1. Energy Conserved “substance” that quantifies an ability to make changes in other objects The ability to make changes in other objects Shape, temperature, motion, position, etc. Exists in a defined system (group of masses) Stored as “Potential Energy” (U)

2. Energy Since energy is conserved, it can only be gained from “outside” the system. Work – a way to transfer energy into (or out of) a system –“Energy transfer method” Do work to gain energy, energy can do work Work EnergyW = ΔE Work – getting something done Energy – ability to do work, to get something done

3. Energy To get something done… –Must apply a force –Must have movement as a result (displacement) –Only force and distance in the same direction do work –Example: Objects slides horizontally while pulled with an angled force

4. Energy To get something done… –Must apply a force –Must have movement as a result (displacement) –Only force and distance in the same direction do work –Example: Objects slides horizontally while pulled with an angled force

5. Energy To get something done… –Must apply a force –Must have movement as a result (displacement) –Only force and distance in the same direction do work –Example: Only the horizontal force causes work Objects slides horizontally while pulled with an angled force

6. Energy To get something done… –Must apply a force –Must have movement as a result (displacement) –Only force and distance in the same direction do work Work = Force × distanceW = F·d·cosθ

7. Energy To get something done… –Must apply a force –Must have movement as a result (displacement) –Only force and distance in the same direction do work Work = Force × distanceW = F·d unit: N·m = Joule (J) –Same unit for work and energy

8. Energy and Work Work done results in change of energy W = ΔE W = F·d ΔE = F·d ΔE = E f - E i

9. Energy Example: How much work is required to lift a 15 kg mass 5 meters? To lift the mass, we must lift against gravity F g = m·g = (15 kg) (10 m/s 2 ) = 150 N Work = F·d = (150 N) (5 m) = 750 J W = ΔE  Work done = energy gained, 750 J

10. Energy The speed at which work is done has no effect on the amount of work being done. Example: Running a mile and walking a mile require the same amount of work, but from experience, we know they are different

11. Power Rate at which work is done (also rate of energy output) Power = Work / time Unit: Joules / seconds = Watt (W) “Watts,” like a light bulb High wattage brighter bulbmore energy used per second

12. Power Example: How much power is required to lift a 15 kg mass 5 meters in 10 seconds? From before, we know work = 750 J Power = W / t = (750 J) / (10 seconds) Power = 75 W

13. Recap Energy – ability to make a change Work – done to gain energy, W = ΔE W = F·din same direction Newton · meter = Joule Power – rate at which work is done P = W / t Joules / second = Watts

14. Types of energy Potential (U) – stored, from particle interactions Elastic (U el ) – springs W = ΔU el Gravitational (U g ) – from F g attraction W = ΔU g Kinetic (E k ) – particle motion W = ΔE k Electric Potential – charges Chemical – bond energy Thermal (heat) – friction from particle collisions Nuclear – nucleus energy

15. Types of energy Gravitational potential (U g )U g = m·g·h W = ΔU g = m·g·Δh Kinetic (E k )E k = ½ m·v 2 W = ΔE k = ½ m·(v 2 – v 0 2 ) Work = ΔE Work = F·d Power = W/t

16. Recap Energy – ability to make a change Work – done to gain energy, W = ΔE W = F·din same direction  cosθ ?? N·m = Joule Lab:slope of F-d graph is spring constant (k) y-intercept of F-d graph is preloading force Ideal spring = no preloading force Area = work done to stretch = ½ k·x 2 ***increasing force

17. Types of energy Elastic potential (U el )U el = ½ k·x 2 W = ΔU el = ½ k·(x 2 – x 0 2 ) Gravitational potential (U g )U g = m·g·h W = ΔU g = m·g·Δh Kinetic (E k )E k = ½ m·v 2 W = ΔE k = ½ m·(v 2 – v 0 2 ) Work = F·d Power = W/t

18. Spring Lab – Hooke’s Law Determine how the force required to stretch a spring depends on the distance it stretches.

19. Spring Lab Four (4) different springs –Name/describe each spring –F, d should vary for each (depending on spring) 5 - 6 data points per spring Distance stretched – change in length Do not over-stretch: 3x, common sense Graph all springs/data sets on one graph

20. Spring Lab Determine how the force required depends on the distance it stretches. On whiteboard: 4 data sets on one graph 4 equations (y-intercept?) Meaning and unit of slope Meaning and unit of y-intercept Meaning and unit of area

21. Hooke’s Law F s = k·xk: spring constant (N/m) x: stretch (compression) on spring (m) F o – Preloading force, zero unless told otherwise

22. Hooke’s Law F s = k·xk: spring constant (N/m) x: stretch (compression) on spring (m) Work done on spring = area under F-d graph *due to changing force W = ½ k · x 2 Work done results in change of energy, W = ΔE