Work, energy and power
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The document discusses concepts related to mechanical energy, including work, kinetic energy, potential energy, and power. It defines energy as the capacity to do work and describes several forms of energy. Work is defined as the dot product of force and displacement. Kinetic energy is defined as 1/2mv^2 and depends on an object's motion. Potential energy exists in gravitational and elastic forms and depends on an object's position or state. The conservation of mechanical energy and work-energy theorem are explained. Power is defined as the rate of energy transfer.
Work, energy and power
- 1. Chapter 5 Work, Energy and Power 01/22/14 IB Physics (IC NL) 1
- 2. ENERGY Energy is the crown for physics. It is found in every branch of physics. Definition: Energy is the capacity of a physical system to perform work. Energy exists in several forms such as heat, kinetic or mechanical energy, light, potential energy, electrical, solar wind, hydroelectric or other forms. 01/22/14 IB Physics (IC NL) 2
- 3. Some Energy Considerations Energy can be transformed from one form to another Essential to the study of physics, chemistry, biology, geology, astronomy and other topics. Can be used in place of Newton’s laws to solve certain problems more simply 01/22/14 IB Physics (IC NL) 3
- 4. Forms of Energy The type of energy to be covered in this power point is the Mechanical Energy. In order to fully cover the subject we have to start with work, Then study energy, And later relate them together. 01/22/14 IB Physics (IC NL) 4
- 5. × ∆ Work Provides a link between force and energy The work, W, done by a constant force on an object is defined as the dot product of the force and the displacement W = F ⋅ ∆x W = ( F cosθ )∆ x 01/22/14 IB Physics (IC NL) 5
- 6. Work, cont. W = ( F cos θ )∆ x F is the magnitude of the force Δ x is the magnitude of the object’s displacement θ is the angle between the force and the displacement 01/22/14 IB Physics (IC NL) 6
- 7. Work, cont. This gives no information about the time it took for the displacement to occur the velocity or acceleration of the object Work is a scalar quantity 01/22/14 IB Physics (IC NL) 7
- 8. Units of Work SI Newton • meter = Joule 01/22/14 N•m=J J = kg • m2 .s-2 IB Physics (IC NL) 8
- 9. Work as a function of θ W = F∆x cos θ If θ = 0 then cos 0 = 1 W= F x ∆x When the work is positive then it is called a motive work ex. The work of any tractive force 01/22/14 IB Physics (IC NL) 9
- 10. Work as a function of θ 0<θ<90o the angle is acute 0<cosθ <1 Positive then W = F x cos θ Also the work is motive ex. A force in a rope pulling a box with an angle 01/22/14 IB Physics (IC NL) 10
- 11. Work as a function of θ If θ = 90o then cos θ = 0 then W = 0 This case is so important so keep it in mind ex. Work done by normal force when this force is perpendicular to direction of motion 01/22/14 IB Physics (IC NL) 11
- 12. Work as a function of θ If 90o <θ<180o Then -1<cosθ <0 then W is negative When the work is negative it is called a resistive work. ex. Pulling back with a rope while motion is forward. 01/22/14 IB Physics (IC NL) 12
- 13. Work as a function of θ If θ = 180o then cos180 = -1 W = - F x∆x This force is also resistive ex. Work done by force of friction. 01/22/14 IB Physics (IC NL) 13
- 14. Conclusion If the work is positive then it is called MOTIVE If the work is negative then it is called RESISTIVE 01/22/14 IB Physics (IC NL) 14
- 15. More About Work The work done by a force is zero when the force is perpendicular to the displacement cos 90° = 0 If there are multiple forces acting on an object, the total work done is the algebraic sum of the amount of work done by each force 01/22/14 IB Physics (IC NL) 15
- 16. When Work is Zero Displacement is horizontal Force is vertical cos 90° = 0 01/22/14 IB Physics (IC NL) 16
- 17. Work done by gravity The work done by a body falling under the action of its weight only is W = mgh cos 0 = mgh Whatever the path followed, the displacement is the shortcut distance between the two levels. Work done by gravity is independent of the path. 01/22/14 IB Physics (IC NL) 17
- 18. Work Can Be Positive or Negative Work is positive when lifting the box Work would be negative if lowering the box 01/22/14 The force would still be upward, but the displacement would be downward IB Physics (IC NL) 18
