In everyday life, gravitation is most commonly thought of as the agency which lends weight to objects with mass.
It is responsible
for keeping the Earth and the other planets in their orbits around the Sun;
for keeping the Moon in its orbit around the Earth,
for the formation of tides;
for convection (by which fluid flow occurs under the influence of a temperature gradient and gravity)
for heating the interiors of forming stars and planets to very high temperatures; and
for various other phenomena that we observe.
Modern physics describes Gravitation as a consequence of the curvature of space time which governs the motion of inertial objects.
Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them. The force is along the line joining the centres of two objects.
Let the force of attraction between two objects be F.
According to the universal law of gravitation,
(a)The force between two objects is directly proportional to the product of their masses. That is,
Where G is the constant of proportionality and is called the universal gravitation constant.
By multiplying crosswise, Eq. gives
N m2 kg–2.
The value of G was found out by Henry Cavendish (1731 – 1810) by using a sensitive balance. The accepted value of G is 6.673 × 10–11N m2 kg–2.
IMPORTANCE OF THE UNIVERSAL LAW OF GRAVITATION
universal gravitational constant, G = 6.7 × 10–11 N m2 kg-2,
mass of the earth, M = 6 × 1024 kg, and
radius of the earth, R = 6.4 × 106 m.
F = m a
MOTION OF OBJECTS UNDER GRAVITATIONAL FORCE OF THE EARTH
Gravitational acceleration experienced by an object is independent of its mass.
This means that all objects hollow or solid, big or small, should fall at the same rate.
According to a story, Galileo dropped different objects from the top of the Leaning Tower of Pisa in Italy to prove the same.
Acceleration of the car, a = + 10 m s–2
v = 10 m s–2 × 0.5 s
= 5 m s–1
= (0 m s–1+ 5 m s–1)/2 = 2.5 m s–1
= ½ × 10 m s–2 × (0.5 s) 2
= ½ × 10 m s–2 × 0.25 s2 = 1.25 m
Example: An object is thrown vertically upwards and rises to a height of 10 m. Calculate (i) the velocity with which the object was thrown upwards and (ii) the time taken by the object to reach the highest point.
Solution: Distance traveled, s = 10 m
We know that the earth attracts every object with a certain force and this force depends on the mass (m) of the object and the acceleration due to the gravity (g).
The weight of an object is the force with which it is attracted towards the earth.
W = m × g
Example: A block of wood is kept on a tabletop. The mass of wooden block is 5 kg and its dimensions are 40 cm × 20 cm × 10 cm. Find the pressure exerted by the wooden block on the table top if it is made to lie on the table top with its sides of dimensions (a) 20 cm × 10 cm and (b) 40 cm × 20 cm.
Solution: The mass of the wooden block = 5 kg The dimensions = 40 cm × 20 cm × 10 cm
From Eq. Pressure = 49/0.02 m2 = 2450 Nm-2
The density of a substance is defined as the mass per unit volume. The density of cork is less than the density of water. This means that the up thrust of water on the cork is greater than the weight of the cork. So it floats.
Archimedes' principle, states that a body immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid.
The principle applies to both floating and submerged bodies and to all fluids, i.e., liquids and gases.
It explains not only the buoyancy of ships and other vessels in water but also the rise of a balloon in the air and the apparent loss of weight of objects underwater.
In determining whether a given body will float in a given fluid, both weight and volume must be considered; that is, the relative density,
weight per unit of volume, of the body compared to the fluid determines the buoyant force. If the body is less dense than the fluid, it will float or, in the case of a balloon, it will rise. If the body is denser than the fluid, it will sink.
Relative density also determines the proportion of a floating body that will be submerged in a fluid. If the body is two thirds as dense as the fluid, then two thirds of its volume will be submerged, displacing in the process a volume of fluid whose weight is equal to the entire weight of the body. In the case of a submerged body, the apparent weight of the body is equal to its weight in air less the weight of an equal volume of fluid.
Relative Density = Density of substance / Density of water
Example: Relative density of silver is 10.8. The density of water is 103 kg m–3. What is the density of silver in SI unit?
Gravitation and Free Fall E-Notes FullDownload File
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