Understanding Work and Energy in Mechanics

1. Work Work – a transfer of energy from one object to another by mechanical means (mechanical - something physically makes the transfer) 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 in the air Eq’n: Work = Force * displacement or W = F*d Units: Joules = Newton * meter

2. 2 Most Common Reasons Work is Done To change an object’s position, usually done against an existing force, so that the 2 forces balance… like lifting something through gravity Ex: a fireman climbing a ladder at a constant speed like dragging something through friction Ex: sliding a box across the floor at a constant speed To more permanently change an object’s speed Ex: riding in a vehicle or airplane Ex: you push off the ground to get yourself going on a skateboard Ex: a car’s brakes apply a force to slow the car to a stop

3. 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 = d Who uses more power? The quicker one Power is the rate at which work gets done Eq’n: Power = Work/time or P = W/t units: Watts = Joule/sec (1 hp = 746 Watts)

4. 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 Kinetic Energy (KE) – energy of motion an object must have speed Eq’ns: KE = ½ mv2 units: Joules = kgm2/s2 (recall from work: J = Nm = kgm2/s2)

5. 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

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

7. 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!

8. II. Thermal NRG – energy of heat – the energy that is produced when it looks like energy isn’t being conserved… Ex: heat from friction sound deformation

9. 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

10. 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 KE & PE in the real world: 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…

11. Consider the Ball on the Double Incline Ramp 2 forms of Mech NRG (ME) that the total amount of NRG fluctuates between: max PEg at either end - #1 & #4 max KE at the bottom - #3 if ideal world: no loss of ME to thermal, so h1= h4 if real world: loss of ME to friction & sound as ball rubs on ramp & air resistance as it rolls along so h1 > h4

12. 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 Mass on a spring – sketch it 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

13. 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 Fd = ½ m Δv2 So as v increases, both KE and the other side of the equation so 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!

14. Multi-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

15. I don’t use the following slide anymore…

16. Sketch the double incline ramp with 4 noted positions: 1: E1 = PEg1 Since there’s h, but no v 2: E2 = PEg2 + KE2 Since still some h, but also v 3: E3 = KE3 Since no more h, and all v 4: E4 = PEg4 Since no v, and back at original h – but is it? L of C of E says:E1 = E2 = E3 = E4 So in the ideal world: PEg1 = PEg4 so mgh1 = mgh4 then h1 = h4 But in the real world: PEg1 = PEg4 + TE4 so mgh1 = mgh4 + TE4 then h1 > h4