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(1)
(2)

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

(3)

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:

(4)

sliding balance

measured using

mass balance

,

or

electronic balance

electronic balance beam balance

(5)

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)

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)

7

Does your

mass change when you go to the moon?

 Does your

(8)

8

Weight

W = m x g

Weight (N) Mass (kg)

(9)

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

(10)

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)

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)

12

• What is the mass of a boy who weighs

450N? Take g = 10 m/s

2

W = mg m = W/g

= 450 N / 10 ms-2

(13)

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

-2

(14)

Mass

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

(15)

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

(16)
(17)

17

(18)

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

(19)
(20)

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)

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

(22)

inertia

mass and weight

A force is required to

overcome inertia

Inertia depends on mass

(23)

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)

24

Inertia

a sumo wrestler has high inertia because it is nearly impossible to push him over!

(25)

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 V

Another unit for density is gram per cubic centimeter (g cm-3)

(26)

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?



=

m

(27)

Volume 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)

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 ,



=

M

(29)

29

Describe an experiment to find

the density of an irregular object.

(30)

30

Finding Volume of Irregular Solid

V1

V2

(31)

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.



=

M

(32)

32

Describe an experiment to find

the density of an irregular object.

(33)

33

(34)

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.



=

M

(35)

35

Describe an experiment to find

(36)

36

Finding Volume of the cork

(37)

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.



=

M

(38)

If I have 10 kg of Styrofoam and

2 kg of iron, which will float and

which will sink?

(39)

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

(40)
(41)

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

(42)

An object with a lower density will float

when placed in an object with a higher

density.

Substance

Density / kg m

-3

Mercury

13600

Water

1000

Polystyrene

16

Pinewood

500

(43)

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)

44

Floating and Sinking

• How can a ship float on the sea?

(45)

45

Floating and Sinking

(46)

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

(47)

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)

48

Floating and Sinking

(49)

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)

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?

(51)

Inertia

density = mass

volume weight = mass x gravitational field strength

Mass

contributes to is a measure of

contributes to contributes to

(52)

52

Summary

• Density = m / V

• Units are kg m

-3

or g cm

-3

• An object will

float

in a liquid denser than

itself and

sink

in a liquid less dense than

itself.

(53)

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)

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)

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)

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.

References

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