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Work, Energy & Power IB Physics There are many different TYPES of Energy. Energy is expressed in JOULES (J) 4.19 J = 1 calorie Energy can be expressed more specifically by using the term WORK(W) Work = Force x Displacement if you apply a force on an object and it covers a displacement you have supplied ENERGY or done WORK on that object. Force must be parallel to displacement W F x Fx cos F and x MUST be parallel. To ensure that they are parallel we add the cosine on the end. FORCE Displacement W F x Fx cos 0 ; cos 0 1 W Fx Work W F x Fx cos FORCE Displacement W F x Fx cos 180 ; cos180 1 W Ff x Work W F x Fx cos FORCE Displacement W F x Fx cos 90 ; cos 90 0 W 0J Work W F x Fx cos the woman is applying a force at an angle. Only the HORIZONTAL COMPONENT actually causes the box to move and thus imparts energy to the box. The vertical component (FsinQ) does NO work on the box because it is NOT parallel to the displacement. The Work Energy Theorem WORK-ENERGY THEOREM says that if we do work on an object it will undergo a CHANGE in speed and thus a change in KINETIC ENERGY. Since both WORK and KINETIC ENERGY are expressed in JOULES, they are EQUIVALENT TERMS! " The net WORK done on an object is equal to the change in kinetic energy of the object." Work-Energy Theorem Due to friction, energy is transferred both into the floor and into the tire when the bicycle skids to a stop. a. An infrared camera reveals the heated tire track on the floor. b. The warmth of the tire is also revealed. Work-Energy Theorem Typical stopping distances for cars equipped with antilock brakes traveling at various speeds. The work done to stop the car is friction force × distance of slide. Example Suppose the woman in the figure above applies a 50 N force to a 25-kg box at an angle of 30 degrees above the horizontal. She manages to pull the box 5 meters. a) Calculate the WORK done by the woman on the box b) The speed of the box after 5 meters if the box started from rest. W Fx cos W (50)(5) cos 30 216.5 J W KE 1 mv 2 2 W 1 (25)v 2 2 v 4.16 m/s Force – displacement graphs F If the applied force on a body varies, the total work done can still be found: F x x Total work done = area under a force-displacement graph. E.g. Extending springs We know that a spring obeys Hooke’s law, i.e. its extension, x is proportional to the force applied, F: As the spring extends the applied force must increase to a maximum value, F: F Average force applied = ½F x Work done on spring = ½Fx (This can also be seen from the area under the graph) Energy stored in spring = ½Fx Lifting mass at a constant speed Suppose you lift a mass upward at a constant speed, v = 0 & K=0. What does the work equal now? Since you are lifting at a constant speed, your APPLIED FORCE equals the WEIGHT of the object you are lifting. Since you are lifting you are raising the object a certain “y” displacement or height above the ground. When you lift an object above the ground it is said to have POTENTIAL ENERGY Potential Energy W Fx cos F mg; x h 0, cos 0 1 W mgh PE h mg Since this man is lifting the package upward at a CONSTANT SPEED, the kinetic energy is NOT CHANGING. Therefore the work that he does goes into what is called the ENERGY OF POSITION or POTENTIAL ENERGY. All potential energy is considering to be energy that is STORED! Potential Energy The man shown lifts a 10 kg package 2 meters above the ground. What is the potential energy given to the package by the man? PE mgh h PE (10)(9.8)( 2) 196 J Suppose you throw a ball upward W KE PE What does work while it is flying through the air? GRAVITY Is the CHANGE in kinetic energy POSITIVE or NEGATIVE? NEGATIVE KE PE ( KE KEo ) PE PEo KE KEo PE PEo KEo PEo KE PE Is the CHANGE in potential energy POSITIVE or NEGATIVE? POSITIVE Energy Before Energy After Potential Energy The potential energy of the 100-N boulder with respect to the ground below is 200 J in each case. a. The boulder is lifted with 100 N of force. Potential Energy The potential energy of the 100-N boulder with respect to the ground below is 200 J in each case. a. The boulder is lifted with 100 N of force. b. The boulder is pushed up the 4-m incline with 50 N of force. Potential Energy The potential energy of the 100-N boulder with respect to the ground below is 200 J in each case. a. The boulder is lifted with 100 N of force. b. The boulder is pushed up the 4-m incline with 50 N of force. c. The boulder is lifted with 100 N of force up each 0.5-m stair. ENERGY IS CONSERVED The law of conservation of mechanical energy states: Energy cannot be created or destroyed, only transformed! Energy Before Energy After Am I moving? If yes, Ko Am I moving? If yes, K Am I above the ground? If yes, Uo Am I above the ground? If yes, U Conservation of Energy A B C D In Figure A, a pendulum In Figure B, is a pendulum In Figure C, is astill pendulum In Figure D, is the at the pendulum has released from above rest at the some ground height ground position, position yet reached and it is moving the same with a height above above the ground alsoposition. moving. maximum velocity. the ground position as A. It has only potential It has energy. BOTH potential It has only energy kinetic Itand has energy. only potential energy. kinetic energy. Conservation of Energy Part of the PE of the wound spring changes into KE. The remaining PE goes into heating the machinery and the surroundings due to friction. No energy is lost. Conservation of Energy When the woman leaps from the burning building, the sum of her PE and KE remains constant at each successive position all the way down to the ground. Energy consistently changes forms ME = PE + KE Energy consistently changes forms Am I above the ground? NO, h = 0, U = 0 J Am I moving? Yes, v = 8 m/s, m = 60 kg K 1 mv 2 1 (60)(8)2 2 2 K 1920 J Position m v U K ME (= U+K) 1 60 kg 8 m/s 0J 1920 J 1920 J Energy consistently changes forms Energy Before = Energy After KO =U+K 1920= (60)(9.8)(1) + (.5)(60)v2 1920= 588 + 30v2 1332 = 30v2 44.4 = v2 v = 6.66 m/s Position m v U 1 60 kg 2 60 kg 8 m/s 0J 6.66 m/s 588 J K ME 1920 J 1332 J 1920 J 1920 J Energy consistently changes forms Am I moving at the top? EB = Using Ko 1920 1920 h No, v = 0 m/s EA position 1 = U = mgh =(60)(9.8)h = 3.27 m Position m v U K ME 1 60 kg 8 m/s 0J 1920 J 1920 J 2 60 kg 6.66 m/s 588 J 1332 J 1920 J 3 60 kg 0 m/s 1920 J 0J 1920 J Power One useful application of Energy is to determine the RATE at which we store or use it. We call this application POWER! As we use this new application, we have to keep in mind all the different kinds of substitutions we can make. Unit = WATT or Horsepower Important formulas and units Quantity Force Work Energy Power Definition mass x accel. force x distance power x time work / time Units newtons joules joules watts Assessment Questions 1. Raising an auto in a service station requires work. Raising it twice as high requires a. half as much work. b. the same work. c. twice the work. d. four times the work. Assessment Questions 1. Raising an auto in a service station requires work. Raising it twice as high requires a. half as much work. b. the same work. c. twice the work. d. four times the work. Answer: C Assessment Questions 2. Raising an auto in a service station requires work. Raising it in half the time requires a. half the power. b. the same power. c. twice the power. d. four times the power. Assessment Questions 2. Raising an auto in a service station requires work. Raising it in half the time requires a. half the power. b. the same power. c. twice the power. d. four times the power. Answer: C Assessment Questions 3. The energy due to the position of something or the energy due to motion is called a. potential energy. b. kinetic energy. c. mechanical energy. d. conservation of energy. Assessment Questions 3. The energy due to the position of something or the energy due to motion is called a. potential energy. b. kinetic energy. c. mechanical energy. d. conservation of energy. Answer: C Assessment Questions 4. After you place a book on a high shelf, we say the book has increased a. elastic potential energy. b. chemical energy. c. kinetic energy. d. gravitational potential energy. Assessment Questions 4. After you place a book on a high shelf, we say the book has increased a. elastic potential energy. b. chemical energy. c. kinetic energy. d. gravitational potential energy. Answer: D Assessment Questions 5. An empty truck traveling at 10 km/h has kinetic energy. How much kinetic energy does it have when it is loaded so its mass is twice, and its speed is increased to twice? a. the same KE b. twice the KE c. four times the KE d. more than four times the KE Assessment Questions 5. An empty truck traveling at 10 km/h has kinetic energy. How much kinetic energy does it have when it is loaded so its mass is twice, and its speed is increased to twice? a. the same KE b. twice the KE c. four times the KE d. more than four times the KE Answer: D Assessment Questions 6. Which of the following equations is most useful for solving a problem that asks for the distance a fast-moving crate slides across a factory floor in coming to a stop? a. F = ma b. Ft = ∆mv c. KE = 1/2mv2 d. Fd = ∆1/2mv2 Assessment Questions 6. Which of the following equations is most useful for solving a problem that asks for the distance a fast-moving crate slides across a factory floor in coming to a stop? a. F = ma b. Ft = ∆mv c. KE = 1/2mv2 d. Fd = ∆1/2mv2 Answer: D Assessment Questions 7. A boulder at the top of a vertical cliff has a potential energy of 100 MJ relative to the ground below. It rolls off the cliff. When it is halfway to the ground its kinetic energy is a. the same as its potential energy at that point. b. negligible. c. about 60 MJ. d. more than 60 MJ. Assessment Questions 7. A boulder at the top of a vertical cliff has a potential energy of 100 MJ relative to the ground below. It rolls off the cliff. When it is halfway to the ground its kinetic energy is a. the same as its potential energy at that point. b. negligible. c. about 60 MJ. d. more than 60 MJ. Answer: A Assessment Questions 8. In an ideal pulley system, a woman lifts a 100-N crate by pulling a rope downward with a force of 25 N. For every 1-meter length of rope she pulls downward, the crate rises a. 25 centimeters. b. 45 centimeters. c. 50 centimeters. d. 100 centimeters. Assessment Questions 8. In an ideal pulley system, a woman lifts a 100-N crate by pulling a rope downward with a force of 25 N. For every 1-meter length of rope she pulls downward, the crate rises a. 25 centimeters. b. 45 centimeters. c. 50 centimeters. d. 100 centimeters. Answer: A Assessment Questions 9. When 100 J are put into a device that puts out 40 J, the efficiency of the device is a. 40%. b. 50%. c. 60%. d. 140%. Assessment Questions 9. When 100 J are put into a device that puts out 40 J, the efficiency of the device is a. 40%. b. 50%. c. 60%. d. 140%. Answer: A Assessment Questions 10. An energy supply is needed for the operation of a(n) a. automobile. b. living cell. c. machine. d. all of these Assessment Questions 10. An energy supply is needed for the operation of a(n) a. automobile. b. living cell. c. machine. d. all of these Answer: D Assessment Questions 11. The main sources of energy on Earth are a. solar and nuclear. b. gasoline and fuel cells. c. wind and tidal. d. potential energy and kinetic energy. Assessment Questions 11. The main sources of energy on Earth are a. solar and nuclear. b. gasoline and fuel cells. c. wind and tidal. d. potential energy and kinetic energy. Answer: A