Stuff you asked about:

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1 Stuff you asked about: you dawings ae slowly becoming bette Why does wok need to be defined as the integal of the dot poduct of the foce and displacement? Why can't wok just be defined as foce * displacement? Postponing the due dates fo the past homewok has helped me find new and exciting ways to slack off. If you move the apple up to a highe shelf, wouldn't you need to still do wok on the apple because its potential enegy is inceasing? Eithe I'm missing something o my high school physics teache lied to me about enegy A physics student was hit by a bick falling fom a house. He fainted, but came to afte a while and stated smiling. The onlookes wee woied, so they asked him why the smile. "I just ealized how lucky I am because the kinetic enegy is only half m v squaed. Physics is a weid cicumnavigating element of pue supise. Wok is a vecto quantity? So the sign is detemined by its diection on the axes? Please define the concept of wok and why it only takes into account kinetic enegy. Also, how much of the calculus fom the pelectue ae we expected to know? I have poblems detemining when the foce is negative o positive as an object moves upwads. Could you please elaboate on the oientation of foces. Also is the Total Wok done= Total mechanical enegy + Heat

2 Seems like we'e getting into the hade stuff, we neve went anywhee nea deiving these equations in high school, they wee just handed to us. You ae old enough & smat enough to see whee the fomulas come fom now.

3 Simply, it took me ove 4 hous to do the last SmatPhysics homewok because of the absolute death of adequate o applicable examples. *I lean by example.* Having just a few choice examples available to me could have cut that homewok time down damatically We have office hous all day Sunday & Monday in 147 Loomis. Having someone explain a poblem to you afte you have stuggled with it is an excellent way to lean. Look at pactice exams. This is also a geat way to study fo the test in 2 weeks. Fist midtem is on Wednesday Oct 3 d at 7pm (see Syllabus) We will give a conflict exam at 5:15 pm the same day. You will be able to sign up fo this in you gade book. If you have a double conflict please talk to me.

4 Today s Concepts: Wok & Kinetic Enegy Physics 211 Lectue 7

5 Wok-Kinetic Enegy Theoem 2 W F dl 1 Integals ae a little scay, but the concepts themselves don't seem to difficult.! The integal IS the concept!!

6 Wok-Kinetic Enegy Theoem The wok done by foce F as it acts on an object that moves between positions 1 and 2 is equal to the change in the object s kinetic enegy: W TOT K 2 W F dl TOT NET 1 K 1 2 m v 2 Doesn't wok-kinetic enegy theoem have anything to do with potential enegy?."

7 Clicke Question W K Does the wok-kinetic enegy theoem have anything to do with potential enegy? A) YES B) NO

8 The Dot Poduct Let's talk about what diection and sign Wok has

9 Wok-Kinetic Enegy Theoem: 1-D Example If the foce is constant and the diections aen t changing then this is vey simple to evaluate: ca F d In this case 2 W F dl F d 1 = Fd since cos(0)=1 This is pobably what you emembe fom High School.

10 Clicke Question A lighte ca and a heavie van, each initially at est, ae pushed with the same constant foce F. Afte both vehicles tavel a distance d, which of the following statements is tue? (Ignoe fiction) ca F d W= Fd same van F d K= W Same too A) They will have the same velocity B) They will have the same kinetic enegy C) They will have the same momentum

11 2 1 F dl K Deivation not so impotant Concept vey impotant A foce pushing ove some distance will change the kinetic enegy. 2 1 F dl K q 2 W F dl 1

12 Wok done by gavity nea the Eath s suface mg

13 Wok done by gavity nea the Eath s suface W W W... W TOT 1 2 N m g dl m g dl... m g dl 1 2 N dl N dl 1 mg dl 2 dl 1 dy 1 dx 1 mg

14 Wok done by gavity nea the Eath s suface W W W... W TOT 1 2 m g dl m g dl... m g dl 1 2 N mgdy mgdy... mgdy 1 2 N m g y N dl 1 dl N y mg dl 2 W mg ( y y ) g final initial

