Unit 1

Chapter 1
Measurements
Units of Measurement

Measurement
You are making a measurement when you
♦Check you weight
♦Read your watch
♦Take your temperature
♦Weigh a cantaloupe
What kinds of measurements did you
make today?

Standards of Measurement
When we measure, we use a measuring tool to
compare some dimension of an object to a
standard.

Units of Measurements
MKS: meters (m), Kilogram (kg), second (s)
kilometer (km), hour (h)
CGS: centimeter (cm), gram (g), second (s)
FPS: foot (ft.), pound (lb.), second (s)
miles (mi.), hour (h)

Learning Check
From the previous slide, state the tool (s)
you would use to measure
A. temperature ____________________
B. volume ____________________
____________________
C. time ____________________
D. weight ____________________

Solution
From the previous slide, state the tool (s) you would
use to measure
A. temperature thermometer
B. volume measuring cup,
graduated cylinder
C. time watch
D. weight scale

Learning Check
What are some U.S. units that are used to
measure each of the following?
A. length
B. volume
C. weight
D. temperature

Solution
Some possible answers are
A. length inch, foot, yard, mile
B. volume cup, teaspoon, gallon, pint, quart
C. weight ounce, pound (lb), ton
D. temperature °F

Metric System (SI)
 Is a decimal system based on
10
 Used in most of the world
 Used by scientists and
hospitals

Units in the Metric System
 length meter m
 volume liter L
 mass gram g
 temperature Celsius °C

Stating a Measurement
In every measurement there is a
♦Number
followed by a
♦ Unit from measuring device

Learning Check
What is the unit of measurement in each of
the following examples?
A. The patient’s temperature is 102°F.
B. The sack holds 5 lbs of potatoes.
C. It is 8 miles from your house to school.
D. The bottle holds 2 L of orange soda.

Solution
A. °F (degrees Fahrenheit)
B. lbs (pounds)
C. miles
D. L (liters)

Learning Check
Identify the measurement in metric units.
A. John’s height is
1) 1.5 yards 2) 6 feet 3) 2
meters
B. The volume of saline in the IV bottle is
1) 1 liters 2) 1 quart 3) 2 pints
C. The mass of a lemon is
1) 12 ounces 2) 145 grams 3) 0.6 pounds

The Seven Base SI Units
Quantity Unit Symbol
Length meter m
Mass kilogram kg
Temperature kelvin K
Time second s
Amount of
Substance
mole mol
Luminous Intensity candela cd
Electric Current ampere a

SI Unit Prefixes - Part I
Name Symbol Factor
tera- T 1012
giga- G 109
mega- M 106
kilo- k 103
hecto- h 102
deka- da 101

SI Unit Prefixes- Part II
Name Symbol Factor
deci- d 10-1
centi- c 10-2
milli- m 10-3
micro- μ 10-6
nano- n 10-9
pico- p 10-12
femto- f 10-15

Derived SI Units (examples)
Quantity unit Symbol
Volume cubic meter m3
Density kilograms per
cubic meter
kg/m3
Speed meter per second m/s
Newton kg m/ s2
N
Energy Joule (kg m2
/s2
) J
Pressure Pascal (kg/(ms2
) Pa

SI Unit Prefixes for Length
Name Symbol Analogy
gigameter Gm 109
megameter Mm 106
kilometer km 103
decimeter dm 10-1
centimeter cm 10-2
millimeter mm 10-3
micrometer μm 10-6
nanometer nm 10-9
picometer pm 10-12

Scientific Notation
M x 10n
M is the coefficient 1<M<10
10 is the base
n is the exponent or power of
10

Factor-Label Method of Unit
Conversion: Example
Example: Convert 789m to km:
789m x 1km =0.789km= 7.89x10-
1
km
1000m

Limits of Measurement
Accuracy and Precision

Accuracy - a measure of
how close a measurement is
to the true value of the
quantity being measured.

