Work and energy

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Work and energy

  1. 1. +Work and EnergyChapter 9Pg.144-
  2. 2. +Work
  3. 3. + What do you think? List five examples of things you have done in the last year that you would consider work. Based on these examples, how do you define work?
  4. 4. + Work  Inphysics, work is the magnitude of the force (F) times the magnitude of the displacement (d) in the same direction as the force. W = Fd  What are the SI units for work?  Force units (N) distance units (m)  N•m are also called joules (J).  How much work is 1 joule?  Liftan apple weighing about 1 N from the floor to the desk, a distance of about 1 m.
  5. 5. + Work  Ifwe lift two loads, we do twice as much work as lifting one load the same distance, because the force needed is twice as great.  Ifwe lift one load twice as far, we do twice as much work because the distance is twice as great.
  6. 6. + Work  Work is done in lifting the barbell. If the barbell could be lifted twice as high, the weight lifter would have to do twice as much work.
  7. 7. + Work  Whilethe weight lifter is holding a barbell over his head, he may get really tired, but he does no work on the barbell.  Work may be done on the muscles by stretching and squeezing them, but this work is not done on the barbell.  When the weight lifter raises the barbell, he is doing work on it.
  8. 8. + Classroom Practice Problem  A 20.0kg suitcase is raised 3.0 m above a platform. How much work is done on the suitcase?  Answer: 600 J  Suppose that you apply a 60-N horizontal force to a 32-kg package, which pushes it 4 meters across a mailroom floor. How much work do you do on the package? W = Fd = 60 N × 4 m = 240 J
  9. 9. + Work is a Scalar  Work can be positive or negative but does not have a direction.
  10. 10. + Sign of Work is Important Work is positive  Force is in the same direction as the displacement Work is negative  Forceis in a different direction as the displacement Sing of the net work lets you know if the object is speeding up or down + for speeding up and work is being on object  - for slowing down and work is done by object
  11. 11. +Energy
  12. 12. + Kinetic Energy Energy associated with an object in motion Wnet = Fd = mad Since v2f = v2i + 2ad v2 f vi2 Then 2 2 Wnet m( ) v f v i 2 ad 2 Finally 1 2 1 2 Wnet mv f mvi 2 2
  13. 13. + Kinetic Energy Kinetic energy depends on speed and mass The net work done on a body equals its change in kinetic energy SI units for KE  kg•m2/s2 or N•m or Joule (J)
  14. 14. + Example A 7.0 Kg bowling ball moves at 3.0 m/s. How fast must a 2.45g ping pong ball move in order to have the same kinetic energy as the bowling ball? Is the speed reasonable for the ping pong ball? Given: Bowling ball: m- 7.0 kg v= 3.0m/s Ping pong: m= 2.45 g (this= 0.00245kg) v-??
  15. 15. + Example 2KE  KE= ½ mv2 v m  KE= ½ (7)(32)  KE= 31.5 J 2(31.5) v 0.00245  Rearrange Equation to get v by itself v = 160.36 m/s
  16. 16. + Classroom Practice Problems  A 6.00 kg cat runs after a mouse at 10.0 m/s. What is the cat’s kinetic energy?  Answer: 3.00 x 102 J or 300 J  Suppose the above cat accelerated to a speed of 12.0 m/s while chasing the mouse. How much work was done on the cat to produce this change in speed?  Answer: 1.32 x 102 J or 132 J
  17. 17. + Work and Kinetic Energy  KEis the work an object can do if the speed changes.  Wnet is positive if the speed increases, and negative is speeds decrease  You must include all the forces that do work on the object in calculating the net work done
  18. 18. + Potential Energy  Energyassociated with an object’s potential to move due to an interaction with its environment basically its stored energy  A book held above the desk  An arrow ready to be released from the bow  Some types of PE are listed below.  Gravitational  Elastic  Electromagnetic
  19. 19. + Gravitational Potential Energy  Energy associated with an object due to the object’s position relative to a gravitational source  SI unit is still a Joule  Theheight (h) depends on the “zero level” chosen where PEg= 0.
  20. 20. + Elastic Potential Energy  Theenergy available for use in deformed elastic objects  Rubber bands, springs in trampolines, pole-vault poles, muscles  For springs, the distance compressed or stretched = x
  21. 21. + Elastic Potential Energy The spring constant (k) depends on the stiffness of the spring.  Stiffer springs have higher k values.  Measured in N/m  Force in newtons needed to stretch a spring 1.0 meters
  22. 22. + Example  A 70.0kg stuntman is attached to a bungee cord with an unstretched length of 15m. He jumps off a bridge from a height of 50m. When he finally stops the cord has a stretched length of 44m. Assuming the spring constant is 71.8 N/m, what is the total PE relative to the water when the man stops falling?
  23. 23. + Example  Given:  m= 70kg k= 71.8 N/mg= 10m/s2  h= 50m – 44m= 6m  x= 44m – 15m= 29m  PEg= mgh  PEelastic = ½ k x2  PEtotal= PEg + PEelastic
