1. UB, Phy101: Chapter 6, Pg 1 Physics 101: Chapter 6 Work and Kinetic Energy l New stuff: Chapter 6, sections 6.1 - 6.7

2. UB, Phy101: Chapter 6, Pg 2 Work & Energy l One of the most important concepts in physics è Alternative approach to mechanics l Many applications beyond mechanics è Thermodynamics (movement of heat) è Quantum mechanics... l Very useful tools è You will learn new (sometimes much easier) ways to solve problems

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6. UB, Phy101: Chapter 6, Pg 6 Work/Kinetic Energy Theorem: NetWork {Net Work done on object} = changekinetic energy {change in kinetic energy of object} l Also works for a variable force KE Demo

7. UB, Phy101: Chapter 6, Pg 7 l Work and Kinetic Energy:   KE = W net W F = |F| |S| cos  KE = 1/2 mv 2 Work-Kinetic Energy Theorem:

8. UB, Phy101: Chapter 6, Pg 8 Chapter 6, Preflight You are towing a car up a hill with constant velocity. The work done on the car by the normal force is: 1. positive 2. negative 3. zero W T FNFN V The normal force is perpendicular to the displacement, hence, does no work correct

9. UB, Phy101: Chapter 6, Pg 9 Chapter 6, Preflight You are towing a car up a hill with constant velocity. The work done on the car by the gravitational force is: 1. positive 2. negative 3. zero with the surface defined as the x-axis, the x component of gravity is in the opposite direction of the displacement, therefore work is negative. W T FNFN V correct

10. UB, Phy101: Chapter 6, Pg 10 Chapter 6, Preflight You are towing a car up a hill with constant velocity. The work done on the car by the tension force is: 1. positive 2. negative 3. zero Tension is in the same direction of the displacement W T FNFN V correct

11. UB, Phy101: Chapter 6, Pg 11 Chapter 6, Preflight You are towing a car up a hill with constant velocity. The total work done on the car by all forces is: 1. positive 2. negative 3. zero The car is not accelerating, so it has a net force of zero and since work=Fcos0(s), work too will equal zero. W T FNFN V correct the initial KE equils the final KE and so the difference is zero

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15. UB, Phy101: Chapter 6, Pg 15 Work Done by Gravity l Example 1: Drop ball Y i = h Y f = 0 W g = (mg)(S)cos  S = h W g = mghcos(0 0 ) = mgh  y = y f -y i = -h W g = -mg  y mg S y x Y i = h Y f = 0 mg S y x

16. UB, Phy101: Chapter 6, Pg 16 Work Done by Gravity Example 2: Toss ball up W g = (mg)(S)cos  S = h W g = mghcos(180 0 ) = -mgh  y = y f -y i = +h W g = -mg  y Y i = h Y f = 0 mg S y x

17. UB, Phy101: Chapter 6, Pg 17 Work Done by Gravity Example 3: Slide block down incline W g = (mg)(S)cos  S = h/cos  W g = mg(h/cos  )cos  W g = mgh  y = y f -y i = -h W g = -mg  y h  mg S

18. UB, Phy101: Chapter 6, Pg 18 Summary: Work Done by Gravity Independent of path W g = -mg(y f - y i ) = -mg  y If you end up where you began, Wg = 0 We call this a “Conservative Force” because we can define a “Potential Energy” to go with it.

19. UB, Phy101: Chapter 6, Pg 19 Chapter 6, Preflight Chapter 6, Preflight (who read section 6.4 in the book ?) Which of the following statements correctly define a Conservative Force: 1. A force is conservative when the work it does on a moving object is independent of the path of the motion between the object's initial and final positions. 2. A force is conservative when it does no net work on an object moving around a closed path, starting and finishing at the same point. 3. Both of the above statements are correct. 4. Neither of the above statements is correct. correct

20. UB, Phy101: Chapter 6, Pg 20 Chapter 6, Preflight Imagine that you are comparing three different ways of having a ball move down through the same height. In which case does the ball get to the bottom first? 1. Dropping 2. Slide on ramp (no friction) 3. Swinging down 4. All the same It seems logical because A has the shortest distance to go, although the answer is probably all 3, for some crazy physics reason. 1 2 3 correct

21. UB, Phy101: Chapter 6, Pg 21 Chapter 6, Preflight 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. Dropping 2. Slide on ramp (no friction) 3. Swinging down 4. 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. 1 2 3 correct

22. UB, Phy101: Chapter 6, Pg 22 Friction Demo

23. UB, Phy101: Chapter 6, Pg 23 Modified Work-Kinetic Energy Theorem Work-Kinetic Energy Theorem: W NC =  KE +  PE g =  KE + mg  y E = total energy = KE + PE g W NC =  E = E f - E ih Conservation of Energy: If W NC = 0, then E f = E i (KE+PE g ) initial = (KE+PE g ) final NC: all forces except gravity Friction Demo 2

24. UB, Phy101: Chapter 6, Pg 24 Chapter 6, Preflight 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. 50J 3. -50J 4. 225J 5. -225J correct 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.

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