The document discusses concepts related to gravitation including Newton's universal law of gravitation, Kepler's laws of planetary motion, acceleration due to gravity, and equations of vertical motion. Some key points covered include:
1) Newton's universal law of gravitation states that the gravitational force between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
2) Kepler's laws describe the motion of planets and include that planets move in elliptical orbits with the sun at one focus.
3) Acceleration due to gravity on Earth is approximately 9.8 m/s2 and causes objects to experience weight. Weight depends on both mass and location.
This PPT is based on Physics on Chapter Motion. In this you will find every thing of that chapter with great images. in this PPT their are many animation and images .
thank you
HEAT
TEMPERATURE
LAND BREEZE
EFFECT OF HEAT
MEASUREMENT OF TEMPERATURE
CLINICAL THERMOMETERS
DIGITAL THERMOMETERS
SEA BREEZE
TRANSFER OF HEAT
CONDUCTION
CONVECTION
CONDUCTORS AND INSULATORS
RADIATION
DARK COLOURED SURFACES AND COLOURED SURFACES
WIND
Presentation on gravitation for class 9th Rahul Shukla
It contains a brief description of gravitation with a video.
This presentation is with a deginer font and a classic theme.
It also consist a beautiful song
This PPT is based on Physics on Chapter Motion. In this you will find every thing of that chapter with great images. in this PPT their are many animation and images .
thank you
HEAT
TEMPERATURE
LAND BREEZE
EFFECT OF HEAT
MEASUREMENT OF TEMPERATURE
CLINICAL THERMOMETERS
DIGITAL THERMOMETERS
SEA BREEZE
TRANSFER OF HEAT
CONDUCTION
CONVECTION
CONDUCTORS AND INSULATORS
RADIATION
DARK COLOURED SURFACES AND COLOURED SURFACES
WIND
Presentation on gravitation for class 9th Rahul Shukla
It contains a brief description of gravitation with a video.
This presentation is with a deginer font and a classic theme.
It also consist a beautiful song
13-1 NEWTON’S LAW OF GRAVITATION
After reading this module, you should be able to . . .
13.01 Apply Newton’s law of gravitation to relate the gravitational force between two particles to their masses and
their separation.
13.02 Identify that a uniform spherical shell of matter attracts
a particle that is outside the shell as if all the shell’s mass
were concentrated as a particle at its center.
13.03 Draw a free-body diagram to indicate the gravitational
force on a particle due to another particle or a uniform,
spherical distribution of matter.
13-2 GRAVITATION AND THE PRINCIPLE OF SUPERPOSITION
After reading this module, you should be able to . . .
13.04 If more than one gravitational force acts on a particle,
draw a free-body diagram showing those forces, with the
tails of the force vectors anchored on the particle.
13.05 If more than one gravitational force acts on a particle,
find the net force by adding the individual forces as
vectors. etc...
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
2. 1. Gravitational Force or Gravity
2. Newton’s Universal Law of Gravitation
3. Properties of Gravitational Force
4. Universal Gravitational Constant
5. Kepler’s Laws of Planetary Motion
6. Newton’s II & III Laws and Gravitation
7. Free Fall
8. Acceleration due to gravity
9. Equations of Vertical Motion
10.Mass and Weight
11.Thrust and Pressure
12.Pressure in Fluids and Buoyancy
13.Archimedes’ Principle
14.Principle of Floatation
15.Density and Relative Density
Created by Shashank Garg .
3. Gravitational force of the earth or Gravity
A force is necessary to produce motion in a body.
A body dropped from a height falls towards the earth. It indicates that the
earth exerts a force of attraction (called gravity) on the body.
In fact, the earth attracts all the objects towards its centre.
The force with which the earth pulls the objects towards it is called the
gravitational force of the earth or gravity.
The gravitational force between the sun and the earth keeps the earth in
uniform circular motion around the sun.
The gravitational force of the earth (or gravity) is responsible –
for holding the atmosphere above the earth
for the rain falling to the earth
for flow of water in the rivers
for keeping us firmly on the earth,
for the revolution of moon around the earth, etc.
