Work, Energy, Power Lecture Notes:

1. Work, Energy, Power Lecture Notes:

2. 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!)

3. 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].

4. 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].

5. KE = ½mv2 &PE = mgh • Kinetic energy has the symbol KE • Gravitational potential energy has the symbol PE • Both are also measured in Joules [J].

6. 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!)

7. 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

8. 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

9. HERE ARE THE EQUATIONS YOU NEED ONE MORE TIME: