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Plan for Quiz 4 to be Tue.Oct.15
... plan for Exam 2 to be Tue.Nov.12

Topic 4 ( Work = Force thru distance => Transfers Energy)

Doing Work means pushing for a ways ; it transfers (or transforms) Energy   =>   W = F·Δx = ΔE
Energy is a scalar quantity that something holds within itself ("en" implies within)
. . . the various Energy   forms   depend on the object's condition at that time
      so each form will change its value (numerical amount) as that condition changes
. . . a moving object will have   Kinetic Energy , often abbreviated KE
      just because it has momentum and has velocity along that momentum.

Work is a process that a subject   does to   some other object
. . . physical Work requires motion ... displacement ... of the place the Force is applied to
      pushing a stationary brick wall does zero Work , no matter how long (duration) you push
. . . Force applied along a displacement does positive Work
      positive Work transfers positive Energy thru the Force all along the accumulated displacement
      ... this Energy goes from the subject pusher into the object pushee
      ... and tends to increase the object's Kinetic Energy (making it faster).
. . . Force applied opposite the displacement does negative Work
      negative Work transfers negative Energy thru that Force arrow
      ... tending to decrease the object's speed , and so decrease its KE.
. . . Force applied perpendicular to the displacement does zero Work
      Force "across" a motion is neither along it nor opposite it.
      ... it neither increases the object's speed (KE) nor decreases that speed
      all it does is deflect the object's path (changes velocity by direction change, at constant speed).

Suppose I hold a 3 kg cylinder at a height of 2 meters, for 5 seconds, then drop it.
. . . while I was holding it for those 5 seconds , I applied 29.4 Newtons upward
      but I did 0 Work , since h_t=5 = 2m, but h_t=0 = 2m , so Δh =0m .
. . . once released, I apply 0 N , but Earth's gravity still applies 29.4 N downward
      gravity's Force does Work as the cylinder falls 2 meters to the floor
. . . gravity's Force is down (−9.8N/kg · 3kg), while the displacement is down (−2m)
      so gravity's Work is   (−29.4N)·(−2m) = + 58.8 N·m
. . . no surprise that the cylinder obtains positive KE from gravity's pull during the fall
      because it is going fast at the bottom, even tho' it was stationary at the top.

(kinematics): that cylinder took 0.639 seconds to fall those 2 meters, achieving 6.26 m/s max.speed
(dynamics): gravity pulled (−29.4N) for those 0.639 s
. . . so , during the fall , gravity did  18.8 N·s impulse to the cylinder
      the cylinder started with 0 kgm/s , but ended its fall with momentum  18.8 kgm/s .
. . . the Work gravity did , is the impulse that it did , times the cylinder's average velocity
      (fall distance = fall time · v_average ... not   = fall time · v_bottom)
=> KE = ½ p · v   at any time or place during its fall ... = ½ m v² = ½ p²/m

gravity has the Potential to do Work to objects that are poised to fall from some height (visualize boulder on cliff-top)
. . . since gravity will do that (+) Work as the object falls, when it does fall, if it has potential to fall
      and we know how much Work gravity will do to the object as it falls from height h : W = (−mg·(−h)
. . . it is typical book-keeping to call that Work a   Potential Energy that the object has due to its high condition
      Wiley Coyote did Work to the boulder to get it up there ... W.C.'s Work stored in the boulder as gravity PE
      when W.C. nudges the boulder, gravity does its Work ... making the gravity Potential Energy be "realized" into Kinetic Energy.
      ... fall ends with Wiley under the boulder pushes up (+F) as the boulder continues down (−d) => Wiley's negative Work stops boulder at bottom.
      ... or say the boulder pushes down (−F) into Wiley as he flattens (−d), so does positive Work (transfers its E) into Wiley.
. . . an object has more gravity Potential Energy , if it has more mass ... and if it is in more intense gravity ... and if it is higher up.
=> gPE = m g h . . . notice that things in a hole (below "ground level") have negative height, so have negative gPE .

springs and rubber bands store elastic Potential Energy in their stretch ... ePE is always positive.
. . . your Force to stretch a spring is outward, the same direction as its end moves (so you do positive Work to the spring)
      the spring's inward Tension is opposite the the motion of those ends, so does negative Work (absorbing the Energy that you give it)
. . . for a compression spring that "click pens" have, your Force points in the same direction as the pen clicker moves (so again you do positive Work to the spring).
. . . a relaxed spring applies zero Force ... its Tension Force increases as it is stretched (or compressed).
      the Work you do is your average Force along ("times") the spring's stretch distance ... ½ your the maximum Force
=> ePE = ½ F_max s   =   ½ k_stiffness s ²   ... s is the total stretch , k_stiffness is the slpoe of its Force vs stretch graph.