4. The gravitational force between the earth and the moon causes tides in
the sea. Think why tides are high during full moon and new moon day !
5. A Few Facts About Lunar Tides (Optional Reading)
The gravitational force of the moon is one ten-millionth that of earth, but
when you combine other forces such as the earth's centrifugal force created
by its spin, you get tides.
The sun's gravitational force on the earth is only 46 percent that of the moon,
making the moon the single most important factor for the creation of tides.
The sun's gravity also produces tides. But since the forces are smaller, as
compared to the moon, the effects are greatly decreased.
Tides are not caused by the direct pull of the moon's gravity. The moon is
pulling upwards on the water while the earth is pulling downward. Slight
advantage to the moon and thus we have tides.
Whenever the Moon, Earth and Sun are aligned, the gravitational pull of the
sun adds to that of the moon causing maximum tides.
Spring tides happen when the sun and moon are on the same side of the
earth (New Moon) or when the sun and moon are on opposite sides of the
earth (Full Moon).
6. When the Moon is at first quarter or last quarter phase (meaning that it is
located at right angles to the Earth-Sun line), the Sun and Moon interfere with
each other in producing tidal bulges and tides are generally weaker; these are
called neap tides.
Offshore, in the deep ocean, the difference in tides is usually less than 1.6 ft.
The surf grows when it approaches a beach, and the tide increases. In bays
and estuaries, this effect is amplified. (In the Bay of Fundy, tides have a range
of 44.6 ft.)
The highest tides in the world are at the Bay of Fundy in Nova Scotia, Canada.
Because the earth rotates on its axis the moon completes one orbit in our sky
every 25 hours (Not to be confused with moon's 27 day orbit around the
earth), we get two tidal peaks as well as two tidal troughs. These events are
separated by about 12 hours.
Since the moon moves around the Earth, it is not always in the same place at
the same time each day. So, each day, the times for high and low tides change
by 50 minutes.
The type of gravitational force that causes tides is know as "Tractive" force.
7. NEWTON’S UNIVERSAL LAW OF GRAVITATION
Every body in the universe attracts every other body with a force which is
directly proportional to the product of their masses and is inversely
proportional to the square of the distance between them.
The direction of force is along the line joining the centres of the two bodies.
r
m1
m2
Let two bodies A and B of masses m1 and m2 are placed at a distance of ‘r’
from each other. Let ‘F’ be the force of attraction between the bodies.
i.e. F α m1 x m2
(ii) the force of attraction is inversely proportional the square of the distance
between them
i.e. F α
1
r2
Then,
(i) the force of attraction is directly proportional the product of their masses
8. or
F α
m1 x m2
r2
where G is a constant called as
“universal gravitational constant”
F = G
m1 x m2
r2
Properties of gravitational force
1. Gravitational force is the weakest force in nature.
2. It is an attractive force. (Unlike electrostatic and magnetic force; they
are both attractive and repulsive)
3. It is a mutual force. (First body attracts the second body and the second
body attracts the first body with equal force)
4. It is a central force. (Acts along the line joining the centres of the bodies)
5. It is mass and distance dependent.
6. It obeys inverse square law.
7. It is a long range force. (It decreases with distance as per inverse square
law and becomes zero only at infinite distance – like electrostatic and
magnetic force)
8. It does not depend on the medium between the interacting bodies.
(There is no gravitational shielding)
9. • The value of Universal Gravitational Constant G is 6.67 x 10-11
N m2
Kg-2
.
• The value of G does not depend on the medium between two bodies.
• The value of G is same throughout the Universe and hence the name.
• Universal Gravitational Constant G is different from acceleration due to
gravity g. Therefore correct symbol must be used accordingly.
• SI unit of G is N m2
Kg-2
.
• If two bodies of mass 1 kg each are separated by 1 m from each other,
then, G = F.
* Therefore, Universal gravitational constant G is numerically equal to the
force of gravitation which exists between two bodies of unit masses kept at
a unit distance from each other.
