#### Mechanical and Heat Energies, Physics tutorial

Concept of Energy:

Energy is the mainspring of the entire life and of all the activities of mankind. It might be stated as a capability or capacity to do work. You utilize energy in your home in the given manners:

a) Chemical energy stored in the food you eat assist you in walking, playing, doing household work and other responsibilities.

b) Chemical energy in wood or load or kerosene is transformed by combustion to heat energy for cooking our food and heating purposes.

c) Light energy which falls on your eyes lets you to see things.

d) Sound energy which enters your ears makes you listen to.

e) Electrical energy operates most of the appliances like TV sets, fan, radios, electric pressing irons, refrigerators and other appliances in your home.

Energy Sources:

You are familiar that the sun is the major source of energy in the universe. Though, we can recognize other sources that we have categorized under:

1) Natural sources that comprise food, natural gas, sun, wood, coals, oils and fats, tides/waves, waters and wind.

2) Manufactured sources comprise energy from generators, batteries, electricity from the mains.

3) Petroleum products comprise that from gasoline, kerosene and refinery gases (such as methane, propane, ethane and butane).

Concept of Work:

In everyday life, various people apply the word work to any form of activity which needs the exertion of physical or mental effort. Though, in Physics (or in mechanics), we utilize the word in a very particular sense.

We state that work is completed whenever a force is applied to cause a body to move.

If you push a car a certain distance, you are stated to do work. When no movement occurs after you have exerted a force to a body like a car, no work is done.

Work is stated to be done if a force moves its point of application a distance in the direction of the force.

Measurement of Work:

You will evaluate the work by obtaining the product of force moving a body and the distance moved through the body in the direction of the force. That is, when a force F moves a body a distance 'S' in the direction of 'd' the force, the work done is given by:

Work = Force x displacement

i.e. W = F x S

The S.I. unit of work is Joule (J)

The Joule is equivalent to Newton - metre (Nm).

In common, if a constant force F at an angle θ with the direction of motion causes a body to move a distance, S, we state the work done by:

W = F Cos θ x S

Here F cos θ is the component of F in the direction of motion

Work done in a Force Field:

(a) Lifting a body:

We are familiar that to lift a body through a height 'h', a pulling force should be applied to overcome the weight of the body. If an object is lifted upwards vertically, work is done against the force of gravity or against the weight of the body.  You will attain the magnitude of the work done from

Work = force x distance

Work = mg x h

Work = mgh

Here, m = mass of the body, g = acceleration due to gravity and h = height

(b) Falling bodies:

If a body falls freely under gravity, we state that the earth's gravitational force does work on the body. For illustration, when a body of mass 'm', falls via vertical distance 'h', the work done by gravity on the body is obtained from.

W = mgh.

As well, when a body of mass 'm' rolls down a hill of height 'h' and length 'l', then the work done is mgh.

Concept of Mechanical Energy:

We are familiar that anything capable of doing work has energy. This signifies that a person pushing a car all along the road is doing work on the car. So far as the car moves a few distance.  A mango fruit falling from the top of tree does work and thus have energy.

Mechanical energy is categorized into two kinds namely Potential Energy and Kinetic Energy.

Potential Energy (P.E.):

The Potential energy can be simply stated as 'stored energy' or energy possessed by a body by virtue of its position or state. The stored energy is employed to do work if the body is free to move. Illustrations of potential energy are:

a) A magnet at rest in a magnetic field (that is, magnetic potential energy).

b) An electric charge at rest in an electric field (that is, electric potential energy).

c) A coiled spring if stretched or compressed (that is, elastic potential energy.

d) Petrol, wood and other fuel sources burn when they burn, chemical potential energy is discharged.

e) A body at rest in a gravitational field example: a mango fruit on a mango tree, gravitational potential energy.

Kinetic Energy (K.E.):

Kinetic energy is the energy possessed through a body by virtue of its motion. Illustrations of kinetic energy are:

a) A student running a race.

b) Electrical charges in the motion.

c) An object falling freely under gravity.

d) Any object in motion.

Measurement of Energy:

A) Measurement of Potential Energy (P.E.)

Gravitational potential energy as we know completely based on the weight and height of an object above the surface of the earth.  To lift an object at a constant speed under gravity, you should apply a force, which is equivalent to its weight.  The work you do if you lift a body of mass 'm' at a uniform speed via a height 'h' is mgh.  The work done in lifting the body to a height 'h' is stored and can be recovered in the form of kinetic energy by letting the body to fall via a distance 'h'. The potential energy of a body is not an absolute quantity. You will evaluate its magnitude relative to a few reference positions.

