1. 1 5 Overview Energy and the Joule Unit. Energy transformation. Energy storage. Power and Watt Unit. Homework: 2, 6, 9, 11, 13, 15, 27, 33, 37, 45, 49, 53, 75, 77, 79, 81, 85, 101.

2. 2 Energy and Transformation chemical fuel energy  vehicle motion electric energy  turning mixer, drill, etc. wind turbine  electrical energy  turn mixer

3. 3 definitions Energy: The work that a physical system is capable of doing in changing from its actual state to a specified reference state … (American Heritage Dictionary) Energy: The capacity to do work. (Physics) What is Work?

4. 4 Work Work is force x distance. energy required Less stored energy is available after productive work is done.

5. 5 Work Work, W SI Unit: J = (N)(m) Work ~ component of force in direction of motion.

6. 6 Example of Work Work = Fcos  x = (80N)(cos40)(11m) = 674 J Given: F = 80N, Angle is 40°,  x is 11m,

7. 7 Energy Positional (Potential), e.g. compressed spring Motional (Kinetic), e.g. moving car

8. 8 Energy Kinetic, K: energy of motion K = ½mv 2. Ex: 2000kg car moving at 10m/s has kinetic energy of 100,000J. Potential, U: stored energy Ex: 1 gallon of gasoline > 100,000,000J.

9. 9 Work-Energy Theorem: The net work done on an object is equal to its change in Kinetic Energy. Ex. Net work = 250J. If m = 20kg, v o = 0, Then final speed is 5m/s: 250 = ½(20)5 2 – 0.

10. 10 Example A 20kg mass is moving at 5m/s. 250J of work (net) are done on it. What is its final speed?

11. 11 A 20kg block slides across a floor. The frictional force on it is 50N. How much work is done on the block by friction in moving 3m? If its initial speed was 5m/s, what is its speed after moving 3m?

12. 12 A 20kg block is pushed with 75N of force. The frictional force on it is 50N. How much net work is done on the block in moving 3m? If its initial speed was 5m/s, what is its speed after moving 3m?

13. 13 How much work does a force perpendicular to an objects displacement do? Answer: Zero. The angle between F and displacement is 90, cos90 = 0.

14. 14 Some Potential Energies Spring: U sp. Gravitational: U g Thermal: U th Chemical, Nuclear first three used in this class

15. 15 Springs F sp = -kx, U sp = ½kx 2. k = “spring constant” in N/m and x is the change in length of the spring. Ex: A 100N/m spring is compressed 0.2m. It exerts (100N/m)(0.2m) = 20N of force. It stores ½(100N/m)(0.2m) 2 = 2J of energy.

16. 16 Gravity F g = mg, U g = mgy Ex: 2kg weighs (2kg)(9.8N/kg) = 19.6N. 3m above floor U g = (2kg)(9.8N/kg)(3m) = 48.8J.

17. 17 Conservation of Energy Individual energy levels change. Net energy is constant. Change in energy is called “work”

18. 18 Energy Conservation Total Energy E = sum of all energies E =  K +  U example: t = 0: K = 0J U = 4000J later: K = 3000J U = 1000J

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20. 20 Conservation of Energy Example: Falling Ball KE increases U (gravitational) decreases E = K + Ug = constant

21. 21 EnergyE1E2E3 Kinetic0½mv 2 2 0 PE-g00mgh PE- spring ½kx 2 00 Totals  ½kx 2 ½mv 2 2 mgh

22. 22 EnergyE(h)E(y) Kinetic0½mv 2 PE-gmghmgy Totals  mgh½mv 2 + mgy Energies and speeds are same at height y Accelerations at y are not same

23. 23 EnergyEiEf Kinetic½mv i 2 0 PE-g00 Thermal0fksfks Totals  ½mv i 2 fksfks Example: The smaller the frictional force fk, the larger the distance, s, it will travel before stopping. s

24. 24 A 2.00kg ball is dropped from rest from a height of 1.0m above the floor. The ball rebounds to a height of 0.500m. A movie- frame type diagram of the motion is shown below. TypeE1E2E3E4E5 gravita- tional mg(1)000mg(1/2) kinetic0½ m(v2) 2 0½ m(v4) 2 0 elastic00PE-elastic00 thermal00PE-thermal

25. 25 By energy conservation, the sum of all energies in each column is the same, = E1 = mg(1) = 19.6J Calculate v2: (use 1st and 2nd columns) mg(1) = ½ m(v2)2. g = ½ (v2)2. v2 = 4.43m/s Calculate PE-thermal: (use 1st and 5th columns) mg(1) = mg(1/2) + PE-thermal mg(1/2) = PE-thermal PE-thermal = 9.8J

26. 26 Calculate PE-elastic: (use 1st and 3rd columns) PE-elastic + PE-thermal = mg(1) PE-elastic + 9.8 = 19.6 PE-elastic = 9.8J Calculate v4: (use 1st and 4th columns) ½ m(v4)2 + PE-thermal = mg(1) ½ m(v4)2 + 9.8 = 19.6 ½ m(v4)2 = 9.8 (v4)2 = 2(9.8)/2 v4 = 3.13m/s

27. 27 Terminology E: total energy of a system E-mech = total energy minus the thermal energy E-mech = E – U th.

28. 28 Power: The time rate of doing work. SI Unit: watt, W = J/s] Example: How much average power is needed to accelerate a 2000kg car from rest to 20m/s in 5.0s? work =  KE

29. 29 Another equation for Power: Ex: A car drives at 20m/s and experiences air- drag of 400N. The engine must use (400N)(20m/s) = 8,000 watts of engine power to overcome this force. 8,000 watts = 10.7 hp. What air drag force acts at 40m/s? How much hp is needed to overcome this drag?

30. 30 Summary Energy measured in joules, related to motion (kinetic) or configuration (potential) work is an energy transfer mechanism (thus can be + or -) power is the rate of energy transfer in joules/s = watts

31. 31 Horsepower: 1 hp = 746 watts For the previous example:

32. 32 What size electric motor is needed to raise 2000lbs = 9000N of bricks at 10cm/s? Minimum Power: P avg = Fv avg = (9000N)(0.1m/s) P = 900 W = 1.2 hp

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