2
Objectives
• State that mass is a measure of amount of substance in a body
• State that mass of a body resists a change in the state of rest or motion of the body
• State gravitational field & define gravitational field strength, g
• Apply relationship between weight, mass and g • Density = mass/volume
Mass is the amount of
matter in an object.
Mass
•has a SI unit of kilogram
(kg)
constant everywhere
(Mass is the
same
on
earth and on the moon)
Note:
sliding balance
measured using
mass balance
,
or
electronic balance
electronic balance beam balance
Weight, W, is the gravitational
force
acting on an object.
has a unit of Newton (N)
measured using spring balance
Weight
change
depending on the
gravitational force.
is directed
towards
the Earth.
(gravity causes all objects to fall
towards the Earth)
6
Weight
• Use spring balance to measure weight.
– Extension spring balance (pulling effect)– Compression spring balance (pushing effect)
extension spring balance
(spring stretches when a pulling force acts on it)
compression spring balance
7
Does your
mass change when you go to the moon?
Does your
8
Weight
W = m x g
Weight (N) Mass (kg)
9
Weight
• All bodies attract one another with a
gravitational force
proportional to their
masses
.
• The
force
also depends on the
distance
between the bodies
– it
decreases
when
separation increases
. (
Sea level and mountain)a = g = 10ms-2 or 10Nkg-1
Force, F = m x a
A small submarine of mass 1 000 kg sinks in water with a uniform speed of 2 m/s.
(a) What is the weight of the submarine? ( g = 10 ms-2 )
W = mg
= ( 1 000 kg ) ( 10 ms-2 ) = 10 000 N
11
What is the weight of a mass of 550g on
Earth and moon?
( Acceleration due to gravity on earth and moon are 10 ms-2 and 1.6 ms-2 respectively)
Weight on Earth, W = 0.55 x 10 550 g = 0.55kg
= 5.5N
12
• What is the mass of a boy who weighs
450N? Take g = 10 m/s
2W = mg m = W/g
= 450 N / 10 ms-2
13
Weight of a 1kg mass is found to be 1.7N
when measured using a spring balance on
moon. A ball is attached to same spring is
found to weigh 5.2N on moon. What is the
mass of the ball?
g = W
m
=
1.7
1
W = m x g
=1.7 ms
-2Mass
Weight
1. Mass is the amount of matter in the body
1. Weight is the force of gravity on the body
2. Scalar: Has only magnitude but no direction
2. Vector: Has both
magnitude and direction
3. SI unit: kg 3. SI unit : N
4. Constant everywhere 4. Change depending on the gravity
5. Measured by a beam balance or an electronic balance
5. Measured by a spring
A gravitational field is a region in which a mass experiences a force due to
gravitational attraction.
Any object in the field will experience a force pulling it towards the earth.
Earth is surrounded by gravitational field
the force is strongest on
the surface of the Earth and gets weaker as the
object moves further away from the surface
17
18
Gravitational Field
• The acceleration due to gravity near the
surface of the Moon is 1.6 m s
-2.
– What is the gravitational field strength? – What is the weight of an astronaut on the
moon if his mass is 80 kg?
Gravitational field strength = acceleration due to gravity = 1.6 m s-2
Weight = mg
= 80 kg x 1.6 m s-2
Inertia is a measure of the
reluctance
of the object
to
change
either its state of rest or,
if it is moving, its motion in a
straight line.
inertia
21
Inertia
•
Inertia
is
consistent
with
Newton’s first law
of motion
which can also be stated as
follows:
A body continues in its state of rest or uniform motion in a straight line unless
inertia
mass and weight
A force is required to
overcome inertia
Inertia depends on mass
23
Do you know?
Supertankers are very large ships, commonly used to carry oil, liquefied natural gas, or liquefied petroleum gas.
A crash stop maneuver (from 'full ahead' to 'full reverse') can stop a fully loaded supertanker within approximately three kilometres, which takes about 14 minutes.
24
Inertia
a sumo wrestler has high inertia because it is nearly impossible to push him over!
25
Density
ρ = density of substance m = mass of substance V = volume of substance
Density of a substance is defined as its
mass per unit volume.
SI unit is kilogram per cubic meter (kg m-3)
ρ =
m V density = volume mass m VAnother unit for density is gram per cubic centimeter (g cm-3)
Volume of concrete block = l x b x h
= (1.0)(0.5)(0.1)
= 0.05 m3
density = mass / volume = 120 x 0.05 = 6 kg m-3
A 1.0 m by 0.5 m by 0.1 m concrete slab has a mass of 120 kg. What is its density?
=
mVolume of concrete block = l x b x h
= (0.4)(0.3)(0.1)
= 0.012 m3
From density = mass / volume 2500 = mass / 0.012 2500 x 0.012 = mass
mass = 30kg
A block of concrete 0.4m long, 0.3m wide and
0.1m high has a density of 2500kgm-3.
28
Describe an experiment to find
the density of a solid cube.
• Find the mass, M, of the cube using a
beam balance.
• Use a ruler to measure the dimensions of
the cube and calculate its volume, V.
