This Week v Work Energy Power Energy makes

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This Week v Work, Energy, Power Energy makes our everyday world work v Where

This Week v Work, Energy, Power Energy makes our everyday world work v Where does energy go? Are we using it up? v How can one store energy? v Where does energy come from. v The heat of the earth v Escape velocity 10/28/2020 Physics 214 summer 2015 1

Work, Energy and Power We all use the words Work, Energy and Power and

Work, Energy and Power We all use the words Work, Energy and Power and indeed our usage is generally correct. Once again, however, we need to write down simple definitions and be able to do calculations. Energy comes in a wide variety of forms. For example if you go on a trip in your car energy is being supplied by the gasoline. Initially some of the energy is used to give the car speed but when you stop gasoline has been used but the car now has no energy. The energy went into the air you passed through, dissipated heat in the tires, brakes and engine and so on. 10/28/2020 Physics 214 summer 2015 2

Energy Conservation If we take a closed system, that is one that nothing can

Energy Conservation If we take a closed system, that is one that nothing can enter or leave, then there is a physical law that energy is conserved. We will define various forms of energy and if we examine the system as a function of time energy may change into different forms but the total is constant. Energy does not have direction just a magnitude and units. Conservation of Energy follows directly from the statement that physical laws do not change as a function of time. 10/28/2020 Physics 214 summer 2015 3

Forms of mechanical energy One obvious form of energy is the energy of a

Forms of mechanical energy One obvious form of