Example: Accuracy
Who is more accurate when
measuring a book that has a
true length of 17.0cm?
Susan:
17.0cm, 16.0cm, 18.0cm, 15.0cm
Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm

Precision – a measure of how
close a series of measurements
are to one another. A measure
of how exact a measurement
is.

Example: Precision
Who is more precise when
measuring the same 17.0cm
book?
Susan:
17.0cm, 16.0cm, 18.0cm, 15.0cm
Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm

Significant Figures
The significant figures in
a measurement include
all of the digits that are
known, plus one last digit
that is estimated.

Finding the Number of Sig Figs:
 When the decimal is present, start counting from the
left.
 When the decimal is absent, start counting from the
right.
 Zeroes encountered before a non zero digit do not
count.

Measuring Tools
 Vernier caliper
 Vernier caliper is a measuring device used to
measure precise increments between two points.
 Micrometer
 Micrometer is a measuring device used for precisely
measuring thickness, inner and outer diameter, depth
of slots.
 SWG
 A gauge for measuring the diameter of wire, usually
consisting of a long graduated plate with similar slots
along its edge.

Vernier caliper
 Function
 To measure smaller distances
 Can measure up to .001 inch or .01mm.
 Features
 Larger, lower jaws are designed to measure outer
points e.g. diameter of a rod.
 Top jaws are designed to measure inside points
e.g. size of a hole.
 A rod extends from the rear of the caliper and can
be used to measure the depth.

Structure of the Vernier caliper
 Main Scale
 Main scale is graduated in cm and mm.
 Vernier Scale
 It slides on the main scale.
 On Vernier scale 0.9cm is divided into 10 equal
parts.
 Jaws
 Two inside jaws (Upper)
 Two outside jaws (Lower)

Least Count
 Least count (L.C) is the smallest reading we
can measure with the instrument.
 L.C = one main scale division – one
vernier scale division
L.C = 1mm – 0.09mm
L.C = 0.1mm = 0.01cm
 Least Count = Value of the smallest division
on MS/ Total number of division on VS
L.C = 1mm / 10 = 0.1 cm / 10 = 0.01cm

Reading of the Instrument
 Reading of the instrument = MS div +
(coinciding VS div x L.C)
 = 3.2 + (3 x 0.01)
 = 3.2 + 0.03
 = 3.23 cm

Micrometer
 Function
 Micrometer allows the measurement of the size of
the body i.e. thickness, depth, inner/outer
diameter.
 Features
 Two jaws (one fixed, one movable)
 Spring loaded twisting handle
 Easy to use and more précised
 Can measure up to .001cm

Structure of Micrometer
 Jaws
 2 jaws (one fixed, one movable)
 Circular Scale
 Movable jaw is attached to a screw, scale on this
screw is called Circular scale.
 Either 50 or 100 divisions
 Linear Scale
 Horizontal Scale

Structure of Micrometer
 Frame
 The C-shaped body that holds the anvil and sleeve in constant
relation to each other.
 Anvil
 The jaw which remains stationary.
 Spindle
 The jaw which moves towards the anvil.
 Lock Nut
 A lever, one can tighten to hold the spindle stationary.
 Sleeve
 The stationary round part with the linear scale on it. (Main Scale)
 Thimble
 Thimble rotates around the sleeve.
 Ratchet Stop
 Device on end of handle that limits applied pressure by slipping at
a calibrated torque.

Pitch of Micrometer
 When the head of the micrometer rotate
through one rotation, called pitch of the
micrometer.
 The screw moves forward or backward 1mm on
the linear scale.
 Pitch of Micrometer = distance on linear
scale / one rotation
Pitch of Micrometer = 1/1 = 1mm

Reading of the Instrument
 Reading of the instrument = MS div +
(coinciding CS div x L.C)
 = 8+ (12 x 0.01)
 = 8 + 0.120mm
 = 8.120 mm = 8120 µm

Scalars A scalar quantity is a quantity that has magnitude
only and has no direction in space
Examples of Scalar Quantities:
 Length
 Area
 Volume
 Time
 Mass

Vectors A vector quantity is a quantity that has both
magnitude and a direction in space
Examples of Vector Quantities:
 Displacement
 Velocity
 Acceleration
 Force

Vector Diagrams Vector diagrams are
shown using an arrow
 The length of the arrow
represents its
magnitude
 The direction of the
arrow shows its direction

April 2, 2014
Speed is defined as the distance travelled per unit time and
has the units of m/s or ms-1.

