We have already read that force is that cause which can produce the following two main effects:
• it can change the state of rest or motion of the body i.e., it can produce motion in the body.

• it can change the size or shape of the body i.e., it can change the dimensions of the body.

`"Types of Forces"`
• Contact and Non-Contact Forces
• Conservative and Non-Conservative Forces

The forces which act on bodies when they are in physical contact, are called the contact forces. Examples of contact forces - frictional force, normal reaction force, tension force etc.

When a body slides (or rolls) over a rough surface, a force starts acting on the body in direction opposite to the motion of the body, along the surface in contact. This is called the frictional force or the force of friction.

When a body is placed on a surface, the body exerts a force downwards equal to its weight on the surface, but the body does not move (or fall) because the surface exerts an equal and opposite force(equal and opposite only when no other forces in that direction is acting) on the body normal to the surface which is called the normal reaction force.

When a body is suspended by a string, the body, due to its weight W, pulls the string vertically downwards and the string in its stretched condition pulls the body upwards by a force which balances the weight of the body. This force developed in the string is called the tension force T (or the force of tension).

The forces experienced by bodies even without being physically touched, are called the non-contact forces or the forces at a distance. The gravitational force, electrostatic force and magnetic force are the non-contact forces.

• In universe, each particle attracts the other particle due to its mass. This force of attraction between them is called the gravitational force.

• The earth also because of its mass, attracts all other masses around it. The force on a body due to earth's attraction is called the pull of gravity or the force of gravity.

• We also attract earth by equal and opposite force by which earth is pulling us.

• Two like charges repel, while two unlike charges attract each other. The force between the charges is called the electrostatic force.

• This force acts between the charged objects even when they are separated. This force generally comes into action when charges are present on bodies.

`"Example:"` When a comb is rubbed on dry hairs, it gets charged. If this comb is brought near the small bits of paper, opposite charges are induced on the bits of paper and they begin to move towards the comb.

`"Conservative Force"`
A force is conservative, if the work done by the force in displacing an object from one point to another point is independent of the path followed by the object and depends only on the end points.

e.g. Gravitational force, electrostatic force and elastic force of a spring are all conservative forces.

`"Non-Conservative Force"`
If the amount of work done in moving an object against a force from one point. to another point depends on the path along which the body moves, then such a force is called a non-conservative force. The work done in moving an object against a non-conservative force along a closed path is not zero.

e.g. Forces of friction and viscosity are non-conservative forces.

`"C.G.S. Unit"`
• In the C.G.S. system, the unit of force is `"dyne"`

• `"1 dyne" = 1 gm xx 1 cm s^(-2)`

• One `"dyne"` is that force which when acting on a body of mass `1 gm`, produces an acceleration of `1 cm s^(-2)` in it.

`"S.I Unit"`
• The S.I. unit of force is newton (N).

• `1 N =1kg xx 1 m s^(-2)`

• One newton (N) is that force which when acting on a body of mass `1 kg`, produces an acceleration of `1 m s^(-2)` in it.

Here `"newton"` and `"dyne"` are called the absolute unit of force

`"Relationship between newton and dyne"`
`1 N = 1 kg xx 1 m s^( - 2) = 1000 g xx 100 cm\ s^(-2) = 100000 g \cm s^(-2) = 10^5` `"dyne"`

Thus, `1 N = 10^5` `"dyne"`

• Work is said to be done when a force applied on a body displaces the body through a certain distance, in the direction of force.

i.e., `"Work (W)= Force (F) x Distance (s)"`

• The S.I. unit of work is the joule.

• Thus in the above formula work is in joules, force in newton and distance in meters.

`"1 Joule"`
Amount of work is said to be 1 joule when the point of application of a force of 1 newton moves through a distance of 1 meter in the direction of the force.

• Work is a scalar quantity.

• If a force 'F' newton is applied to an object at an angle `theta` to the horizontal and the object moves horizontally through d meters, then the work done is `(F cos theta)` d joules.
Here `F cos theta` is the horizontal component of the force F and only this component is available in moving the object.

• In figure, force F applied at a `angle theta`. Its horizontal component is `F cos theta` and work done by it in moving the object through d is `F cos theta xx d`.

Work can be of three types

(i) `text(Positive Work)`
Work is said to be positive, if value of the angle `theta` between the directions of F and sis either zero or an acute angle.

(ii) `text(Negative Work)`
Work is said to be negative, if value of angle e between the directions of F and s is either 180' or an obtuse angle.

(iii) `text(Zero Work)`
As work done `W = F · s = F s cos theta`, hence work done can be zero if both F and s are finite but the angle e between the directions of force and displacement is 90°.

