Transcript Work, Energy, Power Lecture Notes:

Work, Energy, Power
Lecture Notes:
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
• See in slides 3 & 7 that, just like the impulse-momentum
theorem above, we now have the work-energy theorem:
(3) W = F  d = E
• And see in slide 8 that, just like we had the conservation
of momentum in a closed & isolated system above, 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 is a special type of multiplication, and there
is more than one type of energy!)
W = F  d = E
• Lets 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.
• The unit for work is the Joule [J].
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 velocity
will be zero.
• The unit for power is the Watt [W].
KE = ½mv2 & PE = mgh
• Kinetic energy has the symbol KE
• Gravitational potential energy has the
symbol PE
• Both are also measured in Joules [J].
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 table on the next slide 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!)
W = F  d = E …revisited:
• NOTE – the textbook is WRONG here. It says W equals
the change in kinetic energy, but it 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:
W = F  d = PE = PEF – PEI = mghF  mghI
Work done:
Why?
Energy change?
Simple Examples:
+
F & d same dir
increase
(a) Pull or push something (even at an angle) …
increases KE
(b) Raise or lift something … increases PE

F & d opp dir
decrease
(a) Friction … decreases KE
(b) Lower something … decreases PE
0
F & d are perpend;
or no net force
none
overall/total
(a) You carry something … energy stays constant
(b) Something falls … energy is conserved: PE → KE
(c) Something is thrown up … energy is cons: KE → PE
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 slides 3 &
7, 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 = KEfinal + 0, i.e.: KEinitial = PEfinal when rising
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 )