9/19/2013. PHY 113 C General Physics I 11 AM-12:15 PM MWF Olin 101

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1 PHY 3 C General Physcs I AM-:5 PM MF Oln 0 Plan or Lecture 8: Chapter 8 -- Conservaton o energy. Potental and knetc energy or conservatve orces. Energy and non-conservatve orces 3. Power PHY 3 C Fall 03-- Lecture 8 PHY 3 C Fall 03-- Lecture 8 Comments on preparaton or next Thursday s exam PHY 3 C Fall 03-- Lecture 8 3

2 Comments on preparaton or next Thursday s exam -- contnued PHY 3 C Fall 03-- Lecture 8 4 Comments on preparaton or next Thursday s exam contnued hat you should bng to the exam (n addton to your well-rested bran): A pencl or pen Your calculator An 8.5 x sheet o paper wth your avote equatons (to be turned n together wth the exam) hat you should NOT use dung the exam Electronc devces (cell phone, laptop, etc.) Your textbook PHY 3 C Fall 03-- Lecture 8 5 F ma dv a dt dr v dt Problem solvng sklls Math sklls Equaton Sheet Advce:. Keep basc concepts and equatons at the top o your head.. Practce problem solvng and math sklls 3. Develop an equaton sheet that you can consult. 8/7/03 PHY 3 A Fall Lecture 6

3 clcker queston hch o the ollowng best descbes your opnon about the equaton sheet: A. I have not prepared my equaton sheet yet but hope to do so soon B. I have a prelmnary equaton sheet but have not used t or dong homework C. I have a prelmnary equaton sheet and have used t or dong homework D. I am dreamng about prepang the equaton sheet, but have not done t yet E. In my opnon, the equaton sheet s not really necessary PHY 3 C Fall 03-- Lecture 8 7 Revew o energy concepts: Denton o work : F dr Denton o knetc energy : K mv PHY 3 C Fall 03-- Lecture 8 8 r ork - knetc energy theorem : F dr mv mv Some questons rom webassgn Assgnment #7 In 990 alter Areulle o Belgum lted a 8.5-kg object through a dstance o 7. cm usng only hs teeth. (a) How much work was done on the object by Areulle n ths lt, assumng the object was lted at constant velocty? T T mg 0 T mg y r T mg F dr T y y y mgy y mg PHY 3 C Fall 03-- Lecture 8 9 3

4 Some questons rom webassgn Assgnment #7 In 990 alter Areulle o Belgum lted a 8.5-kg object through a dstance o 7. cm usng only hs teeth. How much work was done on the object by gravty? T y T mg y r mg F dr mgy y PHY 3 C Fall 03-- Lecture 8 0 Some questons rom webassgn Assgnment #7 hat s the work done as the partcle moves rom x=0 to x=3m? r F dr 3 0 F x xdx 4.5N3m 6.75N PHY 3 C Fall 03-- Lecture 8 Some questons rom webassgn Assgnment #7 -- contnued hat s the work done as the partcle moves rom x=8 to x=0m? r F dr 0 8 F x xdx 3Nm.5N PHY 3 C Fall 03-- Lecture 8 4

5 Some questons rom webassgn Assgnment #7 A 4.34-kg partcle s subject to a net orce that vaes wth poston as shown n the gure. The partcle starts rom rest at x = 0. hat s ts speed at x = 5.00 m? 5 0 F F x dr mv xdx mv 0 mv PHY 3 C Fall 03-- Lecture 8 3 ork and potental energy Denton o work : r re r Denton o potental energy : r rre r F dr F dr Note: It s assumed that F s conservatve PHY 3 C Fall 03-- Lecture 8 4 ork and potental energy -- contnued Denton o potental energy : r re r r rre F dr Example gravty near the surace o the Earth: y y re mg mg r re r ( y) y yre rre r F dr mg y y mg dy' re PHY 3 C Fall 03-- Lecture 8 5 5

