Physics: It’s all around you…

What is Physics?

What is Physics?

Physics is the science concerned with the

fundamental laws of the universe.

Deals with:

Matter

Energy

Space

Time

And all their interactions

But Wait………….

We need to review your math skills

Scientific notation

SI units

Significant Digits & Calculations

Error

We will be doing this over the few days

Day 1: Scientific Notation

- Extremely large and extremely small numbers are

difficult to work with in common decimal notation

- Scientific notation, or standard notation, expresses a

number by writing it in the form: a x 10n

Expression Common decimal

notation

Scientific notation

124.5 million kilometres 124 500 000 km 1.245 x 105 km

154 thousand

picometres

154 000 pm 1.54 x 105 pm

602 sextillion molecules 602 000 000 000 000

000 000 000 molecules

6.02 x 1023 molecules

Scientific Notation

In scientific notation, the number is expressed by:

1. writing the correct number of significant digits with one

non-zero digit to the left of the decimal point

2. multiplying the number by the appropriate power (+ or

– ) of 10

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Example:

2394

= 2.394 x 1000

= 2.394 x 103

0.067

= 6.7 x 0.01

= 6.7 x 10 -2

Note: scientific notation also enables us to show the correct number of significant digits. As such, it may be necessary to use scientific notation in order to follow the rules for certainty (discussed later)

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Using your calculator….

On many calculators, scientific notation is

entered using a special key; labelled EXP

or EE. This key includes “x 10” from the

scientific notation; you need to enter only

the exponent. For example, to enter

7.5 x 10 4 press 7.5 EXP 4

3.6 x 10-3 press 3.6 EXP +/- 3

Practice 1. Express each of the following in scientific notation (to

2 sig. dig.)

A) 6 807

B) 0.000 053

C) 39 379 280 000

D) 0.000 000 813

E) 0.070 40

F) 400 000 000 000

G) 0.80

H) 68

Practice 2. Express each of the following in

common notation

A) 7 x 101

B) 5.2 x 103

C) 8.3 x 109

D) 10.1 x 10-2

E) 6.3868 x 103

F) 4.086 x 10-3

G) 6.3 x 102

H) 35.0 x 10-3

Investigation: Training on the Job

Problem: How long (in hours) will it take the toy train to travel

across Canada from east to west?

Materials:

- Metre stick -Small wind-up toy - Clock

Procedure:

1. Measure as carefully as you can , in centimetres, how far the

vehicle can travel in 5 seconds

2. Repeat step one two more times and then calculate the

average.

Observations:

Trial Distance (cm)

1

2

3

Average

Questions:

1. How far (in cm) did the train travel in 1 second?

2. How far (in km) did the train travel in 1 second?

3. How many km would it travel in 1 hour?

4. How long would it take (in days) to go across Canada from St.

John’s in Newfoundland to Victoria in British Columbia? (highway

distance) **7314 km

**post your group’s answer to this question on the board

5. Do you think it would make any different if the vehicle travelled

from west to east or east to west?

Day 2. SI Units

International System of Units (SI) Over hundreds of years, physicists (and other

scientists) have developed traditional ways (or

rules) of expressing their measurements. If we

can’t trust the measurements, we can put no

faith in reports of scientific research. As such,

the International System of Units (SI) is used

for scientific work throughout the world –

everyone accepts and uses the same rules, and

understands that there are limitations to the

rules.

SI

SI Rules

In the SI system all physical quantities can be

expressed as some combination of

fundamental units, called base units. (i.e.,

mol, m, kg, …..) . For example:

1N = 1 kg•m/s2 => unit for force

1 J = 1 kg•m2/s2 => unit for energy

SI

SI Rules

The SI convention includes both quantity and

unit symbols.