Forces that yield Potential Energies do NOT depend on the object's orientation or velocity
. . . We can treat them as doing Work (± depending on motion directions - yuk!)
      or treat them as functions (formulas) that depend on the location.
      ... most everybody would rather add or subtract formula results than multiply directionally.
. . . a few other Forces only depend on location (besides gravity and springs)
      Electric Force (Topic 6) in the (microscopic) atomic realm , and nuclear Force in the tiny nuclear realm ;
      Gravity Force in the (astronomical) planetary scale (Topic 5) still depends only on relative location (distance) ...
=> each form of Energy is named after the Force that is expected to do Work.

One Force that DOES depend on velocity's direction is friction => there is NO friction PE !
. . . the friction Force always points opposite the surface slide, so always does negative Work.
      so the friction Force always removes Kinetic Energy , into the surface that was slid along.
. . . both items that slide along each other, against friction's Force, always become warmer (rubbing hands together)
      warmer items contain more Thermal Energy ... roughly proportional to their Temperature
=> friction Work converts organized molecule motion Kinetic Energy into random molecule motion Thermal Energy.
      humans are NOT able to synchronize the random motion of molecules, to make a hot object move in some direction
      so Thermal Energy is NOT counted as a "Potential" Energy ... it cannot become realized as KE.

Efficiency : the fraction (or %) of the Energy that you pay for, which comes out in the Energy form you Want ... E(out,wanted) / E(in,cost)
Energy is conserved, so the same amount always comes out of some process , as went into it .
. . . but often it will come out in 2 or 3 different forms , even when we want one result.
If we want to warm our hands, friction making Thermal Energy (from KE rubbing) is a good thing
. . . but if we want to light a room to read our Science book, Thermal Energy from the light bulb is a waste (in Summer!)
Efficiency describes how "good" some process is , at obtaing some end result ... energy-wise.
. . . an incandescent light bulb (above) is about   6 J / 60 J = 0.1 = 10 % efficient at making (Visible) Light Energy
      but it is about   54 J / 60 J = 0.9 = 90 % efficient at making Thermal Energy

Power   is the rate that Energy is transformed (or transfered)

Power is measured in Watt , in the metric world ... yes, the same Watt that used to label light bulbs
. . . an old 60 Watt (incandescent filament) light bulb transformed 60 Joule Electric Energy each second
      into about 54 Joule Thermal Energy + 6 Joule light.
. . . A typical person transforms about 100 Joules every second from Chemical Energy (food) into Thermal Energy
. . . 100 Joules/second = 100 "Watts" . . . (that's sitting calmly in a chair)

If a good horse "Works" for 7 hours (8 hour − a lunch break) pulling coal up a mine shaft,
      James Watt measured that it did   64 Million Nm   Work
      dividing that into the 24 hour day, the horse did an average   2.7 MJ per hour , or 44 kJ / minute , or 746 J/s
=> 1 "horse power" = 746 Watt   ... even though the horse did 2.5 kW while it was working.

Rate times Duration is Quantity . . . Power × Δ t = Δ Energy
. . . keep track of units!
Many items cost what they do because of the Energy needed to produce them
. . . Electric Energy costs us about 10 centidollars (= 100 millidollar) = 0.100 $ for a   kiloWatt·hour
      how much is that, for 1 Joule?

