Frictional Force
You must have observed that a body probed along a surface moves a certain distance and then stops. According to Newton’s first law of motion, the body once set into motion should continue to move with a constant velocity. But this does not happen. It implies that a retarding force must be acting on the ball which decreases the speed of the ball and stops it. We call this force as the frictional force. ‘The force which opposes the relative motion between two surfaces is called the frictional force;. The frictional force acts tangential to the surface in contact and is in the direction opposite to that of motion of the object. In Figure 3.5, the direction of motion of the body is along AB and the direction of friction f is opposite to AB.
Causes of Friction
The main reason for friction is the roughness of the surfaces. At a macroscopic level of an object, it may appear to be smooth, but when we see it through a microscope, the magnified image will show a number of tiny hills and grooves. When the object tends to slide over the surface of another body, interlocking of hills and grooves resist the relative motion and causes the force of friction.Factors Affecting Friction
 Friction or force of friction (F) is directly proportional to the normal reaction (R) between the two surfaces in contact F ∝ R.
 Force of friction depends on the nature of the surfaces as long as the normal reaction is constant.
 Force of friction always acts in a direction opposite to the direction of force applied on the body.
 Force of friction does not depend on the area of contact of two surfaces as long as the normal reaction is constant.
 Force of friction always acts tangential to the surface.
You may also remember the fact that the frictional force is a selfadjusting force, which means if there is no tendency for the body to move, the frictional force does not act on the body.
Kinds of Friction
Different kinds of motion give rise to different types of friction between objects. Following are the kinds of friction.
 Static friction: The force of friction which completely balances the applied force so that the body on which force is applied does not move at all is called the static friction. The maximum value of static friction which comes into play when a body is just going to start sliding over the surface of another body is known as the limiting force of friction.
 Dynamic or kinetic friction: The force of friction which comes into play when one body moves over the surface of another body is known as the dynamic or kinetic friction. Usually, the dynamic friction is less in value than the static friction, i.e., less force is required to keep a body moving than to start moving it.
 Rolling friction: The force of friction which comes to play when one body rolls over the surface of another body is called the rolling friction (like a rolling wheel).
 Fluid friction: In science, gases and liquids have a common name: fluids. Fluids exert a force of friction on objects in motion through them. The frictional force exerted by fluids is also called drag. It depends on the speed and shape of the object and the nature of the fluid.
Coefficient of Friction
The coefficient of friction (μ) is defined as the ratio of the magnitudes of the force of friction to the normal force between the surfaces.Coefficient of static friction =
Coefficient of kinetic friction =
Coefficient of rolling friction =
_{}μ_{r} < μ_{k} < μ_{s}
The coefficient of friction (μ) depends on the nature and material of the two surfaces and is independent of the area of contact.
Angle of Repose
For the block on the inclined plane to be static, the net force should be zero. So,
where f is the static frictional force and R is the normal reaction; also weight of the block.
As the angle of the inclined plane is gradually increased, also increases (as the force try to move the body down, sin θ keeps increasing). When reaches the limiting value, the block starts sliding.
Therefore, μ_{s} = tan θ_{max} _{}
_{}
where θ_{max} is called angle of repose (Figure 3.6).
Ways of Increasing Friction
 By making the surface rough: The rough surfaces have a better grip on each other. For this reason, the sole of the shoes are made rough and grooves are made in the tyres of vehicles for a better grip.
 By using dry surfaces as against wet or oiled surfaces: Dry surfaces have more friction than the wet surfaces. This is the reason why it is difficult to walk on the wet roads, when the road becomes wet after rains.
 By increasing the weight: By increasing the weight of the moving body, the frictional force can be increased.
Disadvantages of Friction
 The efficiency of machines decreases, as a fraction of its effort is wasted in overcoming friction.
 Friction produces heat which damages the parts of the machine.
 Friction contributes towards the wear and tear of the parts of a machine.
Ways of Reducing Friction
Friction can be reduced in the following ways:
 use of lubricants (oils, grease, fine powder like talcum)
 use of ball bearings (these are called rolling bearings)
 by polishing
 by changing the shape of the object.
Can you think of some advantages of friction without which life becomes difficult?
 It becomes impossible to walk on ice without friction.
 We cannot fix nail in the wood or wall if there is no friction.
 A horse cannot pull a cart unless there is friction.
Gravitational Force
Any two bodies attract each other by virtue of their masses. This force is called the gravitational force. Motion of freely falling objects towards the earth’s surface, motion of planets around the sun, motion of satellites, stars and galaxies are governed by the gravitational force. The gravitational force is the weakest of all fundamental forces.
The gravitational force of interaction between two objects near the earth is negligible, but that exerted by the earth on these objects is considerable.
The gravitational force exerted by the earth on object of mass m is of magnitude mg and is directed towards the centre of the earth. This is called weight of the object.
The gravitational force exerted by the earth on object of mass m is of magnitude mg and is directed towards the centre of the earth. This is called weight of the object.
The Universal Law of Gravitation
Newton identified the relationship between the force of attraction and the distance between planets and the sun and gave his law of gravitation. This law is called the universal law of gravitation because it works for all objects having mass (Figure 3.7).
The law is stated as follows: ‘The gravitational force of attraction between any two particles is directly proportional to the product of their masses and inversely proportional to the square of distance between them. The direction of the force is along the line joining the two particles’.
The law is stated as follows: ‘The gravitational force of attraction between any two particles is directly proportional to the product of their masses and inversely proportional to the square of distance between them. The direction of the force is along the line joining the two particles’.
Let A and B be two particles of mass m_{1} and m_{2}, respectively. Let the distance AB = r. According to Newton’s law of gravitation, the force of attraction (F) acting along the line joining the two particles is
F ∝ m_{1}m_{2} (for a given distance) and F ∝ (for given masses). Hence,
∴ , where G is the universal gravitation constant.
SI unit of G is Nm^{2} kg^{−2}.
In SI the value of G = 6.673 × 10^{−11} Nm^{2} kg^{−2}.
Relation between acceleration due to gravity (g) and gravitational constant (G)
Consider a body of mass m on the surface of the earth of mass M. Let R be the radius of the earth (assumed to be spherical) (Figure 3.8).
We know that the gravitational force exerted by the earth on the body F_{1} is the cause of g, the acceleration due to gravity. This force is called the weight of the body given by F_{1} = mg.
According to Newton’s law of gravitation, the force between the body and the earth is
, where G is the universal gravitational constant.
So F_{1} = F_{2}
∴
∴
Differences between Acceleration due to gravity (g) and universal gravitational constant (G)
Acceleration due to gravity (g) 
Universal gravitation constant (G) 
Its value is 9.81 m s^{−2} on the surface of earth. 
Its value is 6.6734 × 10^{−11} Nm^{2} kg^{−2}. 
Its value varies with place. 
Its value remains constant. 
Its unit is ms^{−2}. 
Its unit is Nm^{2} kg^{−2}. 
It is a vector quantity. 
It is a scalar quantity. 
Denoted by g 
Denoted by G 
Galileo’s Observations on the Falling Bodies
From the equation , we know that g is independent of the mass (m) of the body, falling freely towards earth.
It was Galileo, an Italian scientist, who proved that ‘two objects of different masses when dropped from the same height, hit the ground simultaneously’. This was proved by Galileo by his famous experiment with falling bodies on the leaning tower (with a coin and a feather).
Variation of g with Altitude
 The acceleration due to gravity (g) at a height h above the sea level is given by
 The acceleration due to gravity (g) at a depth h below the earth’s surface is given by
 At the centre of the earth, the depth h = R. Hence,
= 0
Mass and Weight In everyday life, we use the terms ‘weight’ and ‘mass’ without much difference in their meanings. However, in physics they stand for two entirely different quantities.
Consider a body of mass m falling freely. This body is accelerated towards the centre of the earth with uniform acceleration g. The gravitational force on it is given by F = mg
∴ Force F = mg is nothing but weight of the body.
∴ Weight W = Mass Acceleration due to gravity
= mg
Therefore, the force with which earth attracts a body is called the weight of the body on the earth. The mass of the body is defined as the quantity of matter contained in the body.
Distinction between Mass and Weight
Mass