  24. 24. + Example  PEg= mgh  PEelastic = ½ k x2  PEg= (70)(10)(6)  PEelastic= ½ (71.8)(292)  PEg= 4200 J  PEelastic= 30191.9J  PEtotal= PEg + PEelastic  PEtotal= 4200 + 30191.9  PEtotal= 34391.9J
  25. 25. + Classroom Practice Problems  When a 2.00 kg mass is attached to a vertical spring, the spring is stretched 10.0 cm such that the mass is 50.0 cm above the table.  What is the gravitational potential energy associated with the mass relative to the table?  Answer: 9.81 J  What is the spring’s elastic potential energy if the spring constant is 400.0 N/m?  Answer: 2.00 J
  26. 26. +5.3 Conservation of EnergyPg. 173-178
  27. 27. + Mechanical Energy (ME)  ME = KE + PEg + PEelastic  Doesnot include the many other types of energy, such as thermal energy, chemical potential energy, and others  ME is not a new form of energy.  Just a combination of KE and PE
  28. 28. + Conservation of Mechanical Energy  The sum of KE and PE remains constant.  One type of energy changes into another type.  For the falling book, the PE of the book changed into KE as it fell.  As a ball rolls up a hill, KE is changed into PE.
  29. 29. + Example  Starting from rest, a child zooms down a frictionless slide from an initial height of 3.0m. What is her speed at the bottom of the slide? Her mass is 25kg.  Given:  vi= 0m/s hi= 3m m=25kg  vf= ?? hf=0m
  30. 30. + Example *Choose your equations  PE= mgh  KE= ½ mv2  PEf= (25)(10)(0)  KEf= ½ (25)v2  PEf= 0J  KEf= ??  PEi= (25)(10)(3)  KEi= ½ (25)(02)  PEi= 750J  KEi= 0J
  31. 31. + Example *Put together  PEi+ KEi= PEf+ KEf  750 + 0 = 0 + ½ (25)vf2  750= 12.5 vf2  vf2 = √60  vf= 7.75m/s
  32. 32. + Classroom Practice Problems Suppose a 1.00 kg book is dropped from a height of 2.00 m. Assume no air resistance.  Calculate the PE and the KE at the instant the book is released.  Answer: PE = 19.6 J, KE = 0 J  Calculate the KE and PE when the book has fallen 1.0 m. (Hint: you will need an equation from Chapter 2.)  Answer: PE = 9.81 J, KE = 9.81 J  Calculate the PE and the KE just as the book reaches the floor.  Answer: PE = 0 J, KE = 19.6 J
  33. 33. + Table of Values for the Falling Book h (m) PE(J) KE(J) ME(J) 0 19.6 0 19.6 0.5 14.7 4.9 19.6 1.0 9.8 9.8 19.6 1.5 4.9 14.7 19.6 2.0 0 19.6 19.6
  34. 34. + Conservation of Energy  Acceleration does not have to be constant.  ME is not conserved if friction is present.  If friction is negligible, conservation of ME is reasonably accurate.  A pendulum as it swings back and forth a few times  Consider a child going down a slide with friction.  What happens to the ME as he slides down?  Answer: It is not conserved but, instead, becomes less and less.  The “lost” energy? is converted into nonmechanical energy (thermal energy).
  35. 35. + Classroom Practice Problems  A small 10.0 g ball is held to a slingshot that is stretched 6.0 cm. The spring constant is 2.0 102 N/m.  What is the elastic potential energy of the slingshot before release?  What is the kinetic energy of the ball right after the slingshot is released?  What is the ball’s speed at the instant it leaves the slingshot?  How high does the ball rise if it is shot directly upward?
  36. 36. +Power
  37. 37. + What do you think?  Twocars are identical with one exception. One of the cars has a more powerful engine. How does having more power make the car behave differently?  What does power mean?  What units are used to measure power?
  38. 38. + Power Therate at which work is done or energy is transferred  Energy used or work done per second  If we substitute W for Fd then Fd P t
  39. 39. + Power  The unit of power is the joule per second, also known as the watt.  One watt (W) of power is expended when one joule of work is done in one second.  One kilowatt (kW) equals 1000 watts.  One megawatt (MW) equals one million watts.
  40. 40. + Power  SI units for power are J/s.  Calledwatts (W)  Equivalent to kg•m2/s3  Horsepower (hp) is a unit used in the Avoirdupois system.  1.00 hp = 746 W
  41. 41. + Watts  These bulbs all consume different amounts of power.  A 100watt bulb consumes 100 joules of energy every second.
  42. 42. + Example  A 193kg curtain need to be raised 7.5m, at a constant speed, in as close to 5 sec as possible. Unsure which motor would be the best 3 motors were bought. Power ratings are 1.0kW, 3.5kW, and 5.5kW. Which motor is best for the job?  Given:  m= 193kg d= 7.5m t= 5 sec P=??
  43. 43. + Example  P=2895 W or 2.895kW  So the best motor would be the 3.5kW motor
  44. 44. + Classroom Practice Problems  Two horses pull a cart. Each exerts a force of 250.0 N at a speed of 2.0 m/s for 10.0 min.  Calculate the power delivered by the horses.  How much work is done by the two horses?  Answers: 1.0 x 103 W and 6.0 x 105 J
  45. 45. + Now what do you think?  Twocars are identical with one exception. One of the cars has a more powerful engine. How does having more power make the car behave differently?  What does power mean?  What units are used to measure power?

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