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UNIT 4: CONSERVATION LAWS -WHERE PHYSICS GETS REAL . . . http://hyperphysics.phyy-astr.gsu.edu/hbase/shm2.html http://www.youtube.com/watch?v=lIPWyY__N2A&feature=relmfu 2 3 4 5 6 7 FOCI How calculus applies to things we already know about Energy. Keep in mind-the basics are still most important. Calculus will actually make things easier!!! The problems are just more complex. You should use TONS of paper for a WebAssign. You will start turning these in- 50% of problems, BEST GUESS, every other week in Problem Solving Journals You are expected to be reading & solving problems about 1 hour each day. I know that isn’t happening. Time to take responsibility for learning. Energy and Work is a HUGE component of the AP Exam You need to trust me and work with me. It overlaps with every other unit remaining It ties into all other ideas. I have done this before VERY successfully. Are you willing to make this a priority??? This is the unit where we start to move forward quickly. This is an AP class x2!!! It isn’t honors physics again. Complacency kills I EXPECT that you understand the basics. If you don’t, then you had better start to try harder. You are expected to be reading & solving problems about 1 hour each day. I know that isn’t happening. Time to take responsibility for learning. Let’s Go! K.E.=1/2mv•v=1/2mv2 Dot/Scalar Product of velocity OR Speed2 K.E. is a scalar! Joule= 1 kgm2/s2 (“Big” masses) 1 eV=1.6e-19 J “Equation of State”- a snapshot. Depends on the state of motion-NOT CAUSES We just did this in the ΣF=ma lab! (“electron-volt”-small masses) What if instead of measuring this arbitrary “a” thing, we measured initial and final velocities (states)? Knowing some things are conserved & some aren’t. Mechanical Energy (Yeah Right!-Perfect World Only) Momentum (Even if Heat is created- “internal energy”) Total Energy (Was there an energy leak? What’s your system?!) Changes in Energy are All that Matter! SUBTLETIES A Change in Energy!! How do you change energy? Forces acting over a distance Along that axis! +Work-adds energy to a system, –Work removes W=F•x Dot Product!! (Scalar) Vectors involved If force CHANGES with distance (usually does) Then W= ∫F(x) •dx Called an “Integral”/Anti-Derivative WORK Mass on a Spring http://www.youtube.com/watch?v=rbuMJN8P3tY http://www.slideboom.com/presentations/546590/ WORK-%26-ENERGY Simple Harmonic Oscillation http://www.youtube.com/watch?NR=1&v=kZ3SxV XVmlM http://www.youtube.com/watch?feature=fvwp&v =eeYRkW8V7Vg&NR=1 SPRINGS ARE A PERFECT EXAMPLE OF WORK DONE BY F(X) ∆K.E.=Wnet Vfx2=vix2+2axx Constrained along x. If it could move in y direction too . . . Vfy2=viy2+2ayDy V (Speed)=DVfx2+vfy2 Net Forces cause changes in motion- and KE! WORK-K.E. THEOREM WORK DONE BY GRAVITY= -G.P.E. Gravitational Potential Energy (GPE) W=Fdcos mgycos(0 or 180 deg) -work done BY GRAVITY while going up +work done BY GRAVITY while going down With no “non-conservative forces” this is path independent. Potential energy is given by a conservative force only. Gravity Coulomb Force (twixt charges) Magnetic Force (twixt magnetic fields) SAMPLE PROBLEM 7-5 (KIND OF) M=20 kg L=6 m H=2 m h a) Find the work done by the weight as it raises a distance L. b) Find the work done by the Tension. (Assume V=constant) • Now, assuming crate accelerates with a 100 N Tension. Use the W-KE theorem to find the final speed after moving a distance L. NOW- CALCULUS PART II Wn=Fn(x)Dx The idea that small little forces over small distances all contribute to work. Now, just add them up! ΣWn=ΣFn(x)Dx lim Dx->0 Smaller and smaller widths More “Accuracy” W=∫ F(x)• dx From a to b, or (xi to xf) A LITTLE MATH 19 20 LET’S TRY IT!-REIMMAN P=W/t P=dW/dt P=F•v Rate of change of Energy Rate at which work is done. This is why simple machines HELP! Same amount of mechanical work. Faster time! Area under Force vs. Velocity Graph Slope of Work vs. time graph POWER 23