Conservation of Energy

Transcription

1 Add Iportant Conervation of Energy Page: 340 Note/Cue Here NGSS Standard: HS-PS3- Conervation of Energy MA Curriculu Fraework (006):.,.,.3 AP Phyic Learning Objective: 3.E.., 3.E.., 3.E..3, 3.E..4, 4.C.., 4.C.., 4.C.., 5.A.., 5.B.., 5.B.., 5.B.., 5.B.3., 5.B.3., 5.B.3.3, 5.B.4., 5.B.5.4, 5.B.5.5, 5.D.3. Knowledge/Undertanding Goal: Skill: conervation of energy work-energy theore olve proble involving converion of energy between one for and another Language Objective: Accurately decribe and apply the concept decribed in thi ection uing appropriate acadeic language. Set up and olve word proble involving the conervation of energy. Lab, Activitie & Deontration: Note: Golf ball loop-the-loop. Marble raceway. Bowling ball pendulu. In a cloed yte (eaning a yte in which there i no exchange of atter or energy between the yte and the urrounding), the total energy i contant. Energy can be converted fro one for to another. When thi happen, the increae in any one for of energy i the reult of a correponding decreae in another for of energy. Ue thi pace for uary and/or additional note. AP Phyic : Algebra-Baed

2 Add Iportant Conervation of Energy Page: 34 Note/Cue Here In a yte that ha potential energy, kinetic energy and heat, the total energy i given by: U K Q E total In the following diagra, uppoe that the girl drop a ball with a a of kg fro a height of 3. Before the girl let go of the ball, it ha 60 J of potential energy. A the ball fall to the ground, potential energy i gradually converted to kinetic energy. The potential energy continuouly decreae and the kinetic energy continuouly increae, but the total energy i alway 60 J. After the ball hit the ground, 60 N of work wa done by gravity, and the 60 J of kinetic energy i converted to other for, uch a theral energy (the teperature of the ball and the ground increae infiniteially), ound, etc. Ue thi pace for uary and/or additional note. AP Phyic : Algebra-Baed

3 Add Iportant Conervation of Energy Page: 34 Note/Cue Here Work-Energy Theore We have already een that work i the action of a force applied over a ditance. A broader and ore ueful definition i that work i the change in the energy of an object or yte. If we think of a yte a having iaginary boundarie, then work i the flow of energy acro thoe boundarie, either into or out of the yte. For a yte that ha only echanical energy, work change the aount of potential and/or kinetic energy in the yte. W K U Although work i a calar quantity, we ue a poitive nuber for work coing into the yte ( work i done on the yte ), and a negative nuber for work going out of the yte ( the yte doe work on it urrounding ). Note that the unit for work and energy newton-eter and joule are equivalent. J N kg Work-energy theore proble will give you inforation related to the gravitational potential and/or kinetic energy of an object (uch a it a and a change in velocity) and ak you how uch work wa done. A iple rule of thub (eaning that it i not alway trictly true) i: Potential energy i energy in the future (energy that i available for ue). Kinetic energy i energy in the preent (the energy of an object that i currently in otion). Work i the reult of energy in the pat (the reult of potential kinetic energy having acted on an object). Ue thi pace for uary and/or additional note. AP Phyic : Algebra-Baed

4 Add Iportant Conervation of Energy Page: 343 Note/Cue Here Solving Conervation of Energy Proble Conervation of energy proble involve recognizing that energy i changing fro one for to another. Once you have figured out what i being converted, calculate the aount energy that i converted, and ue the equation for the new for to calculate the deired quantity. In echanic, conervation of energy proble uually involve work, gravitational potential energy, and kinetic energy: W F d Fdco ( Fdif force& diplacee ntarei nthe aedi recti on) U g K gh v There are two coon type of conervation of energy proble: One type give you the energy at the tart, and you have to calculate the deired quantity (uch a velocity or height) fro the energy after the converion. Energy of one type = Energy of another type Equation for firt type = Equation for econd type The econd type require you to calculate the ae type of energy at two different tie or location. You have to ue the difference to calculate the deired quantity (uch a velocity or height). Energy after Energy before = Energy Change Energy change of one type = Energy change of another type or work done Ue thi pace for uary and/or additional note. AP Phyic : Algebra-Baed

