1. Work
Work – a transfer of energy from one object to another by mechanical means
mechanical - something physically makes the transfer
(as opposed to a wave, which is pure energy)
Ex: If you lift a book above your head, you did work on the book
you lost some energy,
the book gains that energy, by being higher off the ground

2. The Math of Work Eq’n: Work = Force • displacement W = FΔx
Units: Joules = Newton•meter
J = kg m/s2 • m
J = kg m2/s2
where Δx measurement is the straight line from start to finish, not path dependent
so how much work done if you run in a circle?
so how much work done if you support a book out at your side?
where the F and the Δx it’s moved are assumed to be parallel to each other…

3. So if the force and displacement are parallel to each other, you’d use the entire value of F in the equation,
But if they are at an angle to each other, which is far more likely in the real world, then you need to find the component of the force that’s parallel to the displacement, and only the value of the component is used as F in the equation.

4. Work is actually a scalar quantity
so + or – does not indicate direction!
positive W
Refers to work that’s done on an object, so that object gains energy
When F (or its contributing component) & Δx are in the same direction
negative W
Refers to work that’s done by an object, so that object loses energy
When F (or its contributing component) & Δx are in the opposite directions
Ex: work done by friction or gravity, if going up

5. The Energy Outline Energy - the ability to do work or
the ability to change an object or its surroundings
I. Mechanical NRG – energy due to a physical situation
A. Kinetic NRG (KE) – energy of motion
an object must have speed
Eq’ns: KE = ½ mv2 and ΔKE = ½ m(vf2 - vi2)
units: J = kgm2/s2
(recall from work: J = Nm = kgm2/s2)

6. B. Potential NRG (PE) – energy of position,
stored away, ready to set an object into motion
1. Gravitational PE (PEg) – object’s position is some height different than the reference level, where PEg = 0
Eq’ns: PEg = mgh = Fgh & ΔPEg = mg(hf – hi)

7. 2. Elastic PE – object’s position is some shape different than normal

8. 3. Chemical PE – object’s atoms/molecules have the potential to rearrange
4. Electric PE – the charged particles within the object have the potential to move – create electricity!

9. II. Thermal NRG – energy of heat – the energy that is produced when it looks like energy isn’t being conserved…
Examples of ways to create it:
friction
air resistance
sound
deformation

10. The Work – Energy Theorem
This is the connection between work and energy:
The amount of work done by* / on** an object will equal its change in energy
* “by” – object will lose NRG, so -ΔE
** “on” – object will gain NRG, so +ΔE
In effect, work is the act of changing an object’s NRG,
while energy means work can get done.
PE means it has the potential to get done.
KE means it is presently getting done.
Eq’n: W = ΔE, or more specifically, W = ΔKE + ΔPE

11. Back to KE – what does it mean to have velocity2 in the equation?
Let’s consider how long it takes to stop a vehicle traveling at a particular speed:
At first you may think: if you’re traveling twice as fast,
it will take twice as far to stop,
But that’s not right… W = ΔKE
or F Δx = ½ m Δv2
So as v increases, both KE and the other side of the equation goes up by the square of that increase,
Ex: for 2x’s as much v,
there’s 4x’s as much KE in the vehicle,
there’s 4x’s as much W needed to stop it,
and for a constant braking force,
that means 4x’s as much distance is required!

12. Conservation of Energy
The Law of Conservation of Energy:
NRG can’t be created or destroyed, but it can be changed from one form to another.
Eq’n: Ei = Ef
Possible forms these NRG’s could be in?
in the ideal world: only ME (KE & PE)
in the real world: ME (KE & PE) & TE
Consider the double incline ramp:
Will the ball roll off the short side if released from the long side?
No, but why? Now we can answer that…

13. The double incline ramp with 4 noted positions:
1: E1 = PEg Since there’s h, but no v
2: E2 = PEg2 + KE2 Since still some h, but also v
3: E3 = KE Since no more h*, and all v
4: E4 = PEg Since no v, and back at original h – but is it?
*If RL defined as top of metal track at bottom of ramp
L of C of E says: E1 = E2 = E3 = E4
So in the ideal world: PEg1 = PEg2 + KE2 = KE3 = PEg4
so mgh1 = mgh4
then h1 = h4
But in the real world:
PEg1 = PEg2 + KE2 + TE2 = KE3 + TE3= PEg4 + TE4
so mgh1 = mgh4 + TE4
then h1 > h4

14. Swinging Pendulum on a string
2 forms of ME that the total amount of NRG fluctuates between
max KE at equilibrium (vertical) position
max PEg at either end
if real world: loss of ME to friction where string rubs on support & air resistance
Bobbing Mass on a spring
3 forms of ME that the total amount of NRG fluctuates between
max KE at the equilibrium (midpoint) position
max PEe at the bottom and some at the top
max PEg at the top
if real world: loss of ME to friction inside spring & air resistance

15. Mutli-Color Tracks Which shape track wins? One with its dip 1st, wins
– gets to a faster speed earlier in its trip
Which shape track gets the ball going the fastest by the end?
Ideal: All have = PEg at start, so = KE at end,
so = v too
Real: the shortest distance (straight) track loses least KE to TE, so it’s going a little faster

16. The Math of Conservation of Energy
ID givens, unknown & reference level!
Can draw a diagram of “i” & “f” situations to help
2. state: MEi = MEf (we assume ideal)
3. then: PEgi + KEi = PEgf + KEf only of needed terms
4. then: mghi + ½mvi2 = mghf + ½mvf2
where mass will often cancel
watch units: need kg, m, s  Joules
Ex: A 0.4 kg ball is dropped 2m. What’s its speed when it reaches the ground?

17. The Math of Conservation of Energy
ID givens & unknown
Draw a diagram of “i” & “f” situations
use “fast marks” to indicate speed
ID RL to indicate height
3. state: MEi = MEf (we assume ideal)
4. then: PEgi + KEi = PEgf + KEf
so are any of the terms = 0?
5. then: mghi + ½mvi2 = mghf + ½mvf2
where mass will often cancel
watch units (kg, m, s  Joules)
Ex: A 0.4 kg ball is dropped 2m. What’s its speed when it reaches the ground?

18. Consider a story about 2 students asked to help get books loaded into the cabinets. Both move equal numbers of books up to equal height cabinets, but one does it quickly and efficiently, while the other does not.
Who does more work?
Neither! Both apply same F thru = Δx
Who uses more power?
The quicker one
Power is the rate at which work gets done
Eq’n: P = W/Δt
units: Watts = J/s (1 hp = 746 Watts)