G = F
m1 x m2
r2
Universal Gravitational Constant (G)
10. Gravitational force is the weakest force of all.
If two bodies of mass 1 kg each are separated by 1 m from each other,
then, F = G = 6.67 x 10-11
N
Though the various objects on this earth attract one another constantly, they
do not cause any visible motion because the gravitational force of attraction
between them is very, very small.
Imagine a situation on the earth if the objects continuously move towards
each other due to gravitational force between them !
When both the objects are very big, having very large masses, then the
gravitational force of attraction between them becomes extremely large.
The gravitational force due to earth on an object of mass 1 kg placed on the
ground is 9.8 N.
The gravitational force between the earth and the moon even at a large
distance is very large and is 2 x 1020
N.
11. KEPLER’S LAWS OF PLANETARY MOTION
I LAW (Law of orbits):
Every planet moves around the sun in elliptical orbit with the sun at one of
the foci of the elliptical orbit.
PLANETS IN ORDER
F1
F2
Sun
Elliptical Orbit
12. F1
F2
Sun
S
F1
F2
Sun
S
D
C
A
B
Elliptical Orbit
II LAW (Law of areas):
The line joining the planet to the sun sweeps over equal areas in equal
intervals of time.
ApogeePerigee
II law tells us that a planet does not move with constant speed around the
sun. It speeds up while approaching the nearest point called ‘perigee’ and
slows down while approaching the farthest point called ‘apogee’. Therefore,
distance covered on the orbit with in the given interval of time at perigee is
greater than that at apogee such that areas swept are equal.
Area of SAB = Area of SCD (For the given time)
13. III LAW (Law of periods):
The square of the time period of revolution of a planet around the sun is
directly proportional to the cube of the mean distance of a planet from the
sun.
Though Kepler gave the laws of planetary motion, he could not give a theory
to explain the motion of planets.
Only Newton explained that the cause of the motion of the planets is the
gravitational force which the sun exerts on them.
Newton used Kepler’s III law to develop the law of universal gravitation.
= constant
T2
r3
The law is mathematically expressed as
T2
α r3
or
14. Newton’s II and III Laws and Gravitation
According to Newton’s third law and universal law of gravitation, every
object attracts every other object with gravitational force. These forces are
equal and opposite.
Therefore, both the objects must be moving towards each other due to force.
However, due to very weak nature of force, the normal sized bodies are not
seen moving towards each other.
What happens when a ball is dropped from a certain height from the
ground?
Ball is seen falling towards the earth but the earth is not seen jumping
towards the ball. Why?According to Newton’s second law,
Force = mass x acceleration
i.e. F = ma
Let ‘M’ and ‘m’ be the mass of the earth and the ball respectively and ‘A’ and
‘a’ be the acceleration of the earth and the ball respectively.
By Newton’s third law,
F = MA = ma a =
F
m
or A =
F
M
and
For the given force F, the ball experiences larger acceleration due to smaller
mass but the earth experiences negligibly small acceleration due to larger mass.
15. FREE FALL
When a body falls from a height towards the
earth only under the influence of the
gravitational force (with no other forces acting
on it), the body is said to have a free fall.
The body having a free fall is called a ‘freely
falling body’.
Galileo proved that the acceleration of an object
falling freely towards the earth does not depend
on the mass of the object.
Imagine that vacuum is created by evacuating
the air from the glass jar.
The feather and the coin fall with same
acceleration and reach the ground at the same
time.
16. Acceleration due to gravity (g)
Acceleration due to gravity is defined as the uniform acceleration produced
in a freely falling body due to the gravitational force of the earth.
Acceleration due to gravity (g) = 9.8 m/s2
= 980 cm/s2
.
Calculation of acceleration due to gravity (g)
Suppose a body of mass ‘m’ is placed on the earth of mass ‘M’ and radius ‘R’.
According to Newton’s universal law of gravitation,
Force exerted by the earth on the body is given by
R
m
MF = G
M x m
R2
This force exerted by the earth produces an acceleration on the body.
