Principle of Conversion of Energy

The Conversion law States:

The amount of energy remains constant and energy is neither created nor destroyed. Energy can be converted from one form to another (potential energy can be converted to kinetic energy) but the total energy within the domain remains fixed.

If you take any volume of space, then the total energy inside that volume at a given time is always the amount that was there earlier, plus the total amount that has come in through the surface, minus the total amount that has gone out through the surface.

Albert Einstein's theory of relativity shows that energy and mass are the same thing, and that neither one appears without the other. Thus in closed systems, both mass and energy are conserved separately.

The new feature of relativistic physics is that "matter" particles (such as those constituting atoms) could be converted to non-matter forms of energy, such as light; or kinetic and potential energy (example: heat).

However, this conversion does not affect the total mass of systems, since the latter forms of non-matter energy still retain their mass through any such conversion.



Examples of Conversion of Energy:




For instance, a coal-fired power plant involves these power transfers:

1. Chemical energy in the coal converted to thermal energy
2. Thermal energy converted to kinetic energy in steam
3. Kinetic energy converted to mechanical energy in the turbine
4. Mechanical energy of the turbine converted to electrical energy, which is the ultimate output


The motion of a pendulum is a classic example of mechanical energy conservation. A pendulum consists of a mass (known as a bob) attached by a string to a pivot point.

As the pendulum moves it sweeps out a circular arc, moving back and forth in a periodic fashion. Neglecting air resistance (which would indeed be small for an aerodynamically shaped bob), there are only two forces acting upon the pendulum bob.



In this animation, you see a mass attached to the end of a string which forms a pendulum. The pendulum begins with only gravitational potential energy (GPE) since it is not moving yet. After being released, GPE is turned into kinetic energy (KE). Notice that no matter where the pendulum is, the sum of the GPE and KE is always equal to the original amount of energy the system started with. This demonstrates the Law of Conservation of Energy.
Energy is Conserved)

Questions:

* Where does the pendulum have the highest velocity?
* How does the original height of the pendulum compare to its final height?

This Animation and illustration shows an ideal situatuation.However, using our common sense we know that it's impossible for the pendulum to swing higher than the
height h without giving it a push yourself. If there was no friction, the pendulum would swing back and forth forever because of the law of conservation of energy.

In reality, we know that eventually the pendulum comes to a stop.This is due to the frictional forces.As the pendulum swings, some of its total energy is converted to thermal energy due to frictional forces and dissipated to the surroundings and cannot be converted back to the kinetic or gravitational energy.The thermal energy must have come from the original gain in gravitational potential energy.


Hence, as a result , the pendulum bob cannot attain its initial height. It continues to lose its energy.When all its original gain in potential energy has been converted to thermal energy, the pendulum bob stops moving.

Efficiency:

We all use devices every day that use energy - or more accurately, transfer energy from one form to another. Everything we use wastes energy - some of the energy transfers into forms that are not useful to us.

Very few devices can transfer energy from one form into another without wasting some on the way.

For Example, A light bulb is designed to turn electrical energy into light energy. But most bulbs produce a lot of heat energy too. That energy has not been lost but it has been wasted.

To measure the efficiency of a device, calculate what percentage of the total energy put in, became useful output energy.



For example: a bulb is provided with 100J of electrical energy but only produces 20J of light. The fraction turned into light is 20J out of 100J = 20/100.



In percentages, that's 20/100 x 100% = 20%.

So the equation for efficiency is:

efficiency (%) = (useful energy out ÷ total energy in) x 100.

Efficiency is normally calculated as a percentage - something 90% efficient is considered good at its job. Devices that transfer only 5% of the energy they use into something useful are inefficient (very wasteful).

When energy is transferred,some of the energy turns into forms we don't want.

This energy is called wasted energy.

Wasted energy takes the form of heat and sometimes sound or light.

During any energy transfer, some energy is changed into heat.The heat becomes spread out into the environment.

This dispersed energy becomes increasingly difficult to use in future energy transfers.In the end, all energy is transferred into heat.

Efficiency is not the same as cost-effectiveness.

Energy, Work and Power

Energy


Energy can be defined as the capacity for doing work.In physics we say that work is done on an object when you transfer energy to that object.

If one object transfers (gives) energy to a second object, then the first object does work on the second object.

Work can be generally defined as transfer of energy.

Work and energy are mutually connected and must be considered together as work is often defined in terms of energy and vice versa.In other words, Work shifts energy from one system to another.

The S.I. Unit of Work is the Joule(J).




In summary,

Energy is …

* a scalar quantity,
* abstract and cannot always be perceived,
* given meaning through calculation,
* a central concept in science.