- 19. Work and Dissipative Forces Work can be done by friction The energy lost to friction by an object goes into heating both the object and its environment So energy may be converted into heat, sound or light. 01/22/14 IB Physics (IC NL) 19
- 20. Work due to variable force The area under any force-displacement graph is the work done force Area = work done displacement 01/22/14 IB Physics (IC NL) 20
- 21. Energy Is the ability to do work Work and energy are interchangeable even they have the same unit the joule (J) 01/22/14 IB Physics (IC NL) 21
- 22. Mechanical Energy It could be one of two types or their sum: 1- Kinetic Energy 2- Potential energy which is, from a mechanical point of view, of two types: a- Gravitational P.E. b- Elastic P.E. 01/22/14 IB Physics (IC NL) 22
- 23. Kinetic Energy Energy associated with the motion of an object 1 KE = mv 2 2 Scalar quantity with the same units as work Work is related to kinetic energy 01/22/14 IB Physics (IC NL) 23
- 24. Unit manipulation 01/22/14 IB Physics (IC NL) 24
- 25. Work-Kinetic Energy Theorem When work is done by a net force on an object and the only change in the object is its speed, the work done is equal to the change in the object’s kinetic energy Wnet = ∑Wext = KEf - KEi 01/22/14 Speed will increase if work is positive Speed will decrease if work is negative IB Physics (IC NL) 25
- 26. Work and Kinetic Energy An object’s kinetic energy can also be thought of as the amount of work the moving object could do in coming to rest 01/22/14 The moving hammer has kinetic energy and can do work on the nail IB Physics (IC NL) 26
- 27. Potential Energy Potential energy is associated with the position of the object within some system 01/22/14 Potential energy is a property of the system, not the object A system is a collection of objects interacting via forces or processes that are internal to the system IB Physics (IC NL) 27
- 28. Gravitational Potential Energy Gravitational Potential Energy is the energy associated with the relative position of an object in space near the Earth’s surface 01/22/14 Objects interact with the earth through the gravitational force Actually the potential energy is for the earth-object system IB Physics (IC NL) 28
- 29. Reference level for G.P.E. Whenever gravitational potential energy is mentioned there should be a chosen reference level relative to which the energy must be studied. G.P.E. = mgh mg is the weight and h is the height 01/22/14 IB Physics (IC NL) 29
- 30. Work and Gravitational Potential Energy W gravity = mgh ∆PE = PE f − PE i = − mgh ∆ ⇒ W = − ∆PE This relation holds true in both cases if the body is falling or moving upwards. 01/22/14 IB Physics (IC NL) 30
- 31. Work-Energy Theorem, Extended The work-energy theorem can be extended to include potential energy: W = (KEf – KEi) + (PEf – PEi) If other conservative forces are present, potential energy functions can be developed for them and their change in that potential energy added to the right side of the equation 01/22/14 IB Physics (IC NL) 31
- 32. Reference Levels for Gravitational Potential Energy A location where the gravitational potential energy is zero must be chosen for each problem The choice is arbitrary since the change in the potential energy is the important quantity Choose a convenient location for the zero reference height 01/22/14 often the Earth’s surface may be some other point suggested by the problem Once the position is chosen, it must remain fixed for the entire problem IB Physics (IC NL) 32
- 33. Conservation of Mechanical Energy Conservation in general To say a physical quantity is conserved is to say that the numerical value of the quantity remains constant throughout any physical process In Conservation of Energy, the total mechanical energy remains constant 01/22/14 In any isolated system of objects interacting only through conservative forces, the total mechanical energy of the system remains constant. IB Physics (IC NL) 33
- 34. Conservation of Energy, cont. Total mechanical energy is the sum of the kinetic and potential energies in the system MEi = ME f KEi + PEi = KE f + PE f 01/22/14 Other types of potential energy functions can be added to modify this equation IB Physics (IC NL) 34
