MEASUREMENT

ContentsUnitsMeasurement of LengthMeasurement of VolumeMeasuring Mass and WeightMeasuring DensityMeasurement of Time

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

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

• 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

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

Length

Time

Electric Current

metre

kilogram kg

s

ampere

K

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.

Prefix Meaning Symbol

Micro 1,000,000

Milli 1,000 m

Centi 100 c

Deci 10 d

Kilo 1,000 k

Mega 1,000,000 M

Examples

1. What is 23.4 centimetres in metres?

Write down the relationship between metres and centimetres.

100 cm = 1 m

1 cm = 1 / 100 m

1 cm x 23.4 = (1 / 100) m x 23.4

23.4 cm = 0.234 m

Examples

2. Express the speed of 5600 m/s in km/h.

5600 m/s = 5600 m / 1 s

[ (5600) / (1000) ] km = 5.6 km = 20 160 km/h [ (1) / (3600)] h 0.000278 h

Exercise1. Converting the following values from the units given:

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

Exercise

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

ContentsUnits (Completed)Measurement of LengthMeasurement of VolumeMeasuring Mass and WeightMeasuring DensityMeasurement of Time

RulersThe 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?

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 3 4

100

Main scale:Vernier scale:Reading: _________________

0 cm 1 2 3 4

100

Main scale:Vernier scale: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?

Q3. Write down the readings shown on each of the following micrometer screw gauges.

0 40

35

0 25

20

1. Sleeve:Thimble:Reading: ___________

2. Sleeve:

Thimble:Reading: ___________


0 0

45

40

35

0

3. Sleeve:

Thimble:Reading: ___________

4.

Sleeve:Thimble:Reading: ___________


0 0

45

5.

Sleeve:Thimble: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.

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

40

35

0

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. _______________________________

ContentsUnits (Completed)Measurement of Length

(Completed)Measurement of VolumeMeasuring Mass and WeightMeasuring DensityMeasurement of Time

LiquidsVolume 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. Place the container on a flat horizontal surface.2. The eye must be positioned perpendicularly at the mark of the scale. This is to

avoid errors in measurement due to parallax.

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

10

15

35

40

20

30

Regular SolidsVolumes can be calculated by taking measurements then using formulae.

2 cm

3 cm2 cm

2 m

3 cm

2 cm

Volume of rectangular block =

Volume of sphere =

Volume of cylinder =

Irregular Solids

1. Volume of a small irregular solid that sinks

Irregular Solids

2. Volume of a small irregular solid that floats

Irregular Solids

3. Volume of a larger irregular solid


(Completed)Measurement of Volume

(Completed)Measuring Mass and WeightMeasuring DensityMeasurement of Time

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

MassDefinition:Mass is defined as the amount of matter in a body. 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 = 1000 g1 tonne = 1000 kg

Measurement of MassTo measure mass we can use one of two instruments:

Sliding Mass Balance Electronic Balance(Ohau's 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 Fat Man

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

Inertia

Definition:

Inertia is defined as the reluctance of an object to change its state of rest or uniform motion in a straight line. 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: Weight is defined as the force of earth’s gravitational pull on a body. SI Unit:

Newton (N)

Weight is not constant as it will vary depending upon acceleration due to gravity. Weight has both magnitude and direction.

Measurement of Weight

To measure weight we can use one of two instruments:

Spring Balance Compression Balance

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

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: Spring Balance,Compression

Balance

Mass is defined as the amount of matter in a body.

Weight is defined as the force of earth’s

gravitational pull on a body.kg N

No Yes

No Yes

Sliding Mass Balance,

Electronic Mass Balance



(Completed)Measuring Mass and Weight

(Completed)Measuring DensityMeasurement of Time

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

Density is defined as the mass per unit volume. SI Unit: kg/m3 or kg m-3

Another common unit used is grams per cubic centimetre (g/cm³ or g cm-3).

Density can be calculated from the equation:

Density = Mass / Volume

Or we can write this in symbols as: = m / V where = density

m = massV = volume

Measurement of Density

Method:

1. Volume of the object is calculated using one of the methods listed in Unit 1.3.2. The mass is measured using a sliding mass balance 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?

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? Solution:

m = 2000 g , V = 2000 cm3

Thus, = m / V = 2000 g / 2000 cm3 = 1 g/cm3

or

m = 2 kg, V = ( 2000 / 1000000 ) m3 = 0.002 m3

Thus, = m / V = 2 kg / 0.002 m3 = 1000 kg/m3

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 Float / Sink

Wood (oak) 650 kg/m³

Iron 2700 kg/m³

Gold 19000 kg/m³

Oil 850 kg/m³

Ice 920 kg/m³

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.




(Completed)Measuring Density (Completed)Measurement of Time

SI Unit: second

Other common units for measuring time are: minute, hour 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.

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).• accuracy we require (to the nearest second, minute, day)

PendulumA 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

PendulumA pendulum in the simplest type of clock. It consists of a bob (small weight) swinging back and forth on a string. 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?

Q1. What happens to the period, T, if we change the mass of the bob?

The period T remains unchanged when the mass of the bob is changed. Q2. What happens to the period, T, if we change the amplitude, A? The period T remains unchanged when the amplitude A is changed. Q3. What happens to the period, T, if we change the length of the string, l?

The period T increases when the length of the string is increased. The period T decreases when the length of the string is decreased.




(Completed)Measuring Density (Completed)Measurement of Time

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MEASUREMENT

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