Different forms of energy

Energy can exist in many different forms. All forms of energy are either kinetic or potential. The energy associated with motion is called kinetic energy. The energy associated with position is called potential energy. Potential energy is not "stored energy". Energy can be stored in motion just as well as it can be stored in position. Is kinetic energy "used up energy"?

You should be able to recognise the main types of energy. One way to remember the different types of energy is to learn this sentance where each capital and highlighted letter is the first letter in the name of a type of energy;

Most Kids Hate Learning GCSE Energy Names

Types of Energy

Magnetic - Energy in magnets and electromagnets.

Kinetic - The energy in moving objects. Also called movement energy.

Heat - Also called thermal energy.

Heat is the movement of molecules. It is the sum of the kinetic energy of an object's molecules. In many physics textbooks, they look at heat as some sort of substance and heat energy as something independent of kinetic energy. In our lessons, it is just one subset of kinetic energy.
Electrical energy

Light - Also called radiant energy.Light is the movement of waves and/or light particles (photons). It is usually formed when atoms gain so much kinetic energy from being heated that they give off radiation. This is often from electrons jumping orbits and emitting moving photons.
Nuclear energy



Gravitational potential - Stored energy in raised objects.

Chemical - Stored energy in fuels, foods and batteries.
Chemical energy is potential energy until the chemical reaction puts atoms and molecules in motion. Heat energy (KE) is often the result of a chemical reaction.
Light energy


Sound - Energy released by vibrating objects.

Electrical - Energy in moving or static electric charges.

Electrical energy is the movement of electrons. That is kinetic energy. The voltage in an electrical circuit is the potential energy that can start electrons moving. Electrical forces cause the movement to occur.
Chemical energy

Elastic potential - Stored energy in stretched or squashed objects.

Nuclear - Stored in the nuclei of atoms.

Certain elements have potential nuclear energy, such that there are internal forces pent up on their nucleus. When that potential energy is released, the result is kinetic energy in the form of rapidly moving particles, heat and radiation.

(The most commonly applied forms of energy will be discussed.)


Summary

* kinetic energy — motion
o mechanical energy — motion of macroscopic systems
+ machines
+ wind energy
+ wave energy
+ sound (sonic, acoustic) energy
o thermal energy-- motion of particles of matter
+ geothermal energy
o electrical energy — motion of charges
+ household current
+ lightning
o electromagnetic radiation — disturbance of electric and magnetic fields (classical physics) or the motion of photons (quantum physics)
+ radio, microwaves, infrared, light, ultraviolet, x-rays, gamma rays
+ solar energy
* potential energy — position
o gravitational potential energy
+ roller coaster
+ waterwheel
+ hydroelectric power
o electromagnetic potential energy
+ electric potential energy
+ magnetic potential energy
+ chemical potential energy
+ elastic potential energy
o strong nuclear potential energy
+ nuclear power
+ nuclear weapons
o weak nuclear potential energy
+ radioactive decay
Another scheme (economic)

* solar
o sunshine
o wind
o ocean currents
o ocean thermal temperature gradients
o biomass
+ food
+ wood/charcoal
+ dung
o fossil fuels
+ coal
+ petroleum
+ natural gas
* everything else
o geothermal
o tidal
o nuclear

Centre of Gravity and Stability

Centre of Gravity

The center of gravity is a geometric property of any object.It is defined as the point at which its whole weight appears to act for any orientation of the object. It is the average location of the weight of an object.

In Physics we find it a lot easier to think of objects as point masses. We think of all the mass as being concentrated at the centre of gravity.



The green arrow is the line of action of the force from the centre of gravity. Force due to gravity on a mass is the weight.

When an object is pivoted at a corner,its weight causes a turning effect about the pivot.

However, if you place the pivot a particular position, it s weight has no turning effect. This position is the point at which the moment of its weight is
0 as its perpendicular distance between the pivot and the line of action of weight is 0.

Note that it is called the centre of gravity not centre of weight. This is because if the object were in space, it would still have mass but the weight differs due to the distance from the gravitational field strength

We can completely describe the motion of any object through space in terms of the translation of the center of gravity of the object from one place to another, and the rotation of the object about its center of gravity if it is free to rotate.
If the object is confined to rotate about some other point, like a hinge, we can still describe its motion.

If we allow an object to dangle freely from a single point, we find that the centre of mass is on a line vertically underneath the point from which the object is hung.




Now if we turn the rectangle so that it hangs off one of the holes in the corner, we can use the plumb line to trace a second line like this:



We can trace the line by hanging a plumb line (heavy object on a string) which always hangs vertically.



