Download presentation

Presentation is loading. Please wait.

Published byTobias Nadler Modified over 3 years ago

1
Thursday Dec 12th, 2013 Test Asst: (a) Guided Notes on work, power, and energy pp: , pp

2
**Friday Dec 13th Turn in stuff…**

momentum HW packet Experiment Write-ups New 2-dim HW problem (Name & Date!!) ______________________________ Organize binders: J & p old now. (Next binder check will be ___________) Lecture notes Asst: parts A and B on asst sheet READ THE HINTS!! Check your answers!!

3
**Work, Energy, Power Note – this unit looks VERY similar to the last unit:**

In that unit you had 2 basics equations: (1) J = F t = p, or if the impulse was zero (as it is in a closed & isolated system), then: (2) p initial total = p final total So now, just like the impulse-momentum theorem, we have the work-energy theorem: (3) W = F d = E And just like we had the conservation of momentum in a closed & isolated system, we now have the conservation of energy when the net work done is zero: (4) E initial total = E final total So, you will have both of those types of math-problems to solve on the test, as well as many conceptual problems again. (But note things are slightly more complicated this time, as the F d, written & pronounced “F dot d” is a special type of multiplication, and there is more than one type of energy!)

4
**W = F d = E Let’s talk about just the middle part of that equation…**

It is NOT normal multiplication; It is said as “Work equals F dot d”, where d is displacement. The “dot” means that only that component of the force that is in the direction of the displacement can be used when calculating work. This means that 90% of the time, W = F d = F d cos . But in a few problems, if a weird angle is given to you, it MIGHT be a sine, so be careful! Similarly, if the force and displacement are in opposite directions, the work will be negative. If the force and displacement are perpendicular, the work will be zero. examples: slide a book along the floor & carry a book ... The unit for work is the Joule [J]. Friction does negative work because force and displacement are opposite direction. Carrying something is zero work because your force and the books displacement are perpendicular.

5
P = W / t = F v In the high school textbook, it is most common to use P = W / t, but there are a few problems that require P = F v (The third part comes from making W = F d and then dividing by time.) It is said as “Power is F dot v”, where v is velocity. The “dot” means that only that component of the force that is in the direction of the velocity can be used when calculating power. Similarly, if the force and velocity are in opposite directions, the power will be negative. If the force and velocity are perpendicular, the power will be zero. The unit for power is the Watt [W].

6
**Start your HW…. Parts A & B on sheet**

OOPS! 2.0 x 103 W

7
**Monday Dec 16 Warm-Up / Pop Quiz on “ Work” Questions on HW**

Go over Guided Notes (up to #23) in red pen Quick Lecture notes on … Asst: parts C and D (but cross out #69, answer to #75b = 89 m) on asst sheet

8
W = F d = E …revisited: NOTE – the textbook is WRONG here. It says Work equals the change in kinetic energy, but Work is really the change in over-all energy. High school problems are sometimes: W = F d = KE = KEF – KEI = ½mvF2 ½mvI2 BUT, sometimes those problems are instead: W = F d = PE = PEF – PEI = mghF mghI Work done: Why? Energy change? Simple Examples: + F & d same dir increase Pull or push something (even at an angle) … increases KE Raise or lift something … increases PE F & d opp dir decrease Friction … decreases KE Lower something … decreases PE F & d are perpend; or no net force by anything other than gravity none overall/total You carry something … energy stays constant Something falls … energy is conserved: PE → KE Something rises … energy is cons: KE → PE **Let’s talk about throwing or dropping things: YOU do no work after the release!

9
**There are other types of energy than those listed in the last slide:**

KE and PE are both types of what we call “mechanical energy”, which is the only type of energy we physicists care about. There is also the potential energy of a spring, which is a type of mechanical energy too, but that high school textbooks don’t talk about much. There are other types of non-mechanical energies, such as chemical energy, heat or thermal energy, light energy, sound energy, etc. Fact: The TOTAL amount of energy in the universe is a constant. Confusion: We say in the W-E equation, that Energy could either increase or decrease. Understand: Physicists speak only about mechanical energy. When they say “energy is not conserved (because work was done)” what they really mean, but are too lazy to say, is “mechanical energy is not conserved (because work was done), and it was changed into or came from other types such as chemical, thermal, light or sound energy.” (You see how much harder that is to say? Physicists are inherently lazy!) We lie here for a few months; in June we’ll talk about the conservation of mass-energy in nuclear reactions.

