Microsoft PowerPoint - 7-Work and Energy.ppt

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1 Chapter 7. Work and Energy 일과운동에너지 One of the most important concepts in physics Alternative approach to mechanics Many applications beyond mechanics Thermodynamics (movement of heat) Quantum mechanics... Very useful tools Very useful tools You will learn new (sometimes much easier) ways to solve problems Physics, Page 1

2 Question You toss a ball in the air. What is the work done by gravity as the ball goes up? A) Positive B) Negative C) Zero What is the work done by gravity as the ball goes down? A) Positive B) Negative C) Zero Physics, Page 2

3 Example: F N f F W Find work done by each force. S Answers: F: FS f: -fs F N :0 W: 0 Physics, Page 3

4 Question You are towing a car up a hill with constant velocity. The work done on the car by the normal force is: F N V 1. positive 2. negative 3. zero correct T W because it's pointing in a positive direction The normal force is perpendicular to the surface and because of this it points in the negative x direction force is perpendicular to displacement Physics, Page 4

5 Question 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 correct 3. zero F N T V W It'll be positive because Fg=mg, 9.8m/s^2 will always be positive When the car is heading up the hill the weight or gravitational force points opposite to that of the displacement, producing and angle greater than 90 degrees, producing a negative number, and negative work. there is no displacement by gravity, so no work. Physics, Page 5

6 Question You are towing a car up a hill with constant velocity. The work done on the car by the tension force is: 1. positive correct 2. negative 3. zero F N T V W The force T is going in the direction of the displacement, so it has to be positive. The force of the rope is going the opposite direction, in order to pull the car. Since the car is traveling at a constant velocity it has no acceleration Physics, Page 6

7 Question 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 correct F N T V W The car is going up, is it not? Because the car wants to go in the opposite direction of the way in which it is being pulled up the hill. Physics, Page 7

8 Energy Forms Kinetic Energy ( 운동에너지 ) Potential Energy ( 위치에너지 ) : 8장 Heat : 18장 Mass (E=mc 2 ) : 37장 Units Joules = kg m 2 / s 2 Physics, Page 8

9 운동에너지 (Kinetic Energy) 단위 : Joules = kg m 2 / s 2 ( 보기문제 7-1) Physics, Page 9

10 Definition of Work Ingredients: Force (F), displacement (S) Work, W, done on object by a constant force F acting through a displacement S is: Units: W = F i S = FS cosθ [W] = [F][L] = N-m = Joules (J) 1 Joule = 1 Newton-meter (N-m) F θ F s S displacement Physics, Page 10

in case b, trunk only moves ½ distance you pull rope.

11 Work: Energy Transfer due to Force Force to lift trunk at constant speed Case a T a mg = 0 T = mg Case b 2T b - mg =0 or T = ½ mg But in case b, trunk only moves ½ distance you pull rope. (F x distance) is same in both! T a T b T b mg W = FScosθ mg Physics, Page 11 15

12 1) 2) 3) 4) Work by Constant Force Only component of force parallel to direction of motion does work! W = F Δr cos θ F Δr W>0 W=0 W<0 Δr F Δr Δr F F W F > 0: 0< θ < 90 : cos(θ) > 0 W F = 0: θ =90 : cos(θ) =0 W F < 0: 90< θ < 270 : cos(θ) < 0 W F > 0: 0> θ > -90 : cos(θ) > 0 θ F Δr Physics, Page 12 18

13 A box is pulled up a rough (μ > 0) incline by a rope-pulley-weight arrangement as shown below. How many forces are doing (non-zero) work on the box? correct T Question v N Four forces are on the box. N does no work (perp. to v) T does positive work f does negative work f mg does negative work mg Physics, Page 13

14 일 (Work) 일 W 이란물체에가해진힘을통해서외부에서물체 ( 의에너지 ) 로 (W > 0), 또는, 물체 ( 의에너지 ) 에서외부로 (W < 0) 전달되는에너지이다. 일과운동에너지변화 F = Fcosφ = ma x x 운동에너지변화 Δ K = W 힘이한일 일-운동에너지정리 물체의운동에너지변화량은물체에행해진알짜일과같다. Δ K = K K = W K f = Ki + W f i Physics, Page 14

15 Falling Ball Example Ball falls a distance 5 meters. What is final speed? (g = 10 m/s 2 ) Only force/work done be gravity W g = F g h = m ½ (v f2 v i2 ) F g h = ½m v f 2 mg mgh = ½m v f 2 V f = sqrt( 2 g h ) = 10 m/s Physics, Page 15

16 ( 보기문제 7-2) Physics, Page 16

17 ( 보기문제 7-5) 중력이한일 d W = mg i d g W = mg i d = mgdcos( θ + 90 ) = mgdsinθ = mgh g 장력이한일 Physics, Page 17

18 Work by Variable Force W = F x Δx : constant force Work is area under F-x plot Spring F ~ k x : variable force Force Work Distance Area = ½ k x 2 = W spring Force F~kx Work Distance Physics, Page 18 48

19 변하는힘이한일 변하는힘 Physics, Page 19

20 용수철힘 ( 복원력 ) 이한일 F s = kd ( k : 용수철상수 ) 복원력이 ( 물체에 ) 한일이란복원력증가할때물체의 ( 운동 ) 에너지가감소, 즉, 물체에서외부 ( 용수철 ) 로에너지가전달되므로, W < 0 Physics, Page 20

21 ( 보기문제 7-7) -12mm 까지이동하는동안물체에한일 ( F s = Fa ) F a = F = 6.9N s W = W = 59mJ a s W > 0 : 물체가에너지를받음 Physics, Page 21

22 ( 보기문제 7-8) m d = v = 1.2cm k Physics, Page 22

23 변하는힘에대한일-운동에너지정리 W = K K =ΔK f i ( 일정한힘의경우와동일하게성립 ) Physics, Page 23

24 일률 (Power) P= F i v Physics, Page 24

25 ( 보기문제 7-11) Physics, Page 25

26 Work = transfer of energy using force Can be positive, negative, or zero W = F d cos(θ) Kinetic Energy (Motion) K = ½ m v 2 Work = Change in Kinetic Energy Σ W = ΔK Summary Physics, Page 26

I&IRC5 TG_08권

I&IRC5 TG_08권 I N T E R E S T I N G A N D I N F O R M A T I V E R E A D I N G C L U B The Greatest Physicist of Our Time Written by Denny Sargent Michael Wyatt I&I Reading Club 103 본문 해석 설명하기 위해 근래의 어떤 과학자보다도 더 많은 노력을