To compute the gravitational potential energy P.E. of a body, you will evaluate the mass of the body and its height above a reference level h.

This is given by:

P.E. = mgh.

B) Measurement of Kinetic Energy (K.E.)

The kinetic energy of a body in motion is based on both its mass 'm' and speed 'v'.  To get the kinetic energy of a body in motion you will employ the formula:

K.E = (1/2) mv2

Concept and Measurement of Power:

Power is stated as the rate of doing work or employing energy.

Power = Work done or energy expended/Time taken

Generally, work is measured in joules and time in seconds; therefore, power is deduced in joules per second. One joule per second = 1 watt.

Thus, work is measured in watts (W).

A power of 1 watt is too small for practical use. Therefore, we generally measure power in a bigger unit termed as kilowatt (KW).

Law of Conservation of Energy:

The law of conservation of energy defines that in an isolated or closed system, the net amount of energy is for all time constant; however energy might be changed from one form to the other.

Whenever we talk about an isolated or closed system, we signify a group of objects which neither gets energy from nor gives energy to objects outside the system.

For mechanical energy being considered here, the law simply exhibits that the sum of the P.E. and K.E is for all time constant for a particular body, however the energy might change from P.E. to K.E. or from K.E. to P.E.

Principle of Conservation of Mechanical Energy in a Conservative Field:

A significant feature of a conservative force is that the work done by such a force is recoverable.  For illustration, if you do a work against a gravitational force in mounting a body to a height 'h' above the ground, that work is recovered if the body falls a distance 'h' back to its original position.

The gravitational field of earth is an illustration of field having conservative forces. In such a conservative field, net mechanical energy is conserved.

Friction is an illustration of a non-conservative force. We observed that if friction acts between the moving portions of a machine, some of the mechanical energy is lost however it reappears in the form of heat and the total energy that is now mechanical plus thermal energy remains constant.

The common principle of the conservation of energy defines that the total energy in a given system is for all time constant or energy can neither be created nor destroyed however it can be transformed from one form to other.

Conservation of Mechanical Energy of a Falling Body:

It might be shown above that in the absence of external frictional force the net mechanical energy of a body remains constant.

Assume that a body of mass 'm' falls from a point A, which is at a height 'h' from the ground as shown in figure above.

At A,

Kinetic energy KE = 0

Potential energy Ep = mgh

Total energy E = Ep + Ek = mgh + 0 = mgh

Throughout the fall, the body is at a position B. The body has moved a distance 'x' from A.

At B,

Velocity v2 = u2 + 2as

By applying, v2 = 0 + 2ax = 2ax

Kinetic energy Ek = (1/2) mv2 = (1/2) m x 2gx = mgx

Potential energy Ep = mg (h - x)

Total energy E = Ep + Ek = mg (h-x) + mgx = mgh - mgx + mgx = mgh

When the body reaches at position C:

At C,

Potential energy Ep = 0

Velocity of the body C is: v2 = u2 + 2as

u = 0, a = g, s = h

By applying v2 = 0 + 2gh = 2gh

Kinetic energy Ek = (1/2) mv2 = (1/2) m x 2gh = mgh

Total energy at C,

E = Ep + Ek

E = 0 + mgh

E = mgh

Conservation of Mechanical Energy comprised in a Swinging Pendulum:

The figure represents a vibrating simple pendulum; O is the point of suspension. If the centre of gravity of the bob is vertically beneath the point of suspension, then the position of the pendulum is termed as the rest position or mean position.

Let us state that the bob is relocated to a position E1. If released, the pendulum will begin vibrating among the two extreme positions E1 and E2.

If the bob moves from mean position, to the extreme position E1, its centre of gravity is increased vertically via a height 'h'.

Thus, Potential energy of the bob at the extreme position = mgh

As the bob moves from the extreme position to the mean position, its potential energy goes on reducing as the kinetic energy goes on rising. However, the sum of the two energies is constant. At mean position, the whole potential energy is transformed into kinetic energy.

When 'v' is the velocity of the bob at mean position, then

Kinetic energy at mean position = (1/2) mv2

By applying the law of conservation of energy:

mgh = (1/2) mv2

v = √(2gh)

As bob moves from the mean position to the other extreme position E2, its kinetic energy reduces and potential energy rises. Energy becomes totally potential at E2. As the bob moves from E2 to the mean position, the potential energy goes on reducing and kinetic energy goes on rising. At mean position, the energy is once again, completely kinetic.

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