10
**Work, Energy, Power continued...**

KE = ½mv2 PE = mgh Kinetic energy has the symbol KE Gravitational potential energy has the symbol PE Both are also measured in Joules [J].

11
**HERE ARE THE EQUATIONS YOU NEED ONE MORE TIME:**

W = F d = E E initial total = E final total P = W / t = F v ( PE = mgh & KE = ½ mv2 ) Specifically: (a) W = F d = ½mvF2 ½mvI2 Or (b) W = F d = mghF mghI

12
**Start your HW…. Parts C & D on sheet**

54) actually = 130,000 J Start your HW…. Parts C & D on sheet

13
**Tuesday Dec 17 Questions on last nights HW?**

Turn in ….. Go over more Guided Notes (#24-31) Quick Lecture Notes: Conservation of energy problems (HW part E -next slide) “15-story problem” (HW part F – 3rd next slide) Bill Nye “Energy” ASST: parts E and F on asst sheet

14
**E initial total = E final total**

This is a statement of the conservation of energy. If net Work done = 0, then by the equations in previous slides, Etotal also equals zero. Since Etotal = E final total E initial total = 0, then we will write E initial total = E final total on top of all of our HW problems that use the conservation of energy. For high-school problems, that means we have: (PEinitial + KEinitial) = (PEfinal + KEfinal) Usually in high-school problems either the KEinitial & PEfinal are both zero (when an object is falling), or the PEinitial & KEfinal are both zero (when an object is being thrown up) So you can usually set up problems as: PEinitial + 0 = 0 + KEfinal, i.e.: PEinitial = KEfinal when falling, or 0 + KEinitial = PEfinal + 0, i.e.: KEinitial = PEfinal when rising

15
**HW tonight parts E & F Part E has good hints, its part F we want**

to talk about next …. (see next slide)

16
**Get out your HW paper, and we’ll do a few rows together …**

A 6-kg squirrel is dropped from the top of a 15-story building. At the top of each floor, find the following. (Assume each story is 3.5 meters high.) Floor Height (m) PE (J) TOTAL Energy (J) KE vel (m/s) floor x 3.5 = mgh energy is conserved T - PE KE = ½ mv2 15 14 13 ..... 1 Get out your HW paper, and we’ll do a few rows together …

17
**Wednesday Dec 18 Go over more Guided Notes (#32-34)**

Moved to later day Lecture notes on Collisions Asst: Elastic collisions #1-6 TWO different ways: (b) as stated – they BOUNCE & are perfectly “elastic” (a) NOT as stated, but the two things STICK together after the collision as they did in the last unit; called “inelastic”. (but only do this way for #’s 1&2, 5&6)

18
**Elastic & inelastic collisions:**

**ALL collisions – elastic & inelastic – conserve momentum. **Elastic collisions also conserve (mechanical) energy. **Inelastic collisions don’t conserve (mechanical) energy. (Energy goes in through chemicals or springs; energy comes out through heat and sound) IT is a FACT that the total amount of energy in universe stays same. (Conservation of Energy you learned about in Chem class.) So, for elastic & inelastic, we physicists actually mean MECHANICAL energy - just PE + KE. (That’s why I put the parentheses around “mechanical” up above, because its true, but physicists are often lazy and don’t say it specifically.) In inelastic collisions the chemicals, springs, heat & sound are just OTHER forms of energy. So energy DOES stay constant in the whole universe total. So even inelastic collisions conserve energy, just not the mechanical types we are talking about / care about in this unit, and are really the most important types in Physics. **Elastic collisions are usually “bouncing” collisions, inelastic are usually explosions or “sticking” collisions.