Distance, Speed and Time
April 2, 2014
Speed = distance (in metres)
time (in seconds)
D
TS
1) Dave walks 200 metres in 40 seconds. What is his speed?
2) Laura covers 2km in 1,000 seconds. What is her speed?
3) How long would it take to run 100 metres if you run at 10m/s?
4) Steve travels at 50m/s for 20s. How far does he go?
5) Susan drives her car at 85mph (about 40m/s). How long does it
take her to drive 20km?

April 2, 2014
Speed is defined as the distance travelled per unit time and
has the units of m/s or ms-1.
Velocity is speed in a given direction and has the same units
as speed.

Speed vs. Velocity
April 2, 2014
Speed is simply how fast you are travelling…
Velocity is “speed in a given direction”…
This car is travelling at a
speed of 20m/s
This car is travelling at a
velocity of 20m/s east

April 2, 2014
Speed is defined as the distance travelled per
unit time and has the units of m/s or ms-1.
Velocity is speed in a given direction and has
the same units as speed.

To calculate speed we use the equation:
Average speed = distance travelled/time
taken = d/t
Distance is measured in metres (m) and
time is measured in
seconds (s).
The greater the distance travelled in a
given time then the
greater is the speed.

April 2, 2014
A useful way to illustrate how the distance
throughout a journey varies with time is to plot a
DISTANCE AGAINST TIME graph.
This gives us a visual representation of how the
journey progressed
and allows us to see quickly how long each stage
of the journey took
compared with the other stages.

The steepness (gradient) will also give us the
speed.
The following graphs show how the shape of
distance-time graphs
may vary and how to interpret them

April 2, 2014
Distance
Time0
0
A
B C
AB- constant speed
BC - stationary
Gradient = rise/run
= speed
Rise
Run
Distance - Time GraphsDistance - Time Graphs

April 2, 2014
DISTANCE is a SCALAR quantity and has size only but
DISPLACEMENT is a VECTOR quantity and has size (or
magnitude) and DIRECTION.
10 metres is a distance (size only) but 10 metres due south
(size and direction) is a vector quantity.
If we use DISPLACEMENT instead of distance then the
graph will also give an indication of the direction taken with
respect to its starting point.

April 2, 2014
Displacement
Time0
0
AB - constant velocity
(speed & direction)
BC - stopped
CD - Returning
to its
starting position
at a constant
velocity
A
B C
D
Distance - Time GraphsDistance - Time Graphs

Distance-time graphs
April 2, 2014
40
30
20
10
0
20 40 60 80 100
4) Diagonal line
downwards =
3) Steeper diagonal line =1) Diagonal line =
2) Horizontal line =
Distance
(metres)
Time/s

April 2, 2014
40
30
20
10
0
20 40 60 80 100
1) What is the speed during the first 20 seconds?
2) How far is the object from the start after 60 seconds?
3) What is the speed during the last 40 seconds?
4) When was the object travelling the fastest?
Distance
(metres)
Time/s

April 2, 2014
Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples
A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for
40s. After lunch it continues the journey and it takes a further
120s to reach his final destination which is a further 8m
away.
(a) Plot a distance-time graph.
(b) What was the snail’s speed before lunch?
(c) What was the snail’s speed after lunch?