6 ork and potental energy or gravty (near Earth s surace) y y mg mg r y re r F dr mgy y Alternatvely : r rre F dr re r ( y) PHY 3 C Fall 03-- Lecture 8 6 rre F dr y yre rre r F dr mg y y mg dy' re r r ork and potental energy contnued Potental energy : r re r r rre F dr r rre F dr rre F dr r r clcker queston hy s there a strange - sgn n the denton o potental energy? A. Physcsts lke to be annoyng B. No reason at all C. There s a somewhat good reason PHY 3 C Fall 03-- Lecture 8 7 ork and potental energy contnued ork - knetc energy theorem : F dr mv mv r rre F dr rre F dr r r For the case that the orce actng on the system s conservatve, we can use the denton o potental energy wth the work-knetc energy theorem Rearrangng : r r K K K K E (contant) PHY 3 C Fall 03-- Lecture 8 8 6

7 Summary o work, potental energy, knetc energy relatonshps ork - knetc energy theorem : F dr mv mv conservatve Rearrangng : dsspatve r r K dsspatve dsspatve K K K dsspatve PHY 3 C Fall 03-- Lecture 8 9 Example A block, ntally at rest at a heght h, sldes down a ctonless nclne. hat s ts nal velocty? h h=0.5m : : v v 0; 0; r mgh; r 0; E mv E mgh PHY 3 C Fall 03-- Lecture 8 0 mv mgh v gh m/s Energy dagram E, K, E (J) K m y y PHY 3 C Fall 03-- Lecture 8 7

8 k Example o spng orce: ( r ) kx x F dr x k x dx and ( r ) kx kx kx PHY 3 C Fall 03-- Lecture 8 E mv kx Energy dagrams Note : Note : when x x max when x 0 : : v 0, E (0) 0, kx mv max kx max PHY 3 C Fall 03-- Lecture 8 3 Example: Model potental energy uncton (x) representng the attracton o two atoms PHY 3 C Fall 03-- Lecture 8 4 8

9 Comment on relatonshp between potental energy and (conservatve) orce: r Potental energy : F dr' In one dmenson : Antdevatve : F r ( x) x re r d dx re x rre x xre F x' dx' PHY 3 C Fall 03-- Lecture 8 5 Example: Mass sldng on ctonless loopng track clcker exercse: In order or the ball completes the loop at A, what must the value o h? A. h=r B. h=r C. h>r D. Not enough normaton. PHY 3 C Fall 03-- Lecture 8 6 Example: Mass sldng on ctonless loopng track E mv mgh 0 E mva mgr A E mgh mv 5 h R Condton or stayng on track at A : va n mg m R 0 mva mgr 5 mgr mgr mgr mgr PHY 3 C Fall 03-- Lecture 8 7 9

10 Another example; rst wthout cton Mass m (=0.kg) sldes hozontally on a ctonless table and s ntally at rest. hat s ts velocty when t moves a dstance Dx=0.m (and m (=0.3kg) alls Dy=0.m)? clcker exercse: hat s the relatonshp o the nal velocty o m and m? A. They are equal B. m s aster than m. C. m s aster than m. PHY 3 C Fall 03-- Lecture 8 8 Another example; rst wthout cton T Mass m (=0.kg) sldes hozontally on a T ctonless table and s ntally at rest. hat s ts velocty when t moves a dstance Dx=0.m (and m (=0.3kg) alls Dy=0.m)? K K m g T ma mgy m m v mgy T mg ma mm mgy y mgdx m m v T g m m m gdx m m v TDx gdx m m m m PHY 3 C Fall 03-- Lecture 8 9 Another example; now wth cton T Mass m (=0.kg) sldes hozontally on a table wth T knetc cton and s ntally at rest. hat s ts velocty when t moves a dstance Dx=0.m (and m (=0.3kg) alls Dy=0.m)? m g PHY 3 C Fall 03-- Lecture

11 v K m m v m gy m gy m gdx m m v m gdx m gdx K mg kmg Dx m m dsspatve k k PHY 3 C Fall 03-- Lecture 8 3 clcker exercse: Assume a mass m starts at rest at A and moves on the ctonless surace as shown. At what poston s the speed the largest? A. A B. B C. C D. none o these. PHY 3 C Fall 03-- Lecture 8 3 Power Dened as tme rate o change o P Note that : d dt d F dr d dr F F v dt dt (Joules) nts : P att (s) work : PHY 3 C Fall 03-- Lecture 8 33

12 Power exerted by motor : For P 4 T 0 N, P d F v Tv dt v 3m / s N 3 m / s 60 atts PHY 3 C Fall 03-- Lecture 8 34