Work and energy

1. Workand energy (a) give examples of energy in different forms, its conversion and conservation, and apply the principle of energy conservation to simple Examples (e) recall and apply the formula Ek = ½ mv2 (i) recall and use the formula Ep = mgh for potential energy changes near theEarth’ssurface

2. Introduction • Think of force as a mechanism by which energy is transferred from one body to another. • This only occurs when the object moves in the direction of the force. • Consider the forces on vehicles when accelerating/decelerating. • Consider the effect of the distance over which the force acts rather than the time of action of the force.

3. GREEN SICK • Gravitational • Radiative (e-m waves) • Electrical • Elastic • Nuclear • Sound • Internal (Thermal) • Chemical • Kinetic • That’s it • Really no other types exist • Except maybe dark energy but that is another story

4. Energytransfers • Writethe 9 types of energy in a circleon a double page in yournotebooks. • Draw a straight line fromoneform of energytoanyother and addanarrow • Writeonthearrow a deviceorphenomenonthat causes thatchange.

5. Kinetic Energy • Thisistheenergythat a bodypossessesbyvirtue of itsmotion. • Ifthemass of a bodyism and itsvelocityisv thenitskineticenergyis …….. • Ek= ½ m v2

6. GravitationalPotentialEnergy • Thisistheenergythat a bodypossessesbyvirtue of its position in thegravitationalfield • Ifthemass of a bodyism and itsheightabove a fixed position ish thenitschange in gravitationalpotentialenergy…………. • Ep= mgh • where g = theaccelerationduetogravity

7. ThePrinciple of Conservation of Energy • Energy can betransformedfromoneformtoanother, butitcannotbecreatednordestroyed. • i.e. the total energy of a systemisconstant • Energyismeasured in joules and itis a scalarquantity

8. Examples • Fallingobjects and rollercoasterrides are situationswhereEp + Ek = constant • Ifwe ignore theeffects of air resistance and friction. • Inclined planes and fallingobjects can oftenbesolved more simplyusingthisprincipleratherthanthekinematicsequations

9. Collisions and explosions • In allcollisions and explosionsmomentumisconserved. (seemomentum) • Generallythereis a loss of kineticenergy, usuallytointernalenergy (heat) and to a lesserextenttosound • In aninelasticcollisionthereis a loss of kineticenergy (momentumisstillconserved) • In anelasticcollisionthekineticenergyisconserved (as well as momentum)

10. KE in collisions • In elastic collisions kinetic energy is conserved. • Total KE before collision = Total KE aftercollision • In inelasticcollisionskineticenergyis ‘lost’. • Total KE before collision > Total KE aftercollision

11. Work • (b) show an understanding of the concept of work in terms of the product of a force and displacement in the direction of the force • (c) calculate the work done in a number of situations including the work done by a gas that is expanding against a constant external pressure: W = p ΔV • (h) derive, from the defining equation W = Fs, the formula Ep = mgh for potential energy changes near the Earth’s surface

12. Work • We say that work is done by a force when the object concerned moves in the direction of the force, and the force thereby transfers energy from one object to another. •  Consider the simplest possible case of work done. A force ‘F’ is acting on an object. The object has a displacement ‘S’ in the direction of the force. Then the work done is the product of force and displacement. 

13. Work • What will happen in the case when the applied force is not in the direction of displacement but rather at an angle to it. • Find the component of force in the direction of displacement. • This component will be doing work. • Component of force in the direction of displacement is F Cos θ. •  W = (F Cos θ) S = F. s • Work done is a scalar quantity.

14. An illustrative example • What sort of energy is gained by raising a mass ? • GPE • What is the force acting against the movement? • Weight (mg) • We say that the lifting force is doing work against gravity. • If the object is raised at a steady speed, it is in equilibrium and the lifting force will just balance weight. • This of course ignores any air resistance • What is g? • Gravitational field strength (Force per unit mass

15. What two factors will determine how much energy you lose (and hence the energy transferred to the object)? • The size of the force and the distance h moved in the direction of the force. • Can you state the equation which gives the energy gained? • mgh • Hence how much energy is required to lift object height h? • mgh • This suggests that energy transferred = force  distance moved in direction of force. • This is known as the work done by the force. • The equation GPE = mgh • mgh is simply a particular case of work done.

16. Another example • What happens to the energy if the mass is pushed along a surface? • Work is done against a frictional force. • The energy transferred ends up as heat.

17. force Area = work done displacement Force displacement graph • Theareaunderanyforce-displacementgraphisthework done

18. A P,V dV F dx Work done by an ideal gas during expansion Consider an ideal gas at a pressure P enclosed in a cylinder of cross sectional area A. The gas is then compressed by pushing the piston in a distance Dx, the volume of the gas decreasing by DV. (We assume that the change in volume is small so that the pressure remains almost constant at P). Work done on the gas during this compression = DW Force on piston = P A So the work done during compression = DW = P A Dx = P DV The first law of thermodynamics can then be written as: DU = DQ -DW = DQ - P DV

19. To do • P 67 q2 and 5 • P 108 q 36, 38, 39

20. KineticEnergy • (d) derive, from the equations of motion, the formula Ek = ½ mv2

21. Derivation • See p63 in P4U • Use v2=u2+2as, F=ma and Work =Fs • v2=u2+2as Rearrangefor a • a = (v2-u2)/2s Now use F=ma • F=ma = m (v2-u2)/2s Now use Work = Fs • Work = Fs = sm (v2-u2)/2s Cancel the s • Work = m (v2-u2)/2 • Work = Energytransferred = Ek = m (v2-u2)/2 • For u= 0 Ek = m v2/2

22. Energy and efficiency • (f) distinguish between gravitational potential energy, electric potential energy and elastic potential energy • (g) show an understanding and use the relationship between force and potential energy in a uniform field to solve problems • (j) show an understanding of the concept of internal energy • (k) show an appreciation for the implications of energy losses in practical devices and use the concept of efficiency to solve problems

23. PotentialEnergy • Potentialenergyis “stored” by a body • GravitationalPotentialEnergy– dueto position of body in a gravitationalfield (mgh) • ElectricalpotentialEnergy – dueto position of a chargedparticle in anelectricfield (qEd) • ElasticPotentialenergy – duetothework done against a restoringforce (tensionorcompression) (Averageforce x displacement) • Note all 3 equations are effectively F=ma

24. Force and potentialenergy • Wehavealreadyseenexampleswherework done = Potentialenergystoredforgravitationalfields. • Thesametype of calculation can beusedforpotentialenergy in Uniformelectricfields(betweenparrallelplates) • And more obviouslyforelasticpotentialenergyproblems.

25. Internal energy (U) • Internalenergy (oftenincorrectlycalledHeat) isthe total energy of anobjectduetotheKinetic and potentialenergies of it,sparticles. • For ideal gassesthereis no Potentialelementtointernalenergy • Whyisthis? • Forallothermaterials U isthesum of KE and PE forall of theparticles.

26. Somehelpfulexamples • Hotnessmeanstemperaturenotenergy • E.g. A spark at 1000 K containslessenergythan a cup of tea at 330K • Particles in differentphases of matterhavedifferrentamounts of potentialenergy so differentinternalenergies. • E.g. A steamburnisworsethan a waterburn 1kg of “steam” at 100 C has greaterinternalenergythan 1kg of water at 100C. (dueto PE of particles)

27. Efficiency • Usefulenergyout / total energy in • Alwayslessthan 1 • Oftenquoted as percentage • Can berepresentedon a Sankeydiagramsee p65