When solving problems involving Forces and moments,

Remember to note :

1. Center of gravity of objects
2. The pivot
3. the force applied
4. The Weight of the object
5. The moment of object

Stability

Stability is the extent to which an object resists toppling over. Stable objects do not topple over easily. When designing vehicles, engineers try to design so that the centre of mass is as low as possible. This makes vehicles less likely to turn over when going round corners.

Three cases of Equilibrium:

1. Stable Equilibrium

Place a Bunsen burner on its broad base (figure below). Push the top to one side and see what happens. You will notice that the burner does not fall off unless it is given a hard push. This is because the body is in stable equilibrium, it has a broad base, a heavy bottom, thus lowering its center of gravity. When the burner is tilted more and more, the C.G. gets raised and the burner falls back to make the C.G. as low as possible [Figure (a) below)].

a)Centre of Gravity Rises and then falls
b)the line of action of its weight lies inside its base area
c)The anti clockwise moment of its weight about tthe point of contact causes it to return to its original position

2. Unstable Equilibrium

Place the burner upside down as shown in figure below. A slight push causes the C.G. to be lowered and the burner begins to fall to make the C.G. as low as possible [Figure (b) below)].

a)Centre of Gravity falls and falls further.
b)the line of action of its weight lies outside its base area
c)The clockwise moments of its weigtht about the point of contact causes toppling

3. Neutral Equilibrium

Let the burner lie on its side as in figure below. Push it slightly and see what happens. On further pushing, the C.G. neither gets raised nor lowered. The burner just rolls maintaining its center of gravity at the same level. Objects like cylinders and cones lying on their side roll because they are in neutral equilibrium [Figure (c) below)].

a)Centre of Gravity neither rises nor falls; remains at the same level above the surface supporting it.
b)the line of action of its weight and opposing force coincides
c)No mements provided by its weigtht about the point of contact to turn the bunsen burner



Conditions for Stable Equilibrium

* The body should have a broad base.

* Center of gravity of the body should be as low as possible.

* Vertical line drawn from the center of gravity should fall within the base of
support.

Solved Examples

Example 1:

A uniform meter rod of weight 100 N carries a weight of 40 N and 60 N suspended from 20 cm and 90 cm mark respectively. Where will you provide a knife edge to balance the meter scale?

Suggested answer :

If we assume the fulcrum to be at 50 cm mark, then the moment due to the force at 90 cm mark is greater than the one at 20 cm mark. Therefore, the knife edge should be supported at a distance of 'X' cm away from 50 cm mark.



Taking moments about X,

40(30 + X) + 100 + X = 60 (40 - X)

120 + 4X + 10X = 240 - 6X (dividing by 10)

14X + 6X = 240 - 120

20X = 120

The knife edge should be provided at 56 cm mark.

Example 2 :

A see-saw of 4m is provided with a wedge at the center. Susan and Jason of weights 500 N and 300 N respectively are sitting on the same side of the fulcrum at 2 m and 1.5 m from center respectively. If Karl weighing 600 N is sitting on the opposite side at a distance of 2 m from the center where must Peter weighing 200 N sit to balance the see-saw?

Suggested answer :

Let Peter be at a distance of 'd' m away from center nearer to Karl as the moment on the opposite side is greater.



By the principle of moments,

(600 x 2) + (200 x d) = (500 x 2) + (300 x 1.5)

12 + 2d = 10 + 4.5 (dividing both sides by 100)

2d = 14.5 - 12

from the center near Karl.

Example 3:

Two ropes are attached to points P and Q on a wheel of radius 0.5 m which can turn about O. Equal forces of 10 N are applied on the ropes at P and Q. State whether the wheel will turn, if at all whether clockwise or anticlockwise. Support your answer with a scientific reason.

Suggested answer :

Moment due to force at P

= 10 x 0.5 = 5 N m (clockwise)

Moment due to force at Q.

= 10 x 0.4 = 4 N m (anticlockwise)

*moments of force on a wheel

The force P is tangential perpendicular distance from O = 0.5 m while the perpendicular distance OR from Q = 0.4 m. Hence, the clockwise moment being greater the wheel will turn in that direction.


(a) Center of gravity in loading a ship
When a ship floats in the water the forces of buoyancy and gravity balance each other because they are equal.

The following three diagrams show how loads affect the center of gravity and stability of a ship. A fully loaded ship [figure (a)] brings the center of gravity and the center of buoyant force close together making the ship stable.



When the ship is unloaded [figure (b) above] the center of the gravity and the center of buoyancy have moved far apart, then the ship will be unstable.
In the figure (c) above, weight of the flooded ballast tanks restore balance.

(b) As the C.G. of a body is raised the body becomes more unstable. This is because when the body is tilted the vertical line drawn from the C.G. falls outside the base.