• The work done in lifting the body vertically upwards by a height `h` meters is `m xx g xx h` joules.

• Work in C.G.S. Units: The C.G.S. unit of work is the `erg` which is much smaller than the joule.

• `1 "joule" = 10^5 "dynes" xx 10^2 cm = 10^7 "dyne cm" = 10^7 "ergs"`

• Energy is defined as the capacity or ability of a body to do work.

• Energy is scalar quantity and its units and dimensions are the same as that of work. Thus, SI unit of energy is joule.

• Energy is of two kinds - (i) Kinetic energy, (ii) Potential energy.

• Some commonly used units of energy are-
`1 erg = 10^-7` J
`1 cal = 4.186 J ~~ 4.2 J`
`1 kcal = 4186 J
1 kWh = 3.6 xx 10^6 J`
and 1 electron volt `= 1 eV = 1.60 xx 10^-19 J`

• This is the energy of motion. Any moving body possesses this kind of energy. e.g., Running water, a falling fruit.

• Kinetic Energy (KE) is the capacity of a body to do work by virtue of its motion. Motion may be either transnational or rotational.

• The actual amount of such energy depends on the mass of the moving body as also on its velocity.

A body of mass m, moving with a velocity v, has a kinetic energy
`KE` (kinetic energy) `= 1/2 mv^2`
Thus , `K prop m`
`K prop v^2`
If we use, the S.I. units, `m` is kilogram, `v` is meter per sec `(ms^(-1 ))` and KE will be in Joules.

• Kinetic energy of a body is always positive irrespective of the sign of velocity v. Negative kinetic energy is impossible.

• Kinetic energy is correlated with momentum as
`K = p^2/(2m) ` or `p = sqrt( 2mK)`

• Kinetic energy for a system of particle will be
`K =1/2 sum_i m_i v_i^2`

• Kinetic energy depends on the frame of reference. Kinetic energy of a passenger sitting in a running train is zero in the frame of reference of the train but is finite in the frame of reference of the earth.

• This is the energy possessed by a body by virtue of its position or shape. A body that is elevated from ground level, a compressed spring or bent bow - all these possess potential energy.

• If a body of mass m kilograms is at a height of h meters from the ground, then its potential energy `PE. = m xx g xx h` joules where g is the acceleration due to gravity at the place.

• We cannot measure the actual value of potential energy. It is always measured with respect to a particular reference level. So, we can only measure the change in potential energy of a particular body on changing its configuration and not its actual value. In our example of gravitational potential energy, the potential energy is measured taking ground level (h = 0) as the reference (where PE is assumed zero).

• This energy is potential because it has the capacity - the potential - to do work if given a chance. Thus if coconut on a coconut tree falls down say on a thin sheet of glass, it can break the glass into pieces.

• The relation between potential energy and work done is
`W = - Delta U`
where, `DeltaU` is change in potential energy.

• Change in potential energy of a body between any two points is equal to the negative of work done by the conservative force in displacing the body between these two points, without there being any change in kinetic energy. Thus,
`dU = - dW = - F * dr`
and `U_2 - U_1 = - W`
`= -int_(r_1)^(r_2) F * dr`

• Value of the potential energy in a given position can be defined only by assigning some arbitrary value to the reference point. Generally, reference point is taken at infinity and potential energy at infinity is taken as zero. In that case,
`U = - W = - int_(oo)^r F * dr`

• Potential energy is a scalar quantity but has a sign. It may be positive as well as negative.

`"Generally potential energy is of three types"`

`text(Gravitational Potential Energy)`
• It is the energy associated with the state of separation between two bodies which interact via the gravitational force. The gravitational potential energy of two particles of masses `m_1` and `m_2` separated by a distance r is
`U = (-Gm_1m_2)/r`

• Generally, one of the two bodies is our earth of mass M and radius R If m is the mass of the other body, situated at a distance r(`r >= R`) from the centre of earth, the potential energy of the body
`U(r) = -(GMm)/r`

`text(Some Important Points)`
If a body of mass m is raised to a height h from the surface of earth, the change in potential energy of the system
(earth + body) comes out to be
`DeltaU=(mgh)/(1+h/R)` or `DeltaU~~mgh`, if `h< < R`
Thus, the potential energy of a body at height h, i.e. mgh is really the change in potential energy of the system for `h < < R`.

`text(Elastic Potential Energy)`
Whenever an elastic body (say a spring) is either stretched or compressed, work is being done against the elastic spring force. The work done is `W = 1/2 kx^2`
where, k is spring constant and x is the displacement
and elastic potential energy `U = 1/2kx^2`
Elastic potential energy is always positive.

