ENERGY

1. ENERGY

2. Energy The word energyin today's world is one of the most used one; we talk about consumed energy annually by a nation, we talk of energy crisis, demand of energy. There are also sources of energy as oil, electricity, nuclear energy. The electric meters in our houses indicate the amount of consumed electricity which we pay through the electricity bill. But what is energy? The energy of a body or of a system of bodies is what can be transformed into work. Energy is a real characteristic of objects (or bodies) but, differently from the mass, you can’t touched or seen it. So energy is work. This physical quantity is denoted by the symbol W or E and is measured in Joules (the same unit of work). We have different forms of energy, in fact there are different mechanisms which produce it: thermal energy, electromagnetic energy, light energy, chemical energy, nuclear energy, mechanical energy and all these forms of energy can produced work. Energy is a scalar quantity and its International System Unit (IS) is the Joule (J).

3. Nuclear energy Light energy Thermal energy Electromagnetic energy Chemical energy

4. Energy is the capacity of a body or a system of bodies to fulfill / produce work. Work, in Physics, is defined as a force multiplied by a displacement: W=F•d A Body does a work when it changes its status: heat ↔ cold and viceversastill ↔ in motion and viceversasolid ↔ liquid and viceversa Work means then a change in position, speed, status or shape of the matter. Therefore, Energy is the capacity to change the matter. Energy is so work The unit of measure of Energy is the Joule, the same as the work. 1 Joule expresses, therefore the used energy (or work done) by a force of 1 Newton on a body to move it at a distance of 1 meter.

5. Energy can be presented in various forms: • -Mechanical Energy: Energy, a body has got due to a displacement, that in turn, can be divided into Kinetic and Potential Energy. • a)ThePotential Energy of a body at rest, but in position to effect a transformation without the intervention of external forces (water supply in the mountain ready to go down, an object which is placed at a certain distance above the ground). • b) The Kinetic Energy of a body that is in motion. • - Chemical Energy: which is stored in the bonds between molecules and it is manifested by chemical reactions that may have mechanical (explosions), thermal (heating), electromagnetic effects. • -Nuclear Energy: it is the Energy due to the bonds of particles of atomic nuclei of certain physical elements. It manifests with two physical processes such as nuclear fission and fusion. • Electromagnetic Energy: it is the Energy possessed by waves or participles (such as electrons moving in conductors). • Radiant Energy: it comes from solar radiations. • Thermal Energy: it is manifested by heat passing from body to body. • These six forms of Energy are related to each other and you can switch from one form of energy to another. For example, when wood burns its chemical energy is transformed into thermal (heat) and light energy.

6. Energy sources A source of Energy is any origin of energy. Energy sources are of two types: renewable and non-renevable (exhaustible) Renewable energy sources are: the sun, water and wind; they are unlimited in time, that is they never end. To exploit, renewable energy sources, however, is very difficult and very expensive. Exhaustible sources of energy are: coal, oil, natural gas and uranium. They are limited in time, that is sooner or later they will get exhausted. To exploit exhaustible sources is easier and less expensive. The kinetic energy of the wind energy (aeolian) is transformed into mechanical energy (grindstone) or energy in motion of the blades of the generator and, by means of an electric machine, called alternator, into electric energy (that by means of special eletrical lines, arrives in our houses) or by blowing the sails which let boats sail.

7. The light energy, commonly called light is produced by the sun, natural light source, it is propagated by radiations and allows us to see the world around us; it is stored by plants through a process, known as photosynthesis, and allows plants to live and grow and it permits at the same time the life of all living organisms on the Earth, in fact, herbivores derive the energy to live from plants and carnivores, in turn, they draw it from herbivores.

