When the stone moves in a circular path with a certain speed and changes direction at every point. The change in direction involves change in velocity or acceleration. The force that causes this acceleration and keeps the body moving along the circular path is acting towards the centre. This force is called the centripetal (meaning ‘centre-seeking’) force.
The motion of the moon around the earth is due to the centripetal force. The centripetal force is provided by the force of attraction of the earth.
According to the third law of motion, the apple does attract the earth. But according to the second law of motion, for a given force, acceleration is inversely proportional to the mass of an object. The mass of an apple is negligibly small compared to that of the earth. So, we do not see the earth moving towards the apple.
Newton extend the same argument and concluded that not only does the earth attract an apple and the moon, but all objects in the universe attract each other. This force of attraction between objects is called the gravitational force.
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.
According to the universal law of gravitation, the force between two objects is directly proportional to the product of their masses. That is, F ∝ M x m
And the force between two objects is inversely proportional to the square of the distance between them, that is,
F ∝ 1/d2
F ∝ M x m/d2
Or, F = G( M x m/d2)
Where G is the constant of proportionality and is called the universal gravitation constant.
The SI unit of G can be obtained by substituting the units of force, distance and mass as 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 x 10—11 N m2 kg—2.
The universal law of gravitation successfully explained several phenomena which were believed to be unconnected:
The force that binds us to the earth;
The motion of the moon around the earth;
The motion of planets around the Sun; and
The tides due to the moon and the Sun.
Whenever objects fall towards the earth under this force alone, we say that the objects are in free fall.
Due to the earth's attraction, there will be a change in the magnitude of the velocity. Any change in velocity involves acceleration. Whenever an object falls towards the earth, an acceleration is involved. This acceleration is due to the earth's gravitational force. Therefore, this acceleration is called the acceleration due to the gravitational force of the earth (or acceleration due to gravity). It is denoted by g. The unit of g is the same as that of acceleration, that is, m s—2.
To calculate the value of g, we should put the values of G, M and R in Eq. (10.9), namely, universal gravitational constant, G = 6.7 x 10—11 N m2 kg-2, mass of the earth, M = 6 x 1024 kg, and radius of the earth, R = 6.4 x 106 m.
g = G (M/R2)
= 6.7 x 10-11 Nm2 kg-2 x 6 x 1024kg/(6.4 x 106 m)2
= 9.8 m s—2.
Thus, the value of acceleration due to gravity of the earth, g = 9.8 m s—2.
We know that an object experiences acceleration during free fall. This 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.
The mass of an object is the measure of its inertia. The mass of an object is constant and does not change from place to place.
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.
We know that
F = m x a,
that is, F = m x g.
The force of attraction of the earth on an object is known as the weight of the object. It is denoted by W.
W = m x g
The weight of an object is the force with which it is attracted towards the earth, the SI unit of weight is the same as that of force, that is, newton (N). The weight is a force acting vertically downwards; it has both magnitude and direction.
The weight of an object on the earth is the force with which the earth attracts the object. In the same way, the weight of an object on the moon is the force with which the moon attracts that object. The mass of the moon is less than that of the earth. Due to this the moon exerts lesser force of attraction on objects.
By applying the universal law of gravitation, the weight of the object on the moon will be.
Wm = GMm x m/R2m
The weight of the same object on the earth be We. The mass of the earth is M and its radius is R.
The concepts of the net force in a particular direction (thrust) and the force per unit area (pressure) acting on the object concerned.
The effects of forces of the same magnitude on different areas are different. Therefore the effect of thrust depends on the area on which it acts. The effect of thrust on sand is larger while standing than while lying. The thrust on unit area is called pressure. Thus,
Pressure = thrust/area
The SI unit of thrust and area we get the SI unit of pressure as N/m2 or N m—2.
All liquids and gases are fluids. A solid exerts pressure on a surface due to its weight. fluids have weight, and they also exert pressure on the base and walls of the container in which they are enclosed. Pressure exerted in any confined mass of fluid is transmitted undiminished in all directions.
The upward force exerted by the water on the bottle is known as upthrust or buoyant force. In fact, all objects experience a force of buoyancy when they are immersed in a fluid. The magnitude of this buoyant force depends on the density of the fluid.
The nail sinks. The force due to the gravitational attraction of the earth on the iron nail pulls it downwards. There is an upthrust of water on the nail, which pushes it upwards. But the downward force acting on the nail is greater than the upthrust of water on the nail.
Therefore objects of density less than that of a liquid float on the liquid. The objects of density greater than that of a liquid sink in the liquid.
Archimedes’ principle, stated as follows:
When a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it.
The density of a substance is defined as mass of a unit volume. The unit of density is kilogram per metre cube (kg m—3). The density of a given substance, under specified conditions, remains the same. Therefore the density of a substance is one of its characteristic properties.
It is often convenient to express density of a substance in comparison with that of water. The relative density of a substance is the ratio of its density to that of water:
Relativedensity = Density of a substance/Density of water