical laws governing its behavior.  Dynamic – caused by the instrument not responding very fast enough to follow the changes in a measured variable.

• 3 types of systematic error :-

(i) Instrumental error

(ii) Environmental error

(iii) Observational error

TYPES OF STATIC ERROR (cont)

TYPES OF STATIC ERROR (cont)

(ii) Environmental error

• due to external condition effecting the measurement including surrounding area condition such as change in temperature, humidity, barometer pressure, etc
• to avoid the error :- (a) use air conditioner (b) sealing certain component in the instruments (c) use magnetic shields

(iii) Observational error

• introduce by the observer
• most common : parallax error and estimation error (while reading the scale)
• Eg: an observer who tend to hold his head too far to the left, while reading the position of the needle on the scale.

TYPES OF STATIC ERROR (cont)

3. Random error

• due to unknown causes, occur when all systematic error has accounted
• accumulation of small effect, require at high degree of accuracy
• can be avoid by (a) increasing number of reading (b) use statistical means to obtain best approximation of true value

These errors cause readings to be shifted one way (or the other) from the true reading.

Systematic errors

Your results will be systematically wrong.

Let’s look at some examples...

Example 1

Suppose you are measuring with a ruler:

Systematic errors

If the ruler is wrongly calibrated, or if it expands,

then all the readings will be too low (or all too high):