Note: these are symbols (e.g., 60 km/h) and

are not abbreviations (e.g., mi./hr/)

When converting units, the method most

commonly used is multiplying by conversion

factors, which are memorized or referenced

(e.g., 1 m = 100 cm, 1 h = 60 min = 3600 s)

It is also important to pay close attention to

the units, which are converted by multiplying

by a conversion factor (e.g., 1 m/s = 3.5 km/h)

SI (handout)

Useful conversion factors!

SI Practice:

Note: this is just a partial list – refer to pg.

661 for a complete list or the handout given

Investigation #2:

Measuring Human Reaction Time

With only a metre stick??!!??

Stopwatches

- For a number of different applications it is

necessary to know how quickly a person is able

to react to some situation.

- The first problem with trying to measure reaction

time is that we must find a way to NOT have

reaction time of the measurer influence the

measurement.

Yes we can!!

• With only a common metre stick, a couple of friends, and some common items in the classroom it can be done.

• By measuring the distance a metre stick falls before being caught, we can use a Physics formula to turn distance into time.

• You likely haven’t seen this equation yet, but it is coming soon…

How does this work?

• A couple of conditions are needed to allow a very important Kinematics equation to be simplified and applied here.

• One assumption is that the metre stick is released, not thrown.

• The second assumption is that gravity remains constant (with a value of 9.8 m/s2, but more on that later in the course)

So what is this equation you ask?

∆t is the time in seconds, given the metre stick falls a distance ∆d metres. Be careful with your units, or you will get some peculiar values!

9.4

dt

Your task

• - Develop a simple procedure that clearly shows how you would conduct this investigation to minimize uncertainty

• - Collect data for several trials for each member of your team. Record in a clear, meaningful manner.

• - Convert your measured values into time values using the formula you just saw.

• - Calculate the average reaction time for each member of the group, and then calculate the average reaction time for the whole group.

• - Determine the percent difference between the shortest and longest reaction times in the group.

And what will be handed in? • - It is hoped that on Thursday you will be exchanging labs

with another team who will evaluate your procedure.

• - Their results and evaluation will be added to your lab as an appendix (their evaluation can be left as rough copy)

• - Your lab will include Purpose, Apparatus (sketch), Procedure, Observations, Analysis (including percent difference calculations), Discussion (comments from the other team should help you here) and Conclusion and an STSE (relating science to technology, society, and the environment) example of the significance of reaction times

• - For this lab, you will be submitting a single lab for the team but individual STSE examples (due on Monday)

Day 3. Uncertainty

and Significant

Digits

Uncertainty in Measurements:

There are two types of quantities used in

science: exact values and measurements.

Exact values include defined quantities (1 m =

100cm) and counted values (5 beakers or 10

trials).

Measurements, however, are not exact because

there is always some uncertainty or error

associated with every measurement. As

such, there is an international agreement about

the correct way to record measurements

Significant Digits

The certainty of any measurement is communicated by the number of significant digits in the measurement.

In a measured or calculated value, significant digits are the digits that are known for certain and include the last digit that is estimated or uncertain.

There are a set of rules that can be used to determine whether or not a digit is significant (read pg. 650-651 of text)

Significant Digits Rules:

All non-zero digits are significant: 346.6 N has

four significant digits

In a measurement with a decimal point, zeroes

are placed before other digits are not significant:

0.0056 has two significant digits

Zeroes placed between other digits are always

significant: 7003 has four significant digits

Zeroes placed after other digits behind a decimal

are significant: 9.100 km and 802.0 kg each has

four significant digits

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Significant Digits In a calculation:

When adding or subtracting measured quantities, the final answer should have no more than one estimated digit (the answer should be rounded off to the least number of decimals in the original measurement) **number of decimal places matter

When multiplying or dividing, the final answer should have the same number of significant digits as the original measurement with the least number of significant digits ** significant digits matter

**when doing long calculations, record all of the digits until the final answer is determined, and then round off the answer to the correct number of significant digits

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Significant Digits

Practice:

Significant digits

Precision

Measurements also depend on the

precision of the measuring instruments

used – the amount of information that the

instrument provides

For example, 2.861 cm is more precise

than 2.86 cm

Precision is indicated by the number of

decimal places in a measured or

calculated value

Precision

Rules for precision:

1. All measured quantities are expressed as

precisely as possible. All digits shown

are significant with any error or

uncertainty in the last digit.

For example, in the measurement 87.64 cm,

the uncertainty lies with the digit 4

Precision 2. The precision of a measuring instrument

depends on its degree of fineness and

the size of the unit being used

For example, a ruler calibrated in

millimetres is more precise than a ruler

calibrated in centimetres

Precision

3. Any measurement that falls between the

smallest divisions on the measurement

instrument is an estimate. We should

always try to read any instrument by

estimating tenths of the smallest division.

Precision

4. The estimated digit is always shown

when recording the measurement.

Eg. The 7 in the measurement 6.7 cm

would be the estimated digit

Precision

5. Should the object fall right on a division

mark, the estimated digit would be 0.

Precision

worksheet

Reaction Time Lab – Step 2

Today you are to have your PROCEDURE ready to be evaluated by another team.

When you get another team's procedure to evaluate you are to follow it PRECISELY to determine reaction times for each of the members of your team.

When you are completed, return the lab to the team along with ONE hand written page outlining your thoughts on their procedure and the results of your testing. (i.e. your teams reaction times.)

Day 4. Error

Error in Measurement

Many people believe that all

measurements are reliable (consistant

over many trials), precise (to as many

decimal places as possible), and accurate

(representing the actual value). But there

are many things that can go wrong when

measuring. For example:

Error in Measurement

There may be limitations that make the

instrument or its use unreliable (inconsistent)

The investigator may make a mistake or fail

to follow the correct techniques when reading

the measurement to the available precision

(number of decimal places)

The instrument may be faulty or inaccurate; a

similar instrument may give different readings

What are three things you can do during

an experiment to help eliminate errors?

To be sure that you have measured correctly,

you should repeat your measurement at least

three times

If your measurements appear to be reliable,

calculate the mean and use that value

To be more precise about the accuracy,

repeat the measurements with a different

instrument

Two Types of Error Random error results when an estimate is made to

obtain the last digit for an measurement

The size of the random error is determined by the

precision of the measuring instrument

For example, when measuring length with a

measuring tape, it is necessary to estimate between

the marks on the measuring tape

If these marks are 1 cm apart, the random error will

be greater and the precision will be less than if the

marks were 1 mm apart.

Such errors can be reduced by taking the average of

several readings

Two Types of Error

RANDOM ERROR

- Results when the last digit is estimated

- Reduced by taking the average of several

readings

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Systemic Error

- is associated with an inherent problem with the

measuring system, such as the presence of an

interfering substance, incorrect calibration, or room

conditions.

- For example, if a balance is not zeroed at the beginning,

all measurements will have a systemic error; using a

slightly worn metre stick will also introduce error

- Such errors are reduced by adding or subtracting the

known error or calibrating the instrument

SYSTEMIC ERROR

- Due to a problem with the measuring

device

- Reduced by adding/subtracting the error

or calibrating the device

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Accuracy & Precision

In everday usage, “accuracy” and

“precision” are used interchangeably to

descibe how close a measurement is to a

true value, but in science it is important to

make a distinction between them

Accuracy & Precision Accuracy:

- Refers to how closely a

measurement agrees

with the accepted

value of the object

being measured

Precision:

- Describes how it has

been measurement

- Depends on the

precision of the

measurement

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Percentage Error

No matter how precise a measurement is, it

still may not be accurate.

Percentage Error is the absolute value of

the different between experimental and

accepted values expressed as a percentage

of the accepted value

Percentage Difference

Sometimes if two values of the same

quantity are measured, it is useful to

compare the precision of these values by

calculating the percentage difference

between them

Practice

Worksheet – math skills