Therefore, F = mg (g - acceleration due to gravity)
From the two equations, we have
mg = G
M x m
R2
or g =
G M
R2
17. Acceleration due to gravity on the earth is calculated as follows:
Mass of the earth = 6 x 1024
kg
Radius of the earth = 6.4 x 106
m
Gravitational constant = 6.67 x 10-11
N m2
kg-2
g =
G M
R2
Substituting the values, we get 9 = 9.8 m/s2
For simplified calculations we can take g as 10 m/s2
Variation of acceleration due to gravity (g)
1. Acceleration due to gravity decrease with altitude.
h
m
MR
g =
G M
R2
g’ =
G M
(R+h)2
18. 2. Acceleration due to gravity decrease with depth.
g =
G M
R2
g’ =
G M’
(R-h)2
h
m
3. Acceleration due to gravity is greater at the poles
and less at the equator.
gp =
G M
Rp
2
ge =
G M
Re
2
m
M
Rp
m
Re
Earth is slightly flattened at the poles and bulging at the
equator. The radius of the earth at the poles is 21 km
less than that at the equator.
i.e. Rp < Re
Therefore, from the above equations, G and M being
same and g is inversely proportional to the square of the
radius,
gp > ge
gp = 9.823 m/s2
, ge = 9.789 m/s2
and average value of g = 9.8 m/s2
M
M’
R
19. EQUATIONS OF VERTICAL MOTION (Under the influence of g)
Let a body be thrown vertically downward with initial velocity ‘u’. Let the
final velocity of the body after time ‘t’ be ‘v’. Let ‘h’ be the height (vertical
distance) covered by the body and ‘g’ be the acceleration due to gravity.
Then the equations of motion are:
v = u + gt
h = ut + ½ gt2
v2
= u2
+ 2gh
When a body is dropped freely, the equations of motion are:
v = gt
h = ½ gt2
v2
= 2gh
When a body is thrown vertically upwards, the equations of motion are:
v = u - gt
h = ut - ½ gt2
v2
= u2
- 2gh
-u, -v -g, -h
u = 0, -v -g, -h
+u, +v -g, +h
20. Cartesian Sign Conventions for Vertical Motion
1. The physical quantities having vertically upward motion are assigned
positive values.
2. On the other hand, the physical quantities having vertically downward
motion are assigned negative values.
3. Acceleration due to gravity (g) always acts in the downward direction and
hence taken negative.
TIPS TO SOLVE THE NUMERICAL PROBLEMS
1. g is always taken negative.
2. When a body is dropped freely its initial velocity u = 0.
3. When a body is thrown vertically upwards, its final velocity becomes zero
at the maximum height.
4. The time taken by a body to rise to the highest point is equal to the time it
takes to fall from the same height.
21. 50 g 10 g
50 g 10 g
Mass of the body = 60 g
MASS
22. The mass of a body is the quantity of matter contained in it.
Mass of a body is a measure of inertia of the body and hence called
inertial mass.
Mass is a scalar quantity.
SI unit of mass is kilogramme or kg.
CGS unit of mass is gramme or g.
Mass of a body is constant and does not change from place to place.
Mass is measured by a beam or common balance.
Mass of a body can not be zero.
24. The weight of a body on the earth is the force with which it is attracted
towards the centre of the earth.
Weight = mass x acceleration due to gravity
W = m x g
SI unit of weight is ‘newton’ or N
Weight of 1 kg mass is 9.8 newton.
Weight is a vector quantity since it has both magnitude and direction.
Weight changes from place to place.
Weight is measured by a spring balance.
Weight of a body can be zero. When a body is taken to the centre of
the earth, acceleration due to gravity at the centre is zero and hence
weight is zero.
On the moon, acceleration due to gravity is nearly 1/6th
of that on the
earth and hence the weight of a body on the moon is 1/6th
of its weight
on the earth.
26. THRUST AND PRESSURE
When a blunt pin is applied force it does not go into the wood whereas a
sharp pin goes into the wood with same amount of force.
Thus, the effect of a force depends on the area of the object on which it acts.
27. Weight of a body is also a force and it always acts in the downward direction.
Observe the two different positions of brick on the ground.
REX
REX
Both the bricks exert same amount of force on the ground because they have
same weight but the two bricks exert different pressure due to different area
of contact with the ground.