For the same reason extra passengers are not allowed on the upper deck of a bus. If they are allowed to stand in the upper deck the C.G will be raised and the bus will be more unstable when it takes a sharp turn.



For the same reason even the height of a sports car is reduced to the minimum.



(c) Manufacturers make toys which appear to be unstable but are in fact very stable. For example, the rocking doll will come back to right position even if you tilt it completely on one side. This is because of its heavy base (low C.G).

Principle of moments

Principle of moments

Balancing Moments

Moments have two possible directions, clockwise or anti-clockwise.

-If the clockwise moment is bigger than the anticlockwise moment, then the object will turn clockwise.

-If the anticlockwise moment is bigger than the clockwise moment, then the object will turn anticlockwise.

-If the clockwise moment is equal to the clockwise moment, then the object will stay where it is.


This leads to an important rule in Physics, the Principle of Moments:

If the clockwise moment = anticlockwise moment, the system is in equilibrium



This means that the system is balanced:















Conditions for equilibrium:

1.All forces on it are balanced; resultant force is zero
2.The resultant moment about the pivot is zero(must justify principle of moments)


Example with worked solutions:









clockwise moment = anticlockwise moment

Clockwise moment = 5 N × 0·50 m = 2·50 Nm.

Anticlockwise moment = F × 0·25 m = 2·50 Nm
Force F = 2·50 Nm ÷ 0·25 m = 10 N
In order to balance the 5 N force acting at 0·5 m from the pivot, we require 10 N acting in the opposite direction but at 0·25 m.




















A 5 m uniform plank weighing 600 N is placed on a level road. A man applies a force at one end. What is the minimum force required to lift it up?

A.600 N
B.900 N
C.300 N
D.12 00 N

Answer : 300N

Moment acting on plank: 2.5 x 600 = 1500Nm
Moment needed to lift plank: 1500Nm
Amount of effort needed : 1500Nm/5m = 300N


Sometimes moments can easily become unbalanced - even when we don't want them to!





In these unfortunate examples, it would seem that in loading the cart, some of the boxes must have slipped to the back - further away from the pivot - greatly increasing their turning effect. In the case of the lorry, its weight wasn't enough to balance the heavy bricks.

The result was the lifting of the donkey - who must have been very surprised! For the lorry, it was lucky nobody was hurt.

Many Moments


Sometimes more than one force acts on the same side of the pivot. Their overall turning effect is easy to work out.

2 forces, both acting clockwise, 2 N and 5 N at 0.2 m and 0.5 m respectively




The 2 N force has a moment of 2 × 0·2 m = 0·4 Nm clockwise.
The 5 N force has a moment of 5 × 0·5 m = 2·5 Nm clockwise.

Their combined moment = 0·4 Nm + 2·5 Nm = 2·9 Nm clockwise.

Moments can just be added, but they must act in the same direction.

Turning Effect of Forces

The Moment of a Force (also called torque)

One force on its own isn't much use to us. We normally look at situations where turning effects are balanced (or not!). The turning effect of a force about a pivot is known as its moment about that point.

A moment is NOT a period of time. Nor is it the same as momentum.

The moment of a force is a measure of its turning effect.

Moment = Force × Perpendicular distance of force from "pivot"
Moment =F x d

Where,
F is the force (in N)
d is the perpendicular distance from the line of action of the force to the pivot (in m)

The SI unit is the newton - metre (Nm)

Moment of force is a vector(has magnitude and direction).The direction of the moment can be either clockwise or anticlockwise.









When presenting answers, we need to state:
1.Magnitude in Nm
2.Direction (either clockwise or anti-clockwise)

Some Examples:









When there is more than one force , there is more than one moment about the pivot,
The resultant moment is computed by adding all the moments in the clockwise
direction and subtracting the moments in the anticlockwise direction.

Question 1

A wheel nut is tightened to a moment of 100 Nm. A motorist has to undo the nut with a wheel wrench which is 0.40 m long. What force must he apply?

Answer

Question 2

How can the force applied be reduced?

Answer



Consider a person trying to open a door, by applying a force, of magnitude, F, as shown below.















The two obvious changes the person could make in order to open the door more easily are
i) he/she could increase the distance "r"
ii) he/she could push at 90° to the door.

If the angle between the line of action of the force and the door is 90°, we have
and it is clear that this is the maximum value of the turning effect for a given force.

Why are door knobs located at the far edge of the door?
It is easier to close a heavy door by applying a force as far away as possible from the hinges, hence is larger and the moment, Fd is greater.

Why are hammers so long?

You just require a small force to pull out a nail when you use a hammer with a long handle. Again the principle of generating a large moment with a large value of d, the distance of the force from the pivot is large, even though the force is small.