1. Contents MEASUREMENT Units Measurement of Length Measurement of Volume
Measuring Mass and Weight
Measuring Density
Measurement of Time

2. MEASUREMENT 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

3. MEASUREMENT 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

4. 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”.)

5. Units Physical Quantity SI Unit Symbol m Mass second A Temperaturem
Mass
second A
Temperature
Kelvin
Amount of substance
Mole
mol
Luminous intensity
Candela cd
Length
metre
kilogram kg
Time s
Electric Current
ampere K

6. Units
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.

7. Units Prefix Meaning Symbol Micro ¸ 1,000,000 m Milli ¸ 1,000 Centi
¸ 100 c
Deci
¸ 10 d
Kilo
1,000 k
Mega
1,000,000 M

8. Units 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 = (1 / 100) m x 23.4
23.4 cm = m

9. Units 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 = km/h
[ (1) / (3600)] h h

10. Units
Exercise
1. 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

11. Units
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

12. Contents MEASUREMENT Units (Completed) Measurement of Length
Measurement of Volume
Measuring Mass and Weight
Measuring Density
Measurement of Time

13. 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?

14. Measurement of Length
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

15. Measurement of Length Vernier Callipers
Q1. Give two advantages of using vernier callipers rather than a ruler?

16. Measurement of Length
Q2. What readings are shown on the following scales?
Main scale:
Vernier scale:
Reading: _________________
Main scale:
Vernier scale:
Reading: _________________

17. Measurement of Length
Q2. What readings are shown on the following scales?
Main scale:
Vernier scale:
Reading: _________________
Main scale:
Vernier scale:
Reading: _________________

18. Measurement of Length 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?

19. Measurement of Length
Q3. Write down the readings shown on each of the following micrometer screw gauges. 1.
Sleeve:
Thimble:
Reading: ___________ 2.
Sleeve:
Thimble:
Reading: ___________

20. Measurement of Length
Q3. Write down the readings shown on each of the following micrometer screw gauges. 3.
Sleeve:
Thimble:
Reading: ___________ 4.
Sleeve:
Thimble:
Reading: ___________

21. Measurement of Length
Q3. Write down the readings shown on each of the following micrometer screw gauges. 5.
Sleeve:
Thimble:
Reading: ___________

22. Measurement of Length
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.

23. Measurement of Length 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.

24. Measurement of Length 2.
This micrometer has a zero error. Zero reading is mm so we must add 0.03 mm to all readings taken with this micrometer.

25. Measurement of Length Exercise
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 mm. _______________________________

26. Contents MEASUREMENT Units (Completed)
Measurement of Length (Completed)
Measurement of Volume
Measuring Mass and Weight
Measuring Density
Measurement of Time

27. 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?

28. Measurement of Volume 30 20 15 40 10 35 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

29. Measurement of Volume Regular Solids 2 cm 3 cm
Volumes can be calculated by taking measurements then using formulae.
Volume of rectangular block =
Volume of sphere =
3 cm
2 cm
Volume of cylinder =

30. Measurement of Volume Irregular Solids Irregular Solids
1. Volume of a small irregular solid that sinks
Irregular Solids
2. Volume of a small irregular solid that floats

31. Measurement of Volume Irregular Solids
3. Volume of a larger irregular solid

32. Contents MEASUREMENT Units (Completed)
Measurement of Length (Completed)
Measurement of Volume (Completed)
Measuring Mass and Weight
Measuring Density
Measurement of Time

33. Measuring Mass & Weight
In everyday conversation we use the words mass and weight interchangeably.
In Physics they have two very different meanings.
Mass
Definition: 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 = g
1 tonne = kg

34. Measuring Mass & Weight
Measurement of Mass
To measure mass we can use one of two instruments:
Sliding Mass Balance Electronic Balance
(Ohau's balance)

35. Measuring Mass & Weight
Inertia
The two people shown below put on roller-skates! Who would be 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 .

36. Measuring Mass & Weight
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.

37. Measuring Mass & 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.

38. Measuring Mass & Weight Measuring Mass & Weight
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.

39. Measuring Mass & Weight Measuring Mass & Weight
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
Weight is defined as the force of earth’s gravitational pull on a body.
Mass is defined as the amount of matter in a body. kg N No
Yes No
Yes
Sliding Mass Balance, Electronic Mass Balance

40. Contents MEASUREMENT Units (Completed)
Measurement of Length (Completed)
Measurement of Volume (Completed)
Measuring Mass and Weight (Completed)
Measuring Density
Measurement of Time

41. Measuring Density
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).

42. Measuring Density Density = Mass / Volume
Density can be calculated from the equation:
Density = Mass / Volume
Or we can write this in symbols as:
  r = m / V
where r = density
m = mass
V = volume

43. Measuring Density 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.

44. Measuring Density 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?

45. Measuring Density 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 = g , V = cm Thus, r = m / V = g / cm3 = 1 g/cm3 or
m = 2 kg, V = ( 2000 / ) m3 = m3
Thus, r = m / V = 2 kg / m3 = kg/m3

46. Measuring Density 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

47. Measuring Density 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.

48. Contents MEASUREMENT Units (Completed)
Measurement of Length (Completed)
Measurement of Volume (Completed)
Measuring Mass and Weight (Completed)
Measuring Density (Completed)
Measurement of Time

49. 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)

50. Measurement of Time 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

51. Measurement of Time Pendulum
A 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.

52. Measurement of Time
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?

53. Measurement of Time
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.

54. Contents MEASUREMENT Units (Completed)
Measurement of Length (Completed)
Measurement of Volume (Completed)
Measuring Mass and Weight (Completed)
Measuring Density (Completed)
Measurement of Time (Completed)