A lying brick exerts less pressure on the ground whereas the standing brick
exerts more pressure on the ground.
Therefore, pressure depends on (i) Force applied and
(ii) Area over which it acts.
Pressure is the force acting perpendicularly on a unit area of the object.
Pressure =
Area
Force
or P =
A
F
28. Pressure is a scalar quantity.
Pressure is force per unit area. Force is a vector quantity but still pressure is
a scalar quantity because it does not have any particular direction.
Think of a point inside the liquid or gas in a tank. Pressure at that point acts
in all the directions. That is, through 360º. Therefore pressure can not be
assigned a specific direction and hence is a scalar.
At the same time, if pressure is applied on a surface then the resulting force
is a vector quantity since it has direction of effect of pressure on the surface.
The pressure exerts force on the walls of the container of the liquid or gas.
SI unit of pressure is N/m2
or Nm-2
or pascal (Pa)
Pressure can also be defined in terms of ‘thrust’.
Thrust is the force acting on a body perpendicular to its surface.
Thrust per unit area is called ‘pressure’.
Pressure =
Area
Thrust
29. Everyday observations on the basis of pressure
1. School bags have wide straps.
2. Sharp knife cuts better than a blunt knife.
3. Tip of a needle is made sharp.
4. Pressure of the ground is more when a man is walking than when he is
standing.
5. Depression is much more when a man stands on the cushion than when
he lies down or sits on it.
6. The tractors have broad tyres so that there is less pressure on the ground
and the tyres do not sink into comparatively soft ground in the fields.
7. It is easier to walk on soft sand if we have flat shoes rather than shoes
with sharp heels.
8. Foundations of buildings and dams are laid broad at the bottom to
decrease the pressure.
30. PRESSURE IN FLUIDS
The substances which can flow easily are called fluids.
All the liquids and gases are fluids.
Like solids exert pressure due to their weight liquids also have weight and
they exert pressure.
But a fluid (liquid or gas) exerts pressure in all directions – sideward,
downward and even upwards !
BUOYANCY
When an object is placed in a liquid, the liquid exerts an ‘upward force’ on it.
It is easy to lift a stone as long as it is inside water but feels heavy if it is
lifted above water.
A mug of water inside the water appears lighter but it feels heavier when
lifted above the water.
Therefore, the objects appear to be less heavy when submerged in liquid
than they are in air. This shows that every liquid exerts an upward force on
the objects immersed (partially of wholly) in it.
The tendency of a liquid to exert an upward force on an object placed in it, is
called ‘buoyancy’.
31. Buoyant Force
The upward force acting on an object immersed in a liquid is called buoyant
force.
It is also called ‘upthrust’.
Cause of Buoyant Force
When a mug is inside the water, the pressure
from the sides are equal and no net force is
available.
But pressure at the bottom of the mug is
more due to more depth of water and is less
at the top due to less depth of water.
The difference in pressure exerts net upward
force called upthrust or buoyant force. The
mug usually made of plastic (lighter than
water) is pushed up due to this upthrust.
Buoyant ForceWeight
35. Factors affecting Buoyant Force
The magnitude of buoyant force acting on an object immersed in a liquid
depends on:
(i) Volume of object immersed in the liquid and
(ii) Density of the liquid.
(i) As the volume of solid object immersed inside the liquid increases, the
upthrust or buoyant force also increases. When the solid is fully
immersed, the buoyant force becomes maximum.
The buoyant force depends only on the volume but not the nature of the
solid object. That is, if two balls of equal size but of different metals are
immersed in the liquid, both of them experience same buoyant force.
(ii) Liquids having higher density exert more buoyant force than the liquids
having lower density.
It is easier to swim in sea-water than in lake because density of sea-water
is more when compared to that of lake water.
Even an iron block can float on mercury because of its (mercury) high
density.
36. ARCHIMEDES’ PRINCIPLE
When an object is wholly or partially immersed in a liquid, it experiences a
buoyant force (or upthrust) which is equal to the weight of the liquid
displaced by the object.
Buoyant force (or upthrust) acting on an object = Weight of liquid displaced by it
Applications of Archimedes’ Principle
1. Archimedes’ principle is used in determining the relative density of a
substance.