`text(Electric Potential Energy)`
The electric potential energy of two point charges `q_1` and `q_2` separated by a distance r in vacuum is given by
`U = 1/(4 pi epsi_0) (q_1q_2)/r`
where , `1/(4 piepsi_0) = 9.1 xx 10^9 N-m^2//C^2` = constant

• The rate of doing work or the rate at which energy is transferred or used or transformed is called power.

• If work W is done in time t, then Power, `P = text( work )/text( time )`
` => P = W/t = (F * s)/t = F * v cos theta`

• The SI unit of power is watt in honour of James Watt having the symbol W. We express larger rate of energy transfer in kilowatt (kW).
* ` 1 W = 1 J s^-1`
* ` 1 kW = 1000 W = 1000 Js^-1`
* ` 1 MW = 10^6 W`
* ` 1 HP text((horse power)) = 746 text((watt)) W`

• The commercial unit of electric energy is kilowatt-hour (kWh). It is the amount of electric energy consumed by an appliance of power 100 W in one hour.
* `1 kWh = 1 k W xx 1 h = 1000 W xx 3600 s= 1000 Js^-1 xx 3600 s`
* `1 kWh = 3.6 xx 10^6 J`

• Every moment of our lives, we see that work is being done. And when work is done, there is expenditure of energy.

• There is energy in the running stream, in the moving muscles, in the beating of the heart and in the high level water in a dam.

• Human heart is beating continuously. In 60 sec, it beats 72 joules of work done by the heart muscles which works out to `72/60` J or `1.2` J/s .

• The energy required to make a cup of tea is estimated to be around 75 kilo joules (75 kJ) and the energy obtained by the burning of a liter of petrol to be of the order of `37 xx 10^6 J`.

According to law of conservation of energy, energy can only be transformed from one form to another, it can neither be created nor be destroyed. The total energy before and after transformation, always remains constant.

`"Law of Conservation of Mechanical Energy"`
This law states that, if only the conservative forces are doing work on an object, then the total mechanical energy (KE+ PE) of the object remains constant.
`:. KE+ PE=` constant

• When energy of one form is converted into another form in all cases, 100% conversion may not be possible. Some percentage rnay remain unconverted. Thus when heat energy is converted into mechanical energy, a good deal of the former remains unconverted or unusable.

• In an incandescent lamp, only some part of the electrical energy is converted to light energy. The rest appears as heat energy. But the total energy remains the same.

• But interestingly the entire mechanical energy can be converted into equivalent heat energy i.e. a 1000 joules of mechanical energy can be fully converted into a 1000 joules of heat energy. Experiments conducted by the British Scientist Joule (James Prescott Joule) confirm this.

• A collision is said to occur between two objects, either if they are physically collide against each other or if the path of one object is affected by the force exerted by the other object.

• There are mainly two types of collision
1. `text(Elastic collision)`
If there is no loss of kinetic energy during a collision, then it is called an elastic collision.

Characteristics of elastic collisions are as follows
(i) The kinetic energy is conserved.
(ii) The momentum is conserved.
(iii) Total energy is conserved.
(iv) Forces involved during the collision are conservative.

2. `text(Inelastic collision)`
If there is a loss of kinetic energy during a collision, then it is called an inelastic collision.

Characteristics of inelastic collisions are as follows
(i) The kinetic energy is not conserved.
(ii) The momentum is conserved.
(iii) Total energy is conserved.
(iv) Some or all of the forces involved are non-conservative.

• If particles of masses `m_1` and `m_2` move with velocities `u_1` and `u_2` before collision and after collision with velocities `v_1` and `v_2`, then from law of conservation of momentum,

`m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2`

• If an object of mass m strikes horizontally a wall with velocity v and bounces back with the same velocity, then the change in momentum `= 2mv`.

Consider two perfectly elastic objects A and B of masses `m_1` and `m_2` moving along the same straight line with velocities `u_1` and `u_2` respectively.

Let `u_1 > u_ 2` after some time, the two objects collide head-on and continue moving in the same direction with velocities `v_1` and `v_2` , respectively. The two objects will separate after the collision, if `v_2 > v_1`

As linear momentum is conserved inelastic collision, so

`m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2` .........................(i)

Since, kinetic energy is also conserved in an elastic collision, so

`1/2m u_1^2 + 1/2m_2u_2^2 = 1/2 m_1v_1^2 + 1/2m_2v_2^2` ......................(ii)

After solving the above two equations, we get

`v_1 = ((m_1 -m_2 )/ ( m_1 + m_2) ) u_1 + ((2m_2)/(m_1 + m_2 )) u_2`

`v_2 = (( m_2 - m_1)/ ( m_1 + m_2 )) u_2 + ( ( 2 m_1)/ ( m_1 + m_2)) u_1`