Work via Simple Machines : Inclined Plane , Wedge , Screw , Lever , Wheel , Pulley (block & tackle)

A wedge Works (;>) the same , but sideways . . .
. . . M.F.A. = wedge length / wedge thickness ... ignoring friction

Levers have a pivot ("fulcrum") that can apply huge Force, but does no Work since it doesn't move.
. . . the heavy load close to the pivot moves a short distance,
      while your Force moves a long way, if applied far from the pivot.
=> M.F.A. = distance from pivot to your hand / distance from pivot to the load

Pulley at the ceiling merely changes the direction of th applied Force
. . . you pull the rope down, the rope (other end) pulls the load up
      M.F.A. = 1 . . . maybe we should call it − 1 ?
pulley attached to the load , with rope pulling it upward from both sides
. . . the rope Tension is only half the weight ... each side of rope holds half mg .
      if one rope end is tied to the ceiling, it doesn't move, so does no Work
      the other end moves twice as far as the load
=> M.F.A. ≈ 2   ... ignoring friction, and the pulley's weight !
"shortcut" to complicated Block and Tackle situations:
. . . draw a "system bag" around the load ... count how many rope pieces "pierce the system bag"
=> M.F.A. is simply this count (since Tension is load weight / rope count)

Reminder about momentum: Total Momentum Before , might be Pushed for a while , to yield Total Momentum After

=> Σ p_before   +   Σ F_external· Δ t   =   Σ p_after   . . .   momentum   p = mv

If the scenario is about   time ,   use Force and momentum or acceleration
      (that's one reason to show you the story-book order of terms)
. . . that's why it is good to show the time change (explicitly out in the open)
      rather than hiding it inside the acceleration.
. . . it places the cause in the center, between the 2 aspects of its effect
      that Force merely changes the initial momentum to a different final momentum.
. . . make sure the Force you want to calculate pierces the system bag (comes from outside it)
      . . . and you know all the momentums . . .
      if you want to calculate a Force with this equation.
. . . make sure only known Forces pierce the system boundary (from outside)
      if you want to calculate one of the momentums.

one reason to treat momentum again is to contrast it with Energy
. . . the new perspective in Topic 4.

Total Energy Before , might be Pushed for a ways , to yield Total Energy After

=> Σ E_before   +   Σ F_external· Δ x   =   Σ E_after   . . .   Kinetic Energy   KE = ½ p·v

Energy is a scalar , meaning that it has no direction (:-))
      and Kinetic Energy is always positive.
. . . replacing the momentum with its "formula"   mv  ,
=> KE = ½ m v·v   . . . = ½ m v ² . . . = p·p / 2m   .

Kinetic Energy is a property that is held within the moving object
. . . it got "en" , and it can get out , by Forces doing Work .
a Force does Work (a process) while the point that it's applied to moves
. . . movement in the direction of the Force does positive Work
      and puts Energy into that moving object ;
. . . movement opposite the direction of the Force does negative Work
      and removes Energy from that moving object.
Because Forces come in pairs (equal strength, opposite direction; subject ↔ object switch ; Newton #3)
      any Force pair just transfers Energy from one side (of the contact) to the other
=> the total Energy is always constant (conserved!).

Total Mechanical Energy is reduced only by friction Work
Total Mechanical Energy is PE + KE
. . . if there's zero friction, an object's Total Mechanical Energy is the same at all places.
picture the roller-coaster track as a PE_grav graph
. . . T.M.E. is a horizontal line from the top of the first hill (since v ≈ 0 there)
. . . KE at any place on the graph is how far above the track the T.M.E. line is.
     less KE at the top of any hill ... (since more PE there)

T.M.E. line slopes downward slightly as friction does negative Work (as car moves)
. . . KE cannot be negative, so the car slows to stop if it's KE becomes zero.
      this is where the T.M.E. line crosses the PE curve (track height graph)
      and the roller-coaster motion reverses (goes downhill) after it stops
      this reversing place is called the "turning point" (software is named after it).
=> turning point is farther uphill the more T.M.E the object has.

use either Potential Energy (before and after) , OR   Work done by the Force (during motion)
. . . don't count the same Force's Work both ways !
      that's why we name the PE's after their Force ... use adjectives !
. . . friction Force always does negative Work, so it has no Potential Energy formula ... use it as non-conservative Work !
=> F_friction· Δ x   . . . transforms KE into Thermal Energy

Negative Total Mechanical Energy means that it is trapped in a well (hole)
We are trapped in Earth's gravity PE well
electrons are trapped in the electric PE well that its protons make.