8. Transformation(s) of Energy The reason we transorm energy from a form to another is because this is required by the final use we desire. -For example we use the electrical energy to light bulbs which convert electrical energy into electromagnetic energy, which we perceive as light. -The fuel we use in our car contains chemical energy, and through special devices it can be transformed in energy for the motion of the car (engine) and into light energy (headlights); and/or into thermal energy (in winter for the central heating). -Hydropower stations transform the mechanical energy of the water into electricity which is transported to our houses to be used. -Our body can convert the chemical energy of food ingested, into thermal energy (which enables us to keep the body temperature at about 36° C), electricity, kinetic energy, etc,… part are properly saved, in reserve, so to be used later. Conclusion In many physical phenomena which happen there is a continuous transformation of energy from a form to another. Two are the most important concepts to be emphasized: 1)Energy is the ability or capacity to produce work 2)Energy cannot be created nor destroyed (but it can be transformed from one form to another)

9. The Mechanical energy can be divided into Kinetic energy and Potential energy. Suppose we consider a moving body, it has a mass m. which moves at a velocity v.Such a body has got a kinetic energy equal to: That it is as great as both mass and velocity of the body are greater Kinetic energy is the energy possessed by a body in motion. The kinetic energy represents the work that a body can fulfill/produce due to its motion. It’s quite clear that if the body is at rest: v = 0 , and then KE = 0, that is the kinetic energy of the body at rest is zero. N.B. The mass has to be mesuared in Kilograms. And the speed in m/s. The kinetic energy is measured in Joules. Example What is the kinetic energy possessed by a body of mass 2 kilograms which moves at the speed of 5 meters per second? In symbols: m = 2 Kg. v = 10 m/s KE= ? KE= ½ m v2 = ½ ∙ 2 ∙100= ½ ∙ 200 = 100 J Solve : What is the kinetic energy possessed by a body of mass 400grams which moves at the speed of 5 meters per second? m = 400 g v = 5 m/s KE= ?

10. The work-energy theorem Suppose we apply to a body, which has got kinetic energy K1, a costant force: its kinetic energy will increase from K1 to K2 value. The work done by the force was: And then you can say: the work done by the force applied to the body is equal to the change in the kinetic energy of the body. If the work is positive there is an increase of kinetic energy, if negative a decrease. If the work is positive (motion) it means the force has acted in the same direction of the speed facilitating the motion. The work-energy theorem If instead the work is negative (resistance) it means the force has acted towards the opposite direction to the motion resisting to it. Example: What is the work done by the force acting on a body so that its kinetic energy passes from 200 J to 120 J? In symbols : K1 = 200 Kg K2 = 120 m/s W= ? Negative work = resistant work =120 - 220 = -80 J

11. Gravitational potential energy A body which is at a certain level from the ground possesses, with reference to the ground, a gravitational potential energy. This energy is equivalent to the work the weight of the body would perform in the fall; and it is then calculated by: PE = m∙g∙h Where: m = mass g = the acceleration of gravity h = height Gravitational Potential Energy is the energy a body has got due to its elevation (height) with reference to a lower elevation, that is, the energy that could be obtained by letting it falls to a lower elevation. 

12. The potential energy can be represented as the money you have got in the bank, which can be spent for any shopping, and any part you spend of it, the amount decreases. The potential energy, therefore, represents the energy stored by a body that is the work that a body could fulfill if it had moved, but in reality, in that moment it didn’t do. Example : What is the potetial energy of a body of 4 kg arranged at a height of five metres from the ground? m = 4 Kg h = 5 m Ep = ? PE = m∙g∙h = 4 ∙ 5 ∙9,8 = 196 J This is the work that the body will do in the fall. This is also the work that has been done to bring the body from the horizontal reference to height (h); the work of the body will return as previously said during the fall Solve: What is the potential energy of a body of 600 grams placed at a height of 50 centimeters from the ground?

13. Work and potential energy Suppose a body with a mass m carries out a distance from point A to point B (according the first route). In this case, we indicate h = h1 – h2 , the work is indicated: W = mgh = mg(h1 – h2) = mgh1 – mgh2 W = mgh1 – mgh2 = PE1 – PE2 that is The gravitational force fulfills a work which is the result considering the variation of the potentian energy but changing its positive mark into a negative one. If the work done is positive, the final potential energy decreases, what it happens when a body falls down from a given height to the ground; if , instead, it is negative, the final potetial energy encreases , what it happens when we lift a body from the ground to a given height. What happens , if , the body moves from A point to B according the second route? You could demonstrate that the work done by the weight force completely depends on the difference in height between the starting point A and the final one B, just the same points , and not considering the chosen route to move from A to B, therefore the work done is the same as the preceding case. Generally speaking: a force is conservative, like a weight force, when the work doesn’t depend on the covered route from A to B but it depends only on the position of the two extreme points.

14. Work and potential energy Calculate the work done by a weight force on a body of mass m considering two cases: 1) First case along the vertical h; 2) Second case along a 30° inclined plane , which measures l in lenght. In the first case, as you can see, the weight force and the displacement have the same direction, so the work is: W=F∙s = P∙h = m∙g∙h In the second case, the weight force can be divided into two components, one perpendicular to the plane (it is neutralized by the locked up reaction) the other one parallel. The parallel one has as value: l = 2∙h The inclined plane has 1 metre in lenght, but, from mathematics esteems, we have: Therefore , in the second case, the work is: As it is in the first case. Final considerations The work in both cases is the same: then it doen’t depend on the route, but only on the starting or final positions of the considered points, that is on their heights. Observe , besides, points B e C have the same height from the ground (=0). The force, which the work doesn’t depend on the followed route, they are called conservative forces. The weight force, then, is a conservative force, in fact its work doesn’t depend on the done route.

15. If we give a body with a mass m, which is in the point A Potetial energy PE = mgh and a body which is in the point B or in the point C Potetial energy 0 (as their height from the ground in the first picture is 0), you have that the work to reach from point A to point B is: W = PEA – PEB = startingPE –final PE = mgh – 0 = mgh W = PEA – PEC = startingPE –final PE = mgh – 0 = mgh • Conclusion: • Work is egual to the differencebeteewnstartingpotetialenergy and the finalone; • Work toreachpoint A topoint B is the sameastoreachfrom A to C . In the picture we suppose that the point A is at a certain height h1, while points B and C at the same height h2: W = PEA –PEB = mgh1- mgh2 = = mg(h1- h2) = mgh The work done from point A to point B dipends only on their difference in height, h. W = PEA – PEC = mgh1- mgh2 = mg(h1- h2) = mgh The work done from point A to point C is the same as the one done from A to B, it depends only on their difference in height, h , and not on the followed path.

16. Non conservative forces The force of dynamic friction, acting on a body dragged on a plane, it is, instead, a non conservative or dissipative force . This force is always in the opposite direction of the motion, so the work is negative. In this case the work done by a non conservative force dipends on a particular path which joins the two points, so, it can’t be expressed through potetial energy, it depends only on the position. If you drag a box on a surface from a point A to B along a straight route (2) and after along a curvilinear one (1). In this case the work done from the friction force (dissipative force) depends on the route and it is as much bigger as the lenght of the set distance is. We know that the work done by the friction forces is negative, therefore, the variation of mechanic energy , is negative, so the mechanic energy decreases . Whatever becomes of this energy? It changes into heat and it spreads into the environment.

17. Law of conservation of mechanical energy. Total mechanicalenergyEtotis the sum ofkineticenergyKE and gravitationalpotentialenergyPE. Etot = KE + PE Suppose we have a body which is at a certain height h, respect to the ground. We assume that the potential energy measures: PE=10J and as it is at rest its kinetic energy is zeroJ. During the fall happens that: PE = 10 J KE = 0 J Etot = PE + KE = 10 + 0 = 10 J 2h PE = 5J KE = 5 J Etot = PE + KE = 5 + 5 = 10 J h PE = 0 J KE = 10 J Etot = PE + KE = 0 + 10 = 10 J h=0 According to the example you can see that during the fall the potential energy transforms into kinetic energy so that the sum of the potential energy, during the fall it is preserved, it remains costant, and it is equal to 10Joules. E = cost that is E after = E before that is E2 = E1 In an isolated system, in whih we only have conservative forces, the total mechanical energy is saved.

18. Conservation law of the total energy If there are also non conservative forces, the total mechanical energy is not saved. We have already said that when there are non conservative forces, the total mechanical energy is not saved. It means that the energy we had before , part is lost, changing in heating energy or heat. If we consider all the forces there are present, that is what the friction work can give we can formulate the conservation law of the total energy: the total energy possessed by a body remains costant that is PE + KE + Q = cost The energy doesn’t encrease or decrease in any process: it can change from a form to another, but its quantity remains costant.