19
**(**old way from last chapter)**

Example: A 3.2-kg block is traveling EAST with a speed of 11 m/s. It collides with a 4.8-kg block traveling WEST at 5.0 m/s. What will be the speeds of these two blocks after the collision if it is perfectly/completely (in)/elastic? First, let’s do this the old way (stick/inelastic) with chapter 9 conservation of momentum stuff only, where most collisions stuck together: (**old way from last chapter) p I total = p F total: m1v1I + m2v2I = (m1 + m2)vF (3.2 kg * 11 m/s) + (4.8 kg * 5.0 m/s) = ( kg)*vfinal Solve for vfinal = ... .... = 1.4 m/s

20
**pI total = pF total: m1v1I + m2v2I = m1v1F + m2v2F **

Example: A 3.2-kg block is traveling EAST with a speed of 11 m/s. It collides with a 4.8-kg block traveling WEST at 5.0 m/s. What will be the speeds of these two blocks after the collision if it is perfectly elastic? Now, we do it with the new way where they bounce and the collision is “completely elastic” as the new instructions say: (**new way part 1) pI total = pF total: m1v1I + m2v2I = m1v1F + m2v2F (3.2 kg * 11 m/s) + (4.8 kg *5.0 m/s) = (3.2 kg * v1F) + (4.8 kg * v2F) “elastic” means energy is also conserved. But remember, when a physicist says energy, they usually mean “mechanical energy”, so we mean PE + KE. But, collisions usually always all happen on the same level/height, so the PE all stays at the same level, which we’ll deem our reference level, which we can just call zero. Thus, what we really mean for an elastic collision is: (**new way part 2) KEI total = KEF total: ½m1v1I2 + ½m2v2I2 = ½m1v1F2 + ½m2v2F2 (½ * 3.2 * 112) + (½ * 4.8 *(-5.0)2) = (½ * 3.2 * v1F2) + (½ * 4.8 * v2F2)

21
**(only use 1 parenthesis when doing this, and simplify NOTHING!!!)**

Of the 3 algebraic methods we talked about to solve eqs, substitution is messy (very!) and we can’t use matrices because these are not both equations of lines. So, we must use the graphing method. Thus, let x = v1F and y = v2F and solve both equations for y with as few parentheses as you can get away with : 1 pt pI total = pF total (3.2 kg * 11 m/s) + (4.8 kg *5.0 m/s) = (3.2 kg * x) + (4.8 kg * y) becomes… y1 = ( 3.2* *5.0 3.2x )/4.8 (only use 1 parenthesis when doing this, and simplify NOTHING!!!) KE I total = KE F total (½ * 3.2 * 112) + (½ * 4.8 *(-5.0)2) = (½ * 3.2 * x2) + (½ * 4.8 * y2) y2 = (( .5*3.2* *4.8*5.02 .5*3.2x2 )/( .5*4.8)) (only use 3 parentheses when doing this, and simplify NOTHING!!!) 4 pts 4 pts 1 pt 4 pts 4 pts

22
**y3 = y2 (do not type in y2 all over again, use the y2 “button”)**

Example: A 3.2-kg block is traveling EAST with a speed of 11 m/s. It collides with a 4.8-kg block traveling WEST at 5.0 m/s. What will be the speeds of these two blocks after the collision if it is perfectly elastic? y1 = ( 3.2* *5.0 3.2x ) / 4.8 y2 = (( .5*3.2* *4.8*5.02 .5*3.2x2 )/( .5*4.8 )) y3 = y2 (do not type in y2 all over again, use the y2 “button”) I put the subscripts y1 and y2 there because that’s how your TI will show them. But, you’ll also need to do eq y3, because TI’s won’t calculate the bottom of the circle/ellipse without this little help. (You can find y2 in vars / y-vars / function.) When you graph it, do a -20 to 20 window for both x and y. Find the intersect of the line and circle/ellipse, by doing... 2nd Calc, Intersect, 1st curve, 2nd curve, guess. There are actually 2 intersections. You should find them both and get: 8.2 m/s & 7.8 m/s; and 11 m/s & 5.0 m/s It turns out the second intersection (of the two I have written above) is the exact same answers as the originally velocities, and thus not physically possible, so the other intersection is the correct answer. Note: you only have to do # 1 and 2 on the worksheet the “old way”. See hints and stuff on the assignment ditto itself.

23
**HW #1: A 1. 6-kg block is traveling east with a speed of 5. 5 m/s**

HW #1: A 1.6-kg block is traveling east with a speed of 5.5 m/s. It collides with a 2.4-kg block traveling EAST at 2.5 m/s. What will be the speeds of these two blocks after the collision if it is perfectly elastic? Elastic collisions #1,2,5,6 TWO different ways ... (b) as stated – they are perfectly elastic, and NOT as stated, but the two things STICK together after the collision, called “inelastic”. (but only for #’s 1 & 2, 5 & 6) #3&4 as it says on the worksheet only.

