GRAVITATION : GRAVITATION CLASS: IX
SUBJECT: SCIENCE
PREPARED BY: Tushar Joshi
GRAVITATION : GRAVITATION Gravitation is the force of attraction between two objects in the universe.
Gravitation may be the attraction of objects by the earth.
E.g. If a body is dropped from a certain height, it falls downwards due to earth’s gravity. If a body is thrown upwards, it reaches a certain height and then falls downwards due to the earth’s gravity.
Gravitation may be the attraction between objects in outer space.
E.g. Attraction between the earth and moon.
Attraction between the sun and planets.
CENTRIPETAL FORCE : CENTRIPETAL FORCE When a body moves in a circular path, it changes its direction at every point. The force which keeps the body in the circular path acts towards the centre of the circle. This force is called centripetal force.
If there is no centripetal force, the body will move in a straight line tangent to the circular path.
UNIVERSAL LAW OF GRAVITATION : UNIVERSAL LAW OF GRAVITATION The universal law of gravitation states that, ‘Every object in the universe attracts every other object with a force which is directly proportional to product of their masses and inversely proportional to the square of the distance between them.' This law is also called Newton’s law of gravitation.
Illustration : Illustration If ‘M’ and ‘m’ are the masses of two bodies and
‘d’ is the distance then
F α M x m ------------- 1
F α 1/d2 --------------- 2
By combining 1 and 2 we get
Fα Mm/d2
F = G Mm/d2
The value of G = 6.673 x 10-11 Nm2/kg2
Or, G = Fd2/Mm
Slide 9: According to Newton's 2nd law of motion
F = ma = mg
Therefore mg = GMm/d2
Or, g = GM/d2
Where ‘M’ is the mass of the earth and ‘d’ is the distance between object and the earth.
Let the object be on or near the surface of earth and distance d will be equal to R, i.e radius of the earth.
Therefore g = GM/R2
The value of g = 9.8 m/s2
Value of ‘g’ : Value of ‘g’ G = 6.7 x 10-11 Nm2/Kg2
Mass of the earth = M = 6 x 1024 kg
Radius of earth = R = 6.4 x 106 m
g = GM/R2g
= 6.7 x 10-11 x 6 x 1024/( 6.4 x 106 )2
= 9.8 m/s2
Therefore the value of gravity of earth, g = 9.8m/s2
F = G Mm/R2
Importance of the universal law of gravitation : Importance of the universal law of gravitation The force that binds us to the earth.
The motion of the moon around the earth.
The motion of planets around the sun.
The tides due to the moon and the sun.
Free fall : Free fall The earth attracts objects towards it due to gravitational force. When an object falls towards the earth due to the earth’s gravitational force it is called free fall.
When an object falls towards the earth there is a change in its acceleration due to the gravitational force of the earth. So this acceleration is called acceleration due to gravity.
The acceleration due to gravity is denoted by g.The unit of g is same as the unit of acceleration ms -2
Slide 15: FREE FALL
Mass and weight : Mass and weight Mass: The mass of a body is the quantity of matter contained in it. Greater the mass greater the inertia. It remain same and does not change from place to place. It is scalar quantity. It is measured by beam balance. S.I unit of mass is kg.
Weight: The weight of a body is the force acting on it due to gravity. It is vector quantity. It changes from place to place. Weight is maximum at poles and minimum at equator because the value of g is maximum at poles and minimum at equator due to change in the radius of earth.
W = m x g
Difference between mass and weight : Difference between mass and weight
Weight of an object on moon : Weight of an object on moon Let the mass of an object be ‘m’. Let its weight on moon be Wm. Let the mass of moon be Mm and its radius be Rm.
By applying the universal law of gravitation:
Wm = G Mm x m / Rm2
Let the weight of the same object on the earth be We. The mass of earth is M and its radius is R.
Therefore We = G Mm/R2
By substituting the value of mass and radius of moon and earth we have.
Wm = G 7.36 x 1022kg x m/(1.74 x 106m)2
Slide 19: Wm = 2.431 x 1010 G x m --------1
We = 1.474 x 1011 G x m ---------2
Dividing 1 by 2
= Wm/We
= 2.431 x 1010 G x m/1.474 x 1011 G x m
= 2.431 x 10-1 / 1.474
= 0.165
= 1/6
Weight of the object on the moon/weight of the object on the earth
= 1/6
Therefore weight of the object on the moon = 1/6 x its weight of the earth.
We = Wm x 6
Thrust and pressure : Thrust and pressure Thrust is the force acting on an object perpendicular to the surface.
E.g. When you stand on loose sand the force (weight) of your body is acting on an area equal to the area of your feet. When you lie down, the same force acts on an area equal to the contact area of the whole body. In both cases the force acting on the sand (thrust) is the same. Thus the effect of thrust depends on the area on which it acts. S.I. Unit is Newton. Pressure is the force acting on unit area of a surface. P = Thrust/area
E.g. The effect of thrust on loose sand is larger while standing than while lying down.
The SI unit of thrust is N/m2 or N m-2 . It is called Pascal (Pa).
Pressure in fluid : Pressure in fluid Fluids ( liquid and gases ) exert pressure on the base and walls of the container. Fluids exert pressure in all directions. Pressure exerted on fluids is transmitted equally in all directions.
Buoyancy and buoyant force: When an object is immersed in a fluid it experiences an upward force called buoyant force. This property is called buoyancy or up thrust.
The force of gravity pulls the object downward and the buoyant force pushes it upwards.
The magnitude of the buoyant force depends upon the density of the fluid.
Slide 25: PRESSURE IN ALL DIRECTION
Why objects float or sink in water ? : Why objects float or sink in water ? If the density of an object is less than the density of a liquid, it will float on the liquid and if the density of an object is more than the density of a liquid, it will sink in the liquid. When the down ward force ( gravitational force ) acting on any object is greater than the up thrust or buoyant force then the object sink. Where as when the down ward force is less than the buoyant force then the object float.
Slide 28: Activity:
Take some water in a beaker. Take a piece of cork and an iron nail of the same mass. Place them on the water. The cork floats and the nail sinks.
The cork floats because the density of cork is less than the density of water and the up thrust of water is more than the weight of the cork.
The nail sinks because the density of the iron nail is more than the density of water and the up thrust of water is less than the weight of the nail.
Archimedes’ principle: : Archimedes’ principle: Archimedes’ principle states that, ‘ When a body is partially or fully immersed in a fluid it experiences an upward force that is equal to the weight of the fluid displaced by it.’
Application:
It is used in designing ships and submarines.
Hydrometers are used to determine the density of liquids.
lactometers used to determine purity of milk etc.
Density and relative density : Density and relative density Density: The density of a substance is defined as the mass per unit volume.
Density = Mass / Volume = m/v
The S.I. unit of density is kilogram /meter cube (kgm -3).
Relative density: The relative density of a substance is the ratio of the density of a substance to the density of water.
Relative density = Density of a substance/Density of water.
Since relative density is a ratio of similar quantities, therefore it has no unit.