2. The hydrometers used for determining the density of liquids are based on
Archimedes’ principle.
3. The lactometers used for determining the purity of milk are based on
Archimedes’ principle.
4. Archimedes’ principle is used in designing ships and submarines.
37. WHY OBJECTS FLOAT OR SINK IN A LIQUID
Iron nail sinks whereas cork floats in water
38. When an object is placed in a liquid, two forces act on it:
1. Weight of the object acting downwards (which tends to pull down the
object) and
2. Buoyant force (upthrust) acting upwards (which tends to push up the
object).
Three cases arise:
• If the buoyant force exerted by the liquid is less than the weight of the
object, then the object will sink in the liquid.
• If the buoyant force exerted by the liquid is equal to the weight of the
object, then the object will float in the liquid where it is suspended.
• If the buoyant force exerted by the liquid is more than the weight of the
object, then the object will rise in the liquid and then float.
Now, whether an object will float or sink in a liquid depend on the relative
magnitude of these two forces acting in opposite directions.
39. The Principle of Floatation
An object will float in a liquid if the weight of the object is equal to the weight
of liquid displaced by it.
i.e. Weight of the object = Weight of the liquid displaced by it
A floating body may be partially or wholly submerged in the liquid. The liquid
is displaced by that portion of the body which is submerged under liquid.
1. An object will float in a liquid if its density is less than that of the liquid.
2. An object will also float in a liquid if its density is equal to that of the liquid.
3. An object will sink in a liquid if its density is more than that of the liquid.
The Density of Floating Objects
41. Plimsoll Line
How does a boat float in water?
Plimsoll Line
Plimsoll Line
Buoyant ForceWeight
When a boat is gradually lowered into water, it displaces more and more
water due to which the upward ‘buoyant force’ acting on it increases.
The boat stops sinking further down into water when the buoyant force
acting on it is just enough to support the weight of the boat.
When the boat is floating, the weight of water displaced by the submerged
part of the boat is equal to the weight of the boat.
When more people get into the boat, the boat sinks more. As long as the
weight of the boat and the people together is equal to the weight of the water
displaced by the boat, it floats. When no more water can be displaced by the
boat, it sinks.
42. DENSITY
The density of a substance is defined as mass of the substance per unit
volume.
Density =
Volume of the substance
Mass of the substance
D =
V
M
SI unit of density is kilogramme per cubic metre or kg/m3
or kg m-3
.
CGS unit of density is gramme per cubic centimetre or g/cm3
or g cm-3
.
Density of a substance is one of its characteristic properties.
43. The relative density of a substance is also defined as the ratio of the mass of
any volume of the substance to the mass of an equal volume of water.
Relative density =
Mass of an equal volume of water
Mass of the substance
As the relative density is the ratio of two similar quantities, it has no units.
Relative density of a substance expresses the heaviness of the substance in
comparison to water.
RELATIVE DENSITY
The relative density of a substance is the ratio of its density to that of water.
Relative density =
Density of water
Density of the substance
R D =
Ds
Dw
44. Densities of some common substances
S.No. Substance Density in
kg/m3
Density in
g/cm3
Relative
Density
1 Cork 240 0.24 0.24
2 Wood 800 0.8 0.8
3 Ice 920 0.92 0.92
4 Water 1000 1.0 1.0
5 Glycerine 1260 1.26 1.26
6 Glass 2500 2.5 2.5
7 Aluminium 2700 2.7 2.7
8 Iron 7800 7.8 7.8
9 Silver 10500 10.5 10.5
10 Mercury 13600 13.6 13.6
11 Gold 19300 19.3 19.3
12 Platinum 21400 21.4 21.4
45. Acknowledgemen
t
The objects copied from various sites:
1. Pictures of Kepler, Newton and Archimedes
2. Apple Tree
3. Earth
4. Sun
5. Planets in orbits
6. Tide Animations
7. 5 Rupee coin
8. Feather
Reference Material
1. IX – Science & Technology by NCERT
2. Science for Ninth Class (Part-1: Physics) by S. Chand