24
**#1 : OLD WAY = INELASTIC = ONLY MOMENTUM CONSERVED (usually stick) …..**

pI total = pF total (1.6 kg * 5.5 m/s) + (2.4 kg * 2.5 m/s) = (1.6 kg + 2.4) vfinal NEW WAY = ELASTIC = BOTH MOMENTUM & KE CONSERVED (usually bounce) ….. (1.6 kg * 5.5 m/s) + (2.4 kg * 2.5 m/s) = (1.6 kg * x) + (2.4 kg * y) becomes… y1 = ( 1.6* *2.5 1.6x )/2.4 KE I total = KE F total (½ * 1.6 * 5.52) + (½ * 2.4 * 2.52) = (½ * 1.6 * x2) + (½ * 2.4 * y2) y2 = (( .5*1.6* *2.4*2.52 .5*1.6x2 )/( .5*2.4))

25
**#2 : OLD WAY = INELASTIC = ONLY MOMENTUM CONSERVED (usually stick) …..**

pI total = pF total (1.6 kg * 5.5 m/s) + (2.4 kg * 2.5 m/s) = (1.6 kg + 2.4) vfinal NEW WAY = ELASTIC = BOTH MOMENTUM & KE CONSERVED (usually bounce) ….. (1.6 kg * 5.5 m/s) + (2.4 kg * 2.5 m/s) = (1.6 kg * x) + (2.4 kg * y) becomes… y1 = ( 1.6* *2.5 1.6x )/2.4 KE I total = KE F total (½ * 1.6 * 5.52) + (½ * 2.4 * 2.52) = (½ * 1.6 * x2) + (½ * 2.4 * y2) y2 = (( .5*1.6* *2.4*2.52 .5*1.6x2 )/( .5*2.4))

26
**#3 : OLD WAY = INELASTIC = ONLY MOMENTUM CONSERVED (usually stick) …..**

DON’T DO THIS ONE THIS WAY! (They won’t “stick”) NEW WAY = ELASTIC = BOTH MOMENTUM & KE CONSERVED (usually bounce) ….. pI total = pF total (220 g * 45 m/s) + (46 g * 0 m/s) = (220 g * x) + (46 g * y) becomes… y1 = ( 220* *0 220x )/46 KE I total = KE F total (½ * 220 * 452) + (½ * 46 * 02) = (½ * 220 * x2) + (½ * 46 * y2) y2 = (( .5*220* *46*02 .5*220x2 )/( .5*46))

27
**#4 : OLD WAY = INELASTIC = ONLY MOMENTUM CONSERVED (usually stick) …..**

CAN’T DO THIS ONE THIS WAY! (They explode apart!) NEW WAY = ELASTIC = BOTH MOMENTUM & KE CONSERVED (usually bounce) ….. pI total = pF total (1 kg * 0 m/s) + (2 kg * 0 m/s) = (1 kg * x) + (2 kg * y) becomes… y1 = (1*0 + 2*0 1x)/2 KE I total + 60 Joulesgiven to system= KE F total (½ * 1 * 02) + (½ * 2 * 02) + 60 = (½ * 1 * x2) + (½ * 2 * y2) y2 = (( .5*1* *2* .5*1x2 )/( .5*2))

28
**#5-6 Don’t forget to do these too!**

(5 & 6 you will do inelastic also, 7&8 we’re skipping.) I STRONGLY encourage you to make sure you can use your calculator! Don’t just copy the answers off the sheet, but make sure YOU can get them yourself given a TI calculator! Many students do NOT know how to find the intersection correctly! Some answers: 5) #1 REDO (sticking/inelasti/old way answer = 7.4 m/s & new "elastic" way answers = ?? m/s and 12.2 m/s) 6) Supposed to say #2 REDO (sticking/inelastic/old way answer = NEGATIVE ?? m/s & new "elastic" way answers = -10.## m/s and 0.## m/s)

29
**Thurs Dec 19th Hand in and pass out a few things:**

**quickly talk about squirrel’s velocity IN: Guided Notes, assts A-B, C-D, E-F - if haven’t yet OUT: Study Guide (Merry Christmas!) Experiment: Work & Energy ONE person records data in Excel & send to all three homes Asst a: Make sure collisions done 25% of the test! Come in for help!!!!! Asst b: HAND-Written Introduction-Procedure for experiment write-up (see webpage/ for write-up hints) BINDERS DUE TOMORROW squirrel falling DOWN, so all velocities should be negative; you get that because there are TWO answers to a square root!