15 d dq d F g 2 W F ( ) d GM m e 2 d GM m e G M m e 2 1

16 Close to the Eath s suface: 1 ~ 2 ~ R e : 1 1 W G M m g e G M m e GM m e R e mg -y So: W g = -mgy

17 Wok-Kinetic Enegy Theoem If thee ae seveal foces acting then W is the wok done by the net (total) foce: W NET K W W You can just add up the wok done by each foce W NET W TOT

18 Checkpoint Thee objects having the same mass begin at the same height, and all move down the same vetical distance H. One falls staight down, one slides down a fictionless inclined plane, and one swings on the end of a sting. H Fee Fall Fictionless incline Sting In which case does the object have the biggest net wok done on it by all foces duing its motion? A) Fee Fall B) Incline C) Sting D) All the same

19 Clicke Question Thee objects having the same mass begin at the same height, and all move down the same vetical distance H. One falls staight down, one slides down a fictionless inclined plane, and one swings on the end of a sting. What is the elationship between thei speeds when they each the bottom? H Fee Fall Fictionless incline Sting A) v f > v i > v p B) v f > v p > v i C) v f = v p = v i I still don't buy that dopping a ball in fee fall and dopping a ball on a fictionless amp will be the same. What if the amp is eally long?

20 Checkpoint A ca dives up a hill with constant speed. Which statement best descibes the total wok W TOT done on the ca by all foces as it moves up the hill? A) W TOT > 0 B) W TOT = 0 C) W TOT < 0 Less that 50% got this ight

21 Clicke Question A ca dives up a hill with constant speed. How does the kinetic enegy of the ca change as it moves up the hill? A) It inceases B) It stays the same C) It deceases

22 Clicke Question A ca dives up a hill with constant speed. The acceleation of the ca: A) Points up the hill B) Points down the hill C) Is zeo

23 Clicke Question A ca dives up a hill with constant speed. The net foce on the ca: A) Points up the hill B) Points down the hill C) Is zeo

24 Reminde We know two expessions that involve W TOT W TOT K 2 W F dl TOT NET 1

25 Checkpoint A ca dives up a hill with constant speed. Which statement best descibes the total wok W TOT done on the ca by all foces as it moves up the hill? A) W TOT > 0 B) W TOT = 0 C) W TOT < 0 TOT A) Velocity and displacement ae in the same diection.. B) Constant speed means no acceleation, means no net foce Means no wok done C) mg is pointing downwad and the ca is moving upwad...

26 Spell out the impotant details, like fom which efeence fame you ae asking fom, o which diection is positive. Seiously you should know bette. And futhemoe, I eject you apple example. You say that net wok done is zeo because change in kinetic enegy is zeo, but you neglect to include wok done against gavity, which you then mention in the next slide Hand does positive wok. Gavity does negative wok. The sum of these is zeo since W tot = W hand + W gavity = K = 0

27 Checkpoint A box sits on the hoizontal bed of a moving tuck. Static fiction between the box and the tuck keeps the box fom sliding aound as the tuck dives. a S The wok done on the box by the static fictional foce as the tuck moves a distance D is: Less that 60% got this ight A) Positive B) Negative C) Zeo That tuck looks awfully familia...

28 Fom Last Lectue A box sits on the hoizontal bed of a moving tuck. Static fiction between the box and the tuck keeps the box fom sliding aound as the tuck dives. a S If the tuck moves with constant acceleating to the left as shown, which of the following diagams best descibes the static fictional foce acting on the box: A B C

29 Checkpoint a F S D The wok done on the box by the static fictional foce as the tuck moves a distance D is: A) Positive B) Zeo C) Negative A) The diection of the static foce is the same as the diection of the moving of the object.. B) the box is not moving with elation to the tuck C) fictional foces always against the motion which esult negative diection

30 Wok done by a Sping

31 Can you claify the diections of positive o negativity fo spings when they ae compessing and uncompessing? Use the fomula to get the magnitude of the wok Use a pictue to get the sign (look at diections) In this example the sping does negative wok since F and x ae in opposite diection. The axes don t matte.