5 Add Iportant Conervation of Energy Page: 344 Note/Cue Here Energy Bar Chart A ueful way to repreent conervation of energy i through bar graph that repreent kinetic energy (KE), gravitational potential energy (PE), and total echanical energy (TME). (We ue the ter chart rather than graph becaue the cale i arbitrary and the chart i not eant to be ued quantitatively.) The following i an energy bar chart for a roller coater, tarting fro point A and traveling through point B, C, D, and E. Notice, in thi exaple, that:. The total echanical energy alway reain the ae. (Thi i often the cae in conervation of energy proble.). KE i zero at point A becaue the roller coater i not oving. All of the energy i PE, o PE = TME. 3. PE i zero at point D becaue the roller coater i at it lowet point. All of the energy i KE, o KE = TME. 4. At all point (including point A and D), KE + PE = TME It can be helpful to ketch energy bar chart repreenting the different point in coplicated conervation of energy proble. If energy i being added to or reoved fro the yte, add an Energy Flow diagra to how energy that i being added to or reoved fro the yte. Ue thi pace for uary and/or additional note. AP Phyic : Algebra-Baed

6 Add Iportant Conervation of Energy Page: 345 Note/Cue Here Saple Proble Q: An 875 kg car accelerate fro to 44. a. Draw an energy bar chart repreenting the initial and final energie and the flow of energy into or out of the yte. Notice that: KE = TME, both before and after. There i no gravitational potential energy decribed in the proble. TME i greater at the end than at the beginning, which ean energy ut have been added to the yte. Thi i repreented by the flow of three unit of energy into the yte. (The flow of energy into or out of a yte i work.) b. What were the actual initial and final kinetic energie of the car? K i K f v (875kg)( ) 750 J v (875kg)(44 ) J (Becaue kinetic energy i proportional to v, notice that doubling the velocity reulted in four tie a uch kinetic energy.) c. How uch work did the engine do to accelerate it? W ΔK J 750 J J 63550N The engine did N of work. Ue thi pace for uary and/or additional note. AP Phyic : Algebra-Baed

7 Add Iportant Conervation of Energy Page: 346 Note/Cue Here Q: An 80 kg phyic tudent fall off the roof of a 5 high chool building. How uch kinetic energy doe he have jut before he hit the ground? What i hi final velocity? A: There are two approache to anwer thi quetion.. Recognize that the tudent potential energy at the top of the building i entirely converted to kinetic energy jut before he hit the ground. Calculate hi potential energy at the top of the building, and that will be hi kinetic energy when he hit the ground. U gh (80kg)(0 )(5) 000 J We can now plug 000 J into the forula for kinetic energy and olve for velocity: K 000 ( )(80) v v 40 v v Ue thi pace for uary and/or additional note. AP Phyic : Algebra-Baed

8 Add Iportant Conervation of Energy Page: 347 Note/Cue Here. Ue otion equation to find the tudent velocity when he hit the ground, baed on the height of the building and acceleration due to gravity. Then ue the forula K v. d 5 t 3 t v at (0 v (0 K K K at ) t 3.73 v (80 kg)( J )(.73) 7.3 ) Ue thi pace for uary and/or additional note. AP Phyic : Algebra-Baed

9 Add Iportant Conervation of Energy Page: 348 Note/Cue Here Hoework Proble. A 0.00 kg odel rocket i oberved to rie 00. above the ground after launch. If no additional thrut wa applied to the rocket after launch, what wa it launch peed at the ground? Anwer: A 70. kg pole vaulter convert the kinetic energy of running at ground level into the potential energy needed to clear the crobar at a height of 4.0 above the ground. What i the iniu velocity that the pole vaulter ut have when taking off fro the ground in order to clear the bar? Anwer: 8.9 Ue thi pace for uary and/or additional note. AP Phyic : Algebra-Baed

10 Add Iportant Conervation of Energy Page: 349 Note/Cue Here 3. A 500. kg roller coater car i launched, fro ground level, at 0.. Neglecting friction, how fat will it be oving when it reache the top of a loop, which i 5 above the ground? Anwer: 0 4. A roller coater car with a i launched, fro ground level with a velocity of v o. Neglecting friction, how fat will it be oving when it reache the top of a loop, which a ditance of h above the ground? (You ay ue your work fro proble #3 above to guide your algebra.) Anwer: v o gh Ue thi pace for uary and/or additional note. AP Phyic : Algebra-Baed

11 Add Iportant Conervation of Energy Page: 350 Note/Cue Here 5. A 0.0 kg onkey wing on a vine fro a point which i 40.0 above the jungle floor to a point which i 5.0 above the floor. If the onkey wa oving at.0 initially, what will be it velocity at the 5.0 point? Anwer:.4 Ue thi pace for uary and/or additional note. AP Phyic : Algebra-Baed