30
**Experiment: Proving the “Work=change-in-mechanical-energy” theorem**

Spring scale parallel to incline Dynamics cart goes up with constant speed! Measure height CORRECTLY as shown in figure at right Instead of recording data in a sheet of paper, as instructions say… One peson log in & open “Work-Eenergy 2011” excel template Type in all data as working When finished, that file home to all lab members

31
Friday Dec 20 Collect Collisions; put Momentum assts in old section, take out W-E study guide, then …. Binders due!! Get a book and start … Asst: Concepts, due Mon when we get back: (See list & hints on back of Study Guide!) Page 265 #17, 21-23 Page 278 #36-38**, 44-46**, 89***** Page 292 #12, 14a(no bar graph)&b: Page 301 #22: Page 305 #30&32** together, 33-35**, 36, 38, 39**&46, 51**, 52, 88 MAKE SURE YOUR WRITE-UP is DONE up to & including the Procedure; we will stamp this Monday when we return!

32
**Mon Jan 6 Welcome Back! Equation Review – lecture notes**

Quiz – elastic & inelastic collision I will stamp your write-ups as you are doing this! Go over some Concepts in red pen **(23, 38, 89; 22, 30&32, 34, 35, 51) Asst: (a) Work on ch 10/11 review packet (due Wed, so you have 2 nights; YES WRITE ON IT!!) Note – whole experiment write-up due this Thurs (asst Wed night is to finish); unit TEST is this Friday (in 4 days!).

33
**Quickie equation review LECTURE NOTES**

The dot product part of: W = F d = E If F & d in opp dir, work negative If F & d perpendicular, work = zero If F & d at some weird angle, use cosine Power: P = W / t = F v The work-energy theorem in high-school problems can be either of these two equations: W = F d = KE = KEF – KEI = ½mvF2 ½mvI2 W = F d = PE = PEF – PEI = mghF mghI Conservation of energy problems in high school can be either of these two equations: PEinitial + 0 = 0 + KEfinal, i.e.: PEinitial = KEfinal when falling 0 + KEinitial = PEfinal + 0, i.e.: KEinitial = PEfinal when rising Inelastic & Elastic collisions (see next slide)

34
**Dec lecture notes REVIEW, add point distribution to those notes:**

OLD WAY = INELASTIC = ONLY MOMENTUM CONSERVED (usually stick) ….. pI total = pF total (1.6 kg * 5.5 m/s) + (2.4 kg * 2.5 m/s) = (1.6 kg + 2.4) vfinal NEW WAY = ELASTIC = BOTH MOMENTUM & KE CONSERVED (usually bounce) ….. (1.6 kg * 5.5 m/s) + (2.4 kg * 2.5 m/s) = (1.6 kg * x) + (2.4 kg * y) becomes… y1 = ( 1.6* *2.5 1.6x )/2.4 KE I total = KE F total (½ * 1.6 * 5.52) + (½ * 2.4 * 2.52) = (½ * 1.6 * x2) + (½ * 2.4 * y2) y2 = (( .5*1.6* *2.4*2.52 .5*1.6x2 )/( .5*2.4)) 5 pts total + 4 pts for both coordinate pair answers (with units), 1 pt for knowing which answer valid, 24 pts TOTAL

35
**Tues Jan 7 Go over yesterday’s quiz**

**Remember – experiment data was done in Excel the day of the lab, and that person was to it to all three partners’ homes to print out! Write-up due Friday! Go over yesterday’s quiz Finish going over really important and/or confusing concepts as needed #23, 38, 89; 22, 30&32, 34, 35, and 51specifically Take another quiz Asst: Complete review packet (due TOMORROW, please write on it!)