Weight

• It is the measure of quantity of matter contained in the body.

• It is the force with which the earth attracts the body.

• It is a scalar quantity.

• It is a vector quantity.

• The SI unit of mass is kg.

• SI units of weight (force) is newton (N)

• It has the same value for a body at all places.

• It has different values for a body at different places since g changes from place to place.

• It can be measured by a beam balance or physical balance.

• It can be measured by a spring balance.

Motion of Planets and Satellites
Kepler’s Laws The motion of planets was studied by Tycho Brahe (1546–1601), without the aid of a telescope. His data on the planetary motion were analysed and interpreted by Johannes Kepler and is formulated into a set of laws known as Kepler’s laws of planetary motion.First law: All planets revolve round the sun in elliptical orbits with sun at one of the foci.
Second law: A line joining any planet to the sun sweeps out equal areas in equal intervals of time.
Third law: The square of the period of any planet around the sun is proportional to the cube of the planets’ mean distance from the sun, i.e., T^{2} ∝ r^{3}.
Orbital Velocity of Satellites Orbital velocity is the velocity of a satellite revolving around the earth in a given orbit. It is given by
where v_{0} is the orbital velocity, G the universal gravitational constant, M the mass of the earth, R the radius of the earth and h the height of the satellite above the earth’s surface.
In terms of acceleration due to gravity, , where g is acceleration due to gravity.
Period of a Satellite The period of a satellite is the time taken by it to complete one revolution around the planet. The period of revolution of the satellite depends upon its height above the earth’s surface. The greater the height of the satellite above the earth’s surface, the greater is its period of revolution. Thus,
Escape Velocity The minimum velocity with which a body has to be projected vertically to escape from the gravitational influence of the earth is called the escape velocity. Escape velocity is given by where v_{e} is the escape velocity of a body, g the acceleration due to gravity and R the radius of the earth.