Work, Energy, and Power

1. Work, Energy, and Power Samar Hathout KDTH 101

2. Work Work is the transfer of energy through motion. In order for work to take place, a force must be exerted through a distance. The amount of work done depends on two things: the amount of force exerted and the distance over which the force is applied. There are two factors to keep in mind when deciding when work is being done: something has to move and the motion must be in the direction of the applied force. Work can be calculated by using the following formula: Work=force x distance

3. Work Work is done on the books when they are being lifted, but no work is done on them when they are being held or carried horizontally.

4. Work can be positive or negative • Man does positive work lifting box • Man does negative work lowering box • Gravity does positive work when box lowers • Gravity does negative work when box is raised

5.  Work done by a constant Force • W = Fs = |F| |s| cos  = Fs s • |F| : magnitude of force • |s| = s : magnitude of displacement • Fs = magnitude of force in • direction of displacement : • Fs= |F| cos  • : angle between displacement and force vectors • Kinetic energy : Ekin= 1/2 m v2 • Work-Kinetic Energy Theorem: F s Ekin= Wnet

6. Yi = h Yf = hf Yi = h0 Work Done by Gravity • Example 1: Drop ball Wg = (mg)(S) S = h0-hf Wg = mg(h0-hf) = mg(h0-hf) = Epot,initial – Epot,final S S mg mg y y x x

7. Yi = h0 Yf = hf Work Done by Gravity • Example 2: Toss ball up Wg = (mg)(S) S = h0-hf Wg =-mg(h0-hf) = Epot,initial – Epot,final S mg y x

8. Work Done by Gravity • Example 3: Slide block down incline h0 Wg = (mg)(S)cos S = h/cos Wg = mg(h/cos)cos Wg = mgh with h= h0-hf  h S mg hf • Work done by gravity is independent of path taken between h0 and hf • => The gravitational force is a conservative force.

9. Work done by a Variable Force • The magnitude of the force now depends on the displacement: Fs(s) Then the work done by this force is equal to the area under the graph of Fs versus s, which can be approximated as follows: W = S DWi= S Fs(si) Ds = (Fs(s1)+Fs(s2)+…) Ds

10. correct 1 3 2 Concept Question Imagine that you are comparing three different ways of having a ball move down through the same height. In which case does the ball reach the bottom with the highest speed? 1. Dropping2. Slide on ramp (no friction)3. Swinging down4. All the same In all three experiments, the balls fall from the same height and therefore the same amount of their gravitational potential energy is converted to kinetic energy. If their kinetic energies are all the same, and their masses are the same, the balls must all have the same speed at the end.

11. Types of Energy Kinetic Energy Potential Energy

12. Forms of Energy Chemical Sound Radiant Electrical Mechanical Magnetic Thermal Nuclear

13. Mechanical Energy Mechanical energy is the movement of machine parts. Mechanical energy is also the total amount of kinetic and potential energy in a system. Wind-up toys, grandfather clocks, and pogo sticks are examples of mechanical energy. Wind power uses mechanical energy to help create electricity. Potential energy + Kinetic energy = Mechanical energy

14. Mechanical Energy Potential energy + Kinetic energy = Mechanical energy Example of energy changes in a swing or pendulum.

15. Conservation of Mechanical Energy • Total mechanical energy of an object remains constant provided the net work done by non-conservative forces is zero: Etot = Ekin + Epot = constant or Ekin,f+Epot,f = Ekin,0+Epot,0 Otherwise, in the presence of net work done by non-conservative forces (e.g. friction): Wnc = Ekin,f – Ekin,0 + Epot,f-Epot,i

16. correct Example Problem Suppose the initial kinetic and potential energies of a system are 75J and 250J respectively, and that the final kinetic and potential energies of the same system are 300J and -25J respectively. How much work was done on the system by non-conservative forces? 1. 0J 2. 50J3. -50J4. 225J5. -225J Work done by non-conservative forces equals the difference between final and initial kinetic energies plus the difference between the final and initial gravitational potential energies. W = (300-75) + ((-25) - 250) = 225 - 275 = -50J. Samar Hathout Samar Hathout

17. Kinetic Energy Same units as work Remember the Eq. of motion Multiply both sides by m, Samar Hathout

18. Example Samar Hathout

19. Potential Energy • Potential energy exists whenever an object which has mass has a position within a force field (gravitational, magnetic, electrical). • We will focus primarily on gravitational potential energy (energy an object has because of its height above the Earth)

20. Potential Energy If force depends on distance, For gravity (near Earth’s surface) Samar Hathout

21. Conservation of Energy • Conservative forces: • Gravity, electrical, QCD… • Non-conservative forces: • Friction, air resistance… • Non-conservative forces still conserve energy!Energy just transfers to thermal energy Samar Hathout

22. Example A diver of mass m drops from a board 10.0 m above the water surface, as in the Figure. Find his speed 5.00 m above the water surface. Neglect air resistance. 9.9 m/s

23. Example A skier slides down the frictionless slope as shown. What is the skier’s speed at the bottom? start H=40 m finish L=250 m 28.0 m/s

24. Example Three identical balls are thrown from the top of a building with the same initial speed. Initially, Ball 1 moves horizontally. Ball 2 moves upward. Ball 3 moves downward.Neglecting air resistance, which ball has the fastest speed when it hits the ground? A) Ball 1 B) Ball 2 C) Ball 3 D) All have the same speed.

25. Springs (Hooke’s Law) Proportional to displacement from equilibrium

26. DPE=-FDx F Dx Potential Energy of Spring

27. x Example A 0.50-kg block rests on a horizontal, frictionless surface as in the figure; it is pressed against a light spring having a spring constant of k = 800 N/m, with an initial compression of 2.0 cm. b) To what height h does the block rise when moving up the incline? 3.2 cm

28. Power • Average power is the average rate at which a net force does work: Pav = Wnet / t SI unit: [P] = J/s = watt (W) Or Pav = Fnet s /t = Fnet vav

29. Example A 1967 Corvette has a weight of 3020 lbs. The 427 cu-in engine was rated at 435 hp at 5400 rpm. a) If the engine used all 435 hp at 100% efficiency during acceleration, what speed would the car attain after 6 seconds? b) What is the average acceleration? (in “g”s) a) 120 mph b) 0.91g

30. Example Consider the Corvette (w=3020 lbs) having constantacceleration of a=0.91g a) What is the power when v=10 mph? b) What is the power output when v=100 mph? a) 73.1 hp b) 732 hp (in real world a is larger at low v)