36
**Wed Jan 8 Hand back stamped/checked Concepts questions**

Go over yesterday’s quiz (COME IN FOR HELP ON COLLISIONS!) Note about quick checks for elastic collision: (a) is the other (“ghost”) answer the starting velocities? (b) IF YOU HAVE TIME (not so quick check), and you DO simplify the y= equations, do you get the same answers? Go over review packet in red pen & turn in Asst (a): Redo these 4 problems: p278 #58, 61; p307 #75, 77 Asst (b): get Concepts Key from webpage & finish grading yours in red pen (we will look for corrections when we collect it!) Asst (c): finish the W-E Write-up - which is on your test … You must bring it to class tomorrow to be stamped again Make sure your data is attached Note about R&C: Results are: “The work done on the dynamics cart was shown to be equal to its change in energy with an average percent error of ____” TEST Friday! Next week: Study for comprehensive (covers everything in Physics August-January) FINAL Jan 22-24

37
**Thurs Jan 9 Hand out Friday’s HW (copy both days schedules!)**

Questions on 4 HW problems??? Read (fill-in?) STUDY GUIDE; ASK QUESTIONS! **Work-Energy experiment?; squirrel? Practice test Stamp EXPERIMENT write-ups again… Asst: STUDY! (re-read Guided Notes or see key online, download Concepts Key & go over, go through Study Guide & do the problems, look at Review Packet, etc) Next week: Study for comprehensive (covers everything in Physics August-January) FINAL Jan 22-24

38
Look at Study Guide

39
**Fri, Jan 10 Test (make sure your calc is in degrees!)**

Finals REVIEW HW packet page 1; use old notes and assts to … (a) vectors P4 and P8 (only) with both the graphical AND the component method; (#4 use “set1” in degrees, #8 uses “set2” in NWSE system) (b) speed & velocity problems listed on review ditto (go back & look at old assts & notes if you must!!)

40
Mon, Jan 13 If you have a D or F in Physics, this week is a good time to talk to parents/counselors about whether you want to stay 2nd semester! 1. Work on Standards packet together ...1(a-d, e=skip, f/g/l, h), 2, 3 together 2. REVIEW ASST: a) kinematics (ditto A – you may select any 3 problems; ditto D – do #5, 7, 9, 11) & (b) projectiles (do either 4 or 5 from BOTH types) AND …do the projectiles questions at the bottom: Angles give maximum range, same range? Range & time on Jupiter vs moon? vel and accel on way up, at top, on way down in both x and y **Did you answer the question(s) about equilibrium on the weekend’s HW???

41
**Tues Jan 14 Anything not turned in yesterday? (W-E asst sheet)**

If you have a D or F in Physics, this week is a good time to talk to parents/counselors about whether you want to stay 2nd semester! Anything not turned in yesterday? (W-E asst sheet) Label review HW so far (A, B, C, etc) Did you do everything listed on pages 1 & 2?? Continue work on Standards In-Class packet REVIEW HW: Fill in Standards down left hand-side of entire In-Class review sheet Page 3 of HW Review packet: Newton’s Laws & FVD

42
****Email me if you have questions!) **Final is about 18% of your grade!**

Wed Jan 15 & Thurs Jan 16 & Fri Jan 17 in-class Standards packet Organize binder for check (W-E old; only review stuff = current) Start looking at old tests HW Wed: “Circles Review” last page of In-Class sheet (answer every question the best you can, leave nothing blank!) HW Thurs: page 4 of HW Review Packet Weekend HW: print out finals study guide, which is the 8th you should have in your binder; MAKE NOTECARDS FOR STUDYING! (Bring them in Tuesday!) Tues Jan 21 Hand out ch 14 Guided Notes Look at final format / sample question Organize binders – ALL review material in Current Section (only) Any last minute questions? / whiteboard challenge? 3. HW: STUDY! Wed- Fri Jan 22-24 Final ALL review HW & in-class work due, plus review packet (put it all in the “Current Section” of your binder; that’s all that should be in there! Binders due (last check of semester) HW: Guided Notes to chapter 14 “Waves” ** me if you have questions!) **Final is about 18% of your grade!

Similar presentations

OK

Energy. Analyzing the motion of an object can often get to be very complicated and tedious – requiring detailed knowledge of the path, frictional forces,

Energy. Analyzing the motion of an object can often get to be very complicated and tedious – requiring detailed knowledge of the path, frictional forces,

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Store window display ppt on tv Ppt on intellectual property rights in india Ppt on review of related literature introduction Ppt on main festivals of india Scrolling message display ppt online Ppt on mobile computing pdf Ppt on revolt of 1857 pictures Ppt on centring club Knowledge based view ppt on android Ppt on code switching and code mixing