Transcript Unit 4: Conservation Laws

Unit 4: Conservation Laws
-Where Physics Gets Real . . .
http://hyperphysics.phy-astr.gsu.edu/hbase/shm2.html
http://www.youtube.com/watch?v=lIPWyY__N2A&feature=relmfu
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FOCI
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Energy and Work is a HUGE component of the AP Exam
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It overlaps with every other unit remaining
It ties into all other ideas.
You need to trust me and work with me.
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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, each week.
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.
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.
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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.
Subtleties
 K.E.=1/2mv•v=1/2mv2
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Dot/Scalar Product of velocity OR Speed2
K.E. is a scalar!
 Joule= 1 kgm2/s2 (“Big” masses)
 1 eV=1.6e-19 J (“electron-volt”-small masses)
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“Equation of State”- a snapshot.
 Depends on the state of motion-NOT CAUSES
 We just did this in the ΣF=ma lab!
 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?!)
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Changes in Energy are All that Matter!
Work
 A Change in Energy!!
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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
Springs Are a Perfect Example of
Work done by F(x)
 Mass on a Spring
 http://www.youtube.com/watch?v=rbuMJN8P3t
Y
 http://www.slideboom.com/presentations/54659
0/WORK-%26-ENERGY
 Simple Harmonic Oscillation
 http://www.youtube.com/watch?NR=1&v=kZ3S
xVXVmlM
 http://www.youtube.com/watch?feature=fvwp&v
=eeYRkW8V7Vg&NR=1
Work-K.E. Theorem
 ∆K.E.=Wnet
 Vfx2=vix2+2axx
 Constrained along x.
 If it could move in y direction too . . .
 Vfy2=viy2+2ayy
 V (Speed)=Vfx2+vfy2
 Net Forces cause changes in motion- and KE!
Work done by Gravity= -G.P.E.
 Gravitational Potential Energy (GPE)
 W=Fdcos mgycos(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
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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
Let’s Try It!-Reimman
Let A Computer do the Math!
Power
P=dW/dt
P=F•v
 Rate of change of Energy
 Rate at which work is done.
 This is why simple machines HELP!
 P=W/t
 Same amount of mechanical work.
 Faster time!
 Area under Force vs. Velocity Graph
 Slope of Work vs. time graph