• Calculate the density of the cork ,
=
M29
Describe an experiment to find
the density of an irregular object.
30
Finding Volume of Irregular Solid
V1
V2
31
• Find the mass, M, of the irregular object using a beam balance.
• Fill a measuring cylinder with water and take the reading of the volume the water as V1.
• Tie the irregular object to a string and lower it into the water until it is completely in the water, record the volume V2.
• The volume of the irregular object, V = V2 – V1 • Density of the cork ,
Describe an experiment to find
the density of an irregular object.
=
M32
Describe an experiment to find
the density of an irregular object.
33
34
• Find the mass, M, of the irregular object using a electronic balance.
• Fill the displacement can with water until it over flows. • Place a measuring cylinder at the spout of the
displacement can. Tie the irregular object to a string and lower it into the displacement can.
• The volume of the irregular object is equal to the water being displaced in the displacement can, V
• Density of the cork ,
Describe an experiment to find
the density of an irregular object.
=
M35
Describe an experiment to find
36
Finding Volume of the cork
37
• Find the mass, M, of the cork using a beam balance.
• Fill a measuring cylinder with water and placed the sinker in the measuring cylinder. Take the reading of the volume of the sinker and the
water as V1.
• Tie the cork to the sinker and lower it into the water until the cork is completely in the water, record the volume V2.
• The volume of the cork, V = V2 – V1 • Density of the cork ,
Describe an experiment to find the density
of an irregular object that floats in water.
=
MIf I have 10 kg of Styrofoam and
2 kg of iron, which will float and
which will sink?
39
Misconception
• Which block of aluminium has a bigger
density?
2700 kg 1 m3
density of aluminium = 2 700 kg m-3
27000 kg 10 m3
density of aluminium = 2 700 kg m-3
A
B
floating and sinking
If density of object
>
density of liquid
consider wood: = 0.65 g cm-3
In methylated spirits
= 0.79 g cm-3 In glycerine
= 1.26 g cm-3
object sinks in liquid
If density of object < density of a liquid
An object with a lower density will float
when placed in an object with a higher
density.
Substance
Density / kg m
-3Mercury
13600
Water
1000
Polystyrene
16
Pinewood
500
The hydrometer makes use of these principles:
float in a liquid
measure density of liquid
the higher it floats, the greater the density of liquid
Special hydrometers are used to test whether a car battery is fully charged or whether milk has been diluted with water.
hydrometer
density
44
Floating and Sinking
• How can a ship float on the sea?
45
Floating and Sinking
46
Floating and Sinking
• A steel ship floats in the ocean because
the steel hull is hollow and contains a large volume of air.
• This makes the
Plimsoll lines
All ships have markings (Plimsoll lines) on their hulls. The symbol is painted on the side of a vessel to show the safe maximum level at which it should float in water.
Both the salinity and temperature of water affect buoyancy of a craft.
Since river water has a lower density than sea water, a cargo boat loaded in a sea port may sink in river water.
48
Floating and Sinking
49
Dead Sea Water
The water of the Dead Sea
contains 21
minerals
including magnesium, calcium,
bromime and potassium. Some of the
minerals are recognized for
imparting a
relaxed feeling, nourishing the skin
,
activating the circulatory system and for
easing rheumatic discomfort and
metabolic disorders.
Dead Sea contains
10 times more salts
and minerals than the Mediterranean Sea.
The
high salt and mineral concentration
makes it
very dense
and
enables
everyone to float
in its waters but doesn't
allow the proliferation of fish and other
marine life
50
Ice = Water??
If ice is frozen water, then why
does it float on water? How is ice
different from water?
Let’s use Using Density = Mass/Vol
Qn: Did the density change and why? When water is frozen into ice in a fridge,
Qn: Did the mass change and why?
Inertia
density = mass
volume weight = mass x gravitational field strength
Mass
contributes to is a measure of
contributes to contributes to
52
Summary
• Density = m / V
• Units are kg m
-3or g cm
-3• An object will
float
in a liquid denser than
itself and
sink
in a liquid less dense than
itself.
53 Mass, m kg (SI unit) N (SI unit) kg/m3 (SI unit)
W = m x g D = M/V
g is the gravitational force
per unit mass acting on an object
inertia Amount of substance in a
body Mass per unit
volume
Gravitational force acting on an object Weight Density related to density by defined as related to weight by
54
Objectives
• State that mass is a measure of amount of substance in a body
• State that mass of a body resists a change in the state of rest or motion of the body
• State gravitational field & define gravitational field strength, g
• Apply relationship between weight, mass and g • Density = mass/volume
55
Pure Gold?
• Archimedes, a Greek mathematician around 250BC.
• The King had given his goldsmith some gold to make a crown. But when the crown was
delivered, the King was suspicious. Perhaps the goldsmith had stolen some of the gold and
mixed in cheaper silver instead.
56
Pure Gold?
• The crown was the correct mass. • Silver was less dense than gold. • How to find??????!!!!!!
• Solutions:
– Put crown in a container of water and measured the rise in level.
– Then did the same with an equal mass of pure gold. – The rise in level was different.