Measurement

Contents 1.

Units

2.

Measurement of Length

3.

Measurement of Volume

4.

Measuring Mass and Weight

5.

Measuring Density

6.

Measurement of Time

Exam Topics… At the end of this chapter you should be able to:

• use and describe how to use rulers, micrometers, vernier scales and callipers to determine lengths • use and describe how to use a measuring cylinder to measure a volume • use and describe how to use clocks and other devices for measuring an interval of time including the period of a pendulum • demonstrate an understanding that mass is a measure of the amount of substance in a body • demonstrate an understanding of inertia as the property of a mass which resist change from its state of rest or motion • describe, and use the concept of, weight as the effect of a gravitational field on a mass • demonstrate understanding that two weights, and therefore masses, may be compared using a balance • use appropriate balances to measure mass and weight • describe experiments to determine the density of a liquid, of a regularly shaped solid object and of an irregularly shaped solid object (by the method of displacement) and make the necessary calculations

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1.

Units

SI Units The following table gives SI units for the basic physical quantities (things that can be measured). All scientists throughout the world use these units. (SI from the French “Le Systeme International d'Unites”.) PHYSICAL QUANTITY

SI UNIT

SYMBOL m

Mass Second A Temperature

Kelvin

Amount of substance

Mole

mol

Luminous intensity

Candela

cd

Prefixes • Used to express physical quantities that are very big or very small. • Although metres are the SI unit for length we use other units based on the metre. Small objects will be measured in centimetres, millimetres or micrometres. Large objects will be measured in kilometres.

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PREFIX

MEANING

SYMBOL

Micro

÷ 1,000,000

µ

Milli

÷ 1,000

m

Centi

÷ 100

c

Deci

÷ 10

d

Kilo

× 1,000

k

Mega

× 1,000,000

M

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Examples 1. What is 23.4 centimetres in metres? Write down the relationship between metres and centimetres. __________ m = __________ cm Turn this into a fraction ____________ = 1

or

____________ = 1

However, 23.4 cm can be multiplied by 1 without changing it. 23.4 cm = 23.4 cm × 1 23.4 cm =23.4 cm × ___________ Cancel the units to give the answer.

2.

Express the speed of 5600 m/s in km/h. 1 km = 1 1000 m

60 s = 1 1 min

and

5600 m × 1 km × 60 s = 5600 s 1000 m 1 min

m s

5600 m/s = Exercise 1. Converting the following values from the units given:

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a)

1.5 m = __________ cm

b)

0.23 mm = __________ m

c)

200 g = __________ kg

d)

15.7 cm = 157 _____

e)

0.37 km = 370 _____

f)

3000 mA = __________ A

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2.

2.

Converting the following values from one unit to another: a)

0.75 hour = __________ min

b)

2 m² = ________ cm²

c)

200 cm³ = __________ dm³

d)

1.7 g/cm³ = ________ kg/m³

Measurement of Length

Rulers The following diagrams show correct and incorrect ways to read from a ruler.

Figure 1

Figure 2

Q1.

Which figure shows the correct way to read a ruler? Explain.

Q2.

What is the true length of the object?

Q3.

This type of error shown in the other figure is called _______________ error.

Q4.

Why is the ruler used from the 10 cm marking and not from its end?

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Different measuring instruments are used for measuring different lengths. This will determine the accuracy of the value we obtain. INSTRUMENT

LENGTH TO BE MEASURED ACCURACY

Tape Measure

Greater than 1 m

1 cm

Metre Rule

10 cm to 1 m

1 mm

Vernier Callipers

~2 cm to ~10 cm

0.1 mm

Micrometer Screw Gauge

Less than 2 cm

0.01 mm

Vernier Callipers

Q1.

Give two advantages of using vernier callipers rather than a ruler?

Q2.

What readings are shown on the following scales?

0 cm

1

2 0

3

4

Main scale: Vernier scale:

10

Reading: _________________

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1

0 cm

2

3

4 0

Main scale: Vernier scale:

10

Reading: _________________ 1

0 cm

2

3 0

4

Main scale: Vernier scale:

10

Reading: _________________ 0 cm

1

2 0

3

4

Main scale: Vernier scale:

10

Reading: _________________

Micrometer Screw Gauge

Q1.

What is the advantage of using a micrometer screw gauge rather than vernier callipers?

Q2.

What is the purpose of the ratchet on the micrometer?

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Q3.

Write down the readings shown on each of the following micrometer screw gauges. 1. Sleeve: 40

0

35 2.

Thimble: Reading: ___________ Sleeve:

25

0

20

3.

Thimble: Reading: ___________ Sleeve:

0

0

Thimble:

45

Reading: ___________

4.

Sleeve: 40

0

35

5.

Thimble: Reading: ___________ Sleeve:

0

0

Thimble:

45

Reading: ___________

Zero Error Before using a micrometer we must check for a zero error. Close the micrometer so that the spindle touches the anvil. If there is no zero error then the reading will be 0.00 mm. As shown below.

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1.

This micrometer has a zero error. Zero reading is 0.03 mm so we subtract 0.03 mm from all readings taken with this micrometer. 2.

