1. 1 Work and Energy

2. 2 Why do we do work anyway? Newton single handedly invented mechanics, but missed one concept –Energy (E) the ability to do work –no wonder he avoided work! –we’ll get to this in a second –Work (W) has many definitions, but here it is very precise (remember the beginning of the year) force multiplied by distance –must be the component of force acting in the direction of motion

3. 3 Working 9 to 5 MKS units: Joule –the ability to exert 1 Newton over a distance of one meter –1 J = 1 N * 1 m find units that are all m, kg, sec Work examples weightlifting: the clean and press pulling a wagon waitress earth and moon Efficiency –ratio of work in to work out –can this ever be greater than 100% ?

4. 4 More Power Tim Taylor: More Power (grunt, grunt) Power (P) –the amount of work done per unit time –derive: P = F*v –unit is watt one watt is defined as one joule of work done in one second find units in m, kg, sec

5. 5 Anyone have a Energy Bar? Energy (E) –ability to do work hammer swinging –found in many forms electromagnetic, mechanical, heat, nuclear, sound –also measured in joules –can change forms, but can’t be created or destroyed more on this later –two types: potential and kinetic

6. 6 Neighbor Paul Energy potential energy (PE) –the energy of an object due to position or configuration –two special types: gravitational potential energy elastic potential energy

7. 7 Gravity, It’s Still the Law Gravitational potential energy –energy obtained due to work done against Earth’s gravitational field When we raise or lower an object, the force required to do so is = weight = mg –as long as we’re close to earth; g is constant We raise it a distance h W = F*  x W = mg*h = PE

8. 8 Elastics (not a book in the Bible) Elastic Potential Energy –energy obtained due to work done from a spring or rubber band –force required to stretch or compress a spring is given by Hooke’s law F = k x –k is a spring constant, different for each spring »unit for this is N/m –Work done to stretch a spring is given by ½kx 2 –this also equals what? –Lab: Finding a spring constant

9. 9 Keith Energy kinetic energy (KE) –energy an object has because of its motion –depends on reference frame –KE = ½mv 2 if v = 0, then what is KE? if I double the velocity, then what happens to KE? how can I get KE to be 9 times as big? how can I get KE to be 1/16 as big? work-kinetic energy theorem –the amount of work done on a system is = the change in KE of an object

10. 10 Conservation, Part 2 total energy = kinetic energy + potential energy I raise a student, mass 50 kg, to a height of 2 meters and hold him. –what is the PE? KE? E? Now I drop him, and right before impact, all his potential energy is converted to kinetic energy –from this you can find his velocity at impact This is true for all closed systems and is called the conservation of energy –The total energy of any closed system is conserved  E =  KE +  PE for a closed system,  E = 0

11. 11 Roller coaster Can we use this in the real world? –Well, let’s ride a roller coaster, baby, baby –Can a roller coaster ever be higher than its original point, assuming no outside forces act on it? Can you find the velocity of the roller coaster at any point –Lab: Cart on a ramp (pg. 225)

12. 12 A Change Will Do You Good As said before, energy is conserved in a closed system –but energy can change forms can never be created nor destroyed –neither can mass –In fact, energy and mass are related –E = mc 2 this is from SR energy is mass! how much energy is in a 70 kg object

13. 13 Footnote Conservative vs. Nonconservative Republican vs. Democrat Bush vs. Kerry ? No we’re talking about forces Conservative force –force where mechanical energy remains constant (ex. gravity) –can “get it back” Nonconservative force –force that converts mechanical energy into another form, i.e. heat (ex. friction) for this there is a footnote to the conservation of energy –delta E = delta KE + delta PE + internal energy

14. 14 Collisions Types of collisions –completely elastic kinetic energy is conserved –completely inelastic kinetic energy not conserved, two masses clump together –none of the above a little bit of this, a little bit of that Is momentum conserved? How about total energy? Again the ballistic pendulum

15. 15 Executive toy One ball hits on one side, one ball flies off the other side What is conserved? –momentum and KE Why doesn’t two balls fly off the other end with the same speed? –hint find momentum before and after –find KE before and after