April 2, 2014
A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it
continues the journey and it takes a further 120s to reach his final destination
which is a further 8m away.
Plot a distance-time graph.
What was the snail’s speed before lunch?
What was the snail’s speed after lunch?
Distance (m)
Time (s)

April 2, 2014
Distance (m)
Time (s)
0
4
8
12
16
800 160 240

April 2, 2014
Distance (m)
Time (s)
0
4
8
12
16
0 80 160 240

April 2, 2014
Distance (m)
Time (s)
0
0
4
8
12
16
80 160 240

April 2, 2014
Distance (m)
Time (s)
0
0
(a) See graph
(b) Speed before lunch = initial gradient
= rise/run
= 8/80
= 0.1m/s
4
8
12
16
80 160 240

April 2, 2014
Distance (m)
Time (s)
0
0
(a) See graph
(b) Speed before lunch = initial gradient
= rise/run
= 8/80
= 0.1m/s
(c) Speed after lunch = final gradient
= rise/run
= 8/120
= 0.067 m/s4
8
12
16
80 160 240

April 2, 2014
Consider a car starting from rest and its speed is increasing continuously.
Distance (m)
Time (s)
0
200
400
600
800
200 40 60

April 2, 2014
Consider a car starting from rest and its speed is increasing continuously.
Find the speed of the car at 40 seconds after the start of the journey.
Distance (m)
Time (s)
0
200
400
600
800
200 40 60

April 2, 2014
Acceleration is defined as the change in velocity in
unit time and has the units m/s/s or m/s2
or ms-2
Acceleration is a vector quantity and so has size and
direction.
Velocity - Time GraphsVelocity - Time Graphs

To calculate acceleration we use the equation:
Average acceleration = change in
velocity/time taken
= (final velocity – initial
velocity)/time taken
= (v – u)/t
Velocity is measured in metres per second (m/s)
and time is measured in seconds (s).
The greater the change in velocity in a given time
then the greater is the acceleration.

Acceleration
April 2, 2014
V-U
TA
Acceleration = change in velocity (in m/s)
(in m/s2
) time taken (in s)
1) A cyclist accelerates from 0 to 10m/s in 5 seconds. What is her
acceleration?
2) A ball is dropped and accelerates downwards at a rate of 10m/s2
for 12
seconds. How much will the ball’s velocity increase by?
3) A car accelerates from 10 to 20m/s with an acceleration of 2m/s2
. How
long did this take?
4) A rocket accelerates from 1,000m/s to 5,000m/s in 2 seconds. What is
its acceleration?

April 2, 2014
A useful way to illustrate how the velocity throughout a
journey varies with time is to plot a VELOCITY
AGAINST TIME graph.
This gives us a visual representation of how the journey
progressed
and allows us to see quickly how long each stage of the
journey took
compared with the other stages.
.

The steepness (gradient) will also give us the
ACCELERATION.
The area under a velocity-time graph gives us the
distance travelled.
The following graphs show how the shape of velocity-
time graphs
may vary and how to interpret them

April 2, 2014
Velocity
Time0
0
A
B C
AB- constant acceleration
BC - constant velocity
Gradient = rise/run
= acceleration (m/s2
)
Rise
Run

April 2, 2014
Velocity
Time0
0
A
B
C
D E
Constant Acceleration
Constant Velocity
At B,C & D there is
instantaneous change in acceleration
Area Under Graph = Total Distance Travelled

April 2, 2014
Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples
(a) Constant Velocity
Velocity (ms-1
)
Time (s)
10
8
6
4
2
0
0 2 4 6 8 10

April 2, 2014
(a) Constant Velocity
Velocity (ms-1
)
Time (s)
10
8
6
4
2
0
0 2 4 6 8 10
Distance travelled
= area under graph
= area of rectangle
= length x breadth
= 8 x 8
= 64m

April 2, 2014
(b) Uniform Acceleration
Velocity (ms-1
)
Time (s)
10
8
6
4
2
0
0 2 4 6 8 10

April 2, 2014
Velocity (ms-1
)
Time (s)
10
8
6
4
2
0
0 2 4 6 8 10
Distance travelled
= area under graph
= area of triangle
= ½ base x height
= ½ 8 x 8
= 32 m

April 2, 2014
Velocity (ms-1
)
Time (s)
10
8
6
4
2
0
0 2 4 6 8 10
Distance travelled= area under graph
= area of triangle
= ½ base x height
= ½ 8 x 8
= 32 m
Acceleration = gradient
= rise/run
= 8/8
= 1 ms-2

April 2, 2014
(c) Uniform Deceleration
Velocity (ms-1
)
Time (s)
10
8
6
4
2
0
0 2 4 6 8 10

April 2, 2014
Velocity (ms-1
)
Time (s)
10
8
6
4
2
0
0 2 4 6 8 10
= ½ base x height
= ½ 10 x 10
= 50m

April 2, 2014
Velocity (ms-1
)
Time (s)
10
8
6
4
2
0
0 2 4 6 8 10
= ½ base x height
= ½ 10 x 10
= 50m
Acceleration = gradient
= rise/run
= -10/10
= -1 ms-2
(Deceleration = +1 ms-2

April 2, 2014
A car starts from rest and accelerates uniformly to 20m/s in 10
seconds.
It travels at this velocity for a further 30 seconds before decelerating
uniformly to rest in 5 seconds.
(a) draw a velocity - time graph of the car’s journey
(b) calculate the car’s initial acceleration
(c) calculate the car’s final deceleration
(d) calculate the total distance travelled by the car
(e) calculate the distance travelled by the car in the final 25
seconds
Velocity - Time Graphs: ExampleVelocity - Time Graphs: Example

April 2, 2014
Velocity
Time0
0
20
(m/s)
(s)
10 40 45
Initial acceleration
= initial gradient
= rise/run
= 20/10
= 2m/s2

April 2, 2014
Velocity
Time0
0
20
(m/s)
(s)
10 40 45
final acceleration
= final gradient
= rise/run
= -20/5
= -4m/s2

April 2, 2014
Velocity
Time0
0
20
(m/s)
(s)
10 40 45
A B C
Total distance travelled = total area under graph
= area A + B + C = ½ x 10 x 20 + 30 x 20 + ½ x 5 x 20
= 100 + 600 + 50 = 750m

April 2, 2014
Velocity
Time0
0
20
(m/s)
(s)
10 40 45
C
Distance travelled in final 25s = part area under graph
= area D + C = 20 x 20 + ½ x 5 x 20
= 400 + 50 = 450m
D
20

Velocity-time graphs
April 2, 2014
80
60
40
20
0
10 20 30 40 50
Velocity
m/s
T/s
1) Upwards line =
2) Horizontal line = 3) Steeper line =
4) Downward line =

April 2, 2014
80
60
40
20
0
1) How fast was the object going after 10 seconds?
2) What is the acceleration from 20 to 30 seconds?
3) What was the deceleration from 30 to 50s?
4) How far did the object travel altogether?
10 20 30 40 50
Velocity
m/s
T/s

Questions:
 Do heavier objects fall faster than lighter ones when
starting from the same position?
 Does air resistance matter?
 If the free fall motion has a constant acceleration,
what is this acceleration and how was it found?
 How do we solve problems involving free fall?

Galileo (1564 –
1642) and the
leaning tower
of Pisa.

Air Resistance
 The force of friction or drag acting on an
object in a direction opposing its motion
as it moves through air.

Hammer & Feather in the
presence of air

Hammer & Feather in the
absence of air

 If the free fall motion has a constant
acceleration, what is this acceleration
and how was it found?

If there were no air resistance both
objects would fall with the same
downward acceleration ;9.8 m/s2.this is
called the acceleration of free fall

 The acceleration of free fall if represented
by the symbol ‘g’.
 Its value varies from one place on earth to
another
 Moving away from the earth and out into
space ,g decreases
 The value of g near the earth surafce is
close to 10 m/s

Unit 1

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