This micrometer has a zero error. Zero reading is -0.03 mm so we must add 0.03 mm to all readings taken with this micrometer.

Exercise 0

40 35

What would be the true length being measured above if the micrometer had i)

a zero reading of 0.00 mm. _______________________________

ii)

a zero reading of 0.02 mm. _______________________________

iii)

a zero reading of -0.03 mm.

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_______________________________

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3.

Measurement of Volume

Liquids Volume of a liquid

Q1.

Which of the above are used to find the volume of a small volume of liquid?

Q2.

Which of the above are used to find the volume of a large volume of liquid?

Precautions Always take the following precautions when reading the volume of a liquid: 1. 2. Q.

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What are the readings on the following measuring cylinders? (Scales in cm³.) a)

b)

c)

15

40

30

10

35

20

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Regular Solids Volumes can be calculated by taking measurements then using formulae. Volume of a rectangular block can be found from the equation: Volume of rectangular block =

2 cm 2 cm 3 cm Volume of a sphere can be found from the equation: Volume of sphere =

2m

Volume of a cylinder can be found from the equation: Volume of cylinder =

2 cm 3 cm

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Irregular Solids 1.

Volume of a small irregular solid that sinks

2.

Volume of a small irregular solid that floats

3.

Volume of a larger irregular solid

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4.

Measurement of Mass and Weight

In everyday conversation we use the words mass and weight interchangeably. In Physics they have two very different meanings.

Mass Definition:

SI Unit: • The mass of a body is constant and does not change. • Mass has only a magnitude. • Other units used for mass are the gram (g) and the tonne. 1 kg = __________ g 1 tonne = __________ kg

Measurement of Mass To measure mass we can use one of two instruments:

Sliding Mass Balance (Ohau's balance)

Electronic Balance

Inertia The two people shown below put on roller-skates! Who would be 1. easy to push? 2.

hardest to stop if coming towards you? Thin Man

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Fat Man

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The difference is due to the difference in mass of the two men. The more massive an object the greater its inertia. Definition:

Q.

Explain why you can easily stop a ball thrown towards you at 30 km/h but are not able to stop a car coming towards you at only 5 km/h.

Weight Definition:

SI Unit: Weight is not constant it will vary depending upon the _______________ . Weight has both _______________ and _______________ .

Measurement of Weight To measure weight we can use one of two instruments:

Spring Balance

Compression Balance

Exercise Q. You go to the moon. Will your mass and weight change? Explain your answer.

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Mass and Weight The following table summarises the differences between mass and weight: MASS

WEIGHT

Definition:

Units: Does It Have Direction? Is Location Important? Measured Using:

5.

1.

1.

2.

2.

Density

Different objects of the same size and shape often have a different weight. We then say that their densities are different. Definition:

SI Unit: Another common unit used is grams per cubic centimetre (g/cm³ or g cm-3). Density can be calculated from the equation:

Density = ________________________

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Or we can write this in symbols as:

ρ= m= V=

Where

Measurement of Density Method: 1.

Volume of the object is calculated using one of the methods on pages 9-10.

2.

The mass is measured using a __________________ or an electronic balance.

3.

Density calculated using the above equation.

Precaution: The units must be kg and m³ or g and cm³. DO NOT MIX.

Density of Water One important density for you to know is that of water. Exercise: Q1. A 2 litre coke bottle is filled with pure water and is found to have a mass of 2000 g (excluding the mass of the bottle). What is the density of pure water?

So density of pure water is: ρwater = _________ kg/m³

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or:

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ρwater = ______ g/cm³

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Floating and Sinking When placed in water some objects will float and others will sink. Q1.

Which of the following objects will float when placed in water? OBJECT

DENSITY

Wood (oak)

650 kg/m³

Iron

2700 kg/m³

Gold

19000 kg/m³

Oil

850 kg/m³

Ice

920 kg/m³

FLOAT / SINK

Q2.

Use your results to complete the following.

Q3.

If the density of an object is less than that of water it will _______________.

Q4.

If the density of an object is more than that of water it will ______________.

Q5.

Write the densities of gold and oak in g/cm³. Gold Oak

Q6.

Will ice sink or float in oil? Explain your answer.

6.

Measurement of Time

SI Unit: Other common units for measuring time are: All clocks measure time by counting the number of times something vibrates, or moves, back and forth. This type of repeated movement is called an oscillation. The time taken to make one complete oscillation is called the period of the oscillation.

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There are several different devices that can be used to measure time intervals. These will depend on: • how long the time interval is (a fraction of a second - years). • the accuracy we require (to the nearest second, minute, day). Pendulum A pendulum in the simplest type of clock. It consists of a bob (small weight) swinging back and forth on a string.

Side View

Front View

• The length of the string, from clamp to centre of the bob, is l. • The distance from A to B is called the amplitude of the oscillation, A. • The period is the time taken, T, to swing from A to C and back to A again. Q1.

What happens to the period, T, if we change the mass of the bob?

Q2.

What happens to the period, T, if we change the amplitude, A?

Q3.

What happens to the period, T, if we change the length of the string, l?

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