- 35. Conservation cont. Suppose a body is falling under the action of gravity in an isolated system. Wext = − ∆PE ∑W ext = ∆KE ⇒ ∆KE = − ∆PE KE f − KE i = −( PE f − PE i ) ⇒ KE f + PE f = KE i + PEi ⇒ ME f = ME i ∑ 01/22/14 IB Physics (IC NL) 35
- 36. Problem Solving with Conservation of Energy Define the system Select the location of zero gravitational potential energy Do not change this location while solving the problem Identify two points the object of interest moves between 01/22/14 One point should be where information is given The other point should be where you want to find out something IB Physics (IC NL) 36
- 37. Problem Solving, cont Verify that only conservative forces are present Apply the conservation of energy equation to the system Immediately substitute zero values, then do the algebra before substituting the other values Solve for the unknown(s) 01/22/14 IB Physics (IC NL) 37
- 38. Potential Energy Stored in a Spring Involves the spring constant, k Hooke’s Law gives the force F=-kx 01/22/14 F is the restoring force F is in the opposite direction of x k depends on how the spring was formed, the material it is made from, thickness of the wire, etc. (unit N/m) IB Physics (IC NL) 38
- 39. Potential Energy in a Spring Elastic Potential Energy related to the work required to compress a spring from its equilibrium position to some final, arbitrary, position x 1 2 PEelastic = kx 2 01/22/14 IB Physics (IC NL) 39
- 40. Work-Energy Theorem Including a Spring W = (KEf – KEi) + (PEgf – PEgi) + (PEef – PEei) 01/22/14 PEg is the gravitational potential energy PEe is the elastic potential energy associated with a spring PE will now be used to denote the total potential energy of the system IB Physics (IC NL) 40
- 41. Conservation of Energy Including a Spring The PE of the spring is added to both sides of the conservation of energy equation ( KE + PEg + PEe )i = ( KE + PEg + PEe ) f The same problem-solving strategies apply 01/22/14 IB Physics (IC NL) 41
- 42. Transferring Energy By Work 01/22/14 By applying a force Produces a displacement of the system IB Physics (IC NL) 42
- 43. Transferring Energy Heat 01/22/14 The process of transferring heat by collisions between molecules For example, the spoon becomes hot because some of the KE of the molecules in the coffee is transferred to the molecules of the spoon as internal energy IB Physics (IC NL) 43
- 44. Transferring Energy Mechanical Waves 01/22/14 A disturbance propagates through a medium Examples include sound, water, seismic IB Physics (IC NL) 44
- 45. Transferring Energy Electrical transmission 01/22/14 Transfer by means of electrical current This is how energy enters any electrical device IB Physics (IC NL) 45
- 46. Transferring Energy Electromagnetic radiation Any form of electromagnetic waves 01/22/14 Light, microwaves, radio waves IB Physics (IC NL) 46
- 47. Notes About Conservation of Energy We can neither create nor destroy energy 01/22/14 Another way of saying energy is conserved If the total energy of the system does not remain constant, the energy must have crossed the boundary by some mechanism Applies to areas other than physics IB Physics (IC NL) 47
- 48. Power Often also interested in the rate at which the energy transfer takes place Power is defined as this rate of energy transfer W ℘= = Fv t SI units are Watts (W) 01/22/14 J kg.m 2 W = = 3 = kg.m 2 .s − 3 s s IB Physics (IC NL) 48
- 49. Power, cont. US Customary units are generally hp Need a conversion factor 1 hp = 746 W Can define units of work or energy in terms of units of power: 01/22/14 kilowatt hours (kWh) are often used in electric bills This is a unit of energy, not power IB Physics (IC NL) 49
- 50. Efficiency 01/22/14 Efficiency is defined as the ratio of the useful output to the total input This can be calculated using energy or power values as long as you are consistent Efficiency is normally expressed as a percentage IB Physics (IC NL) 50
- 51. Spring Example Spring is slowly stretched from 0 to xmax r r Fapplied = -Frestoring = kx W = ½kx² 01/22/14 IB Physics (IC NL) 51
- 52. Spring Example, cont. The work is also equal to the area under the curve In this case, the “curve” is a triangle A = ½ B h gives W = ½ k x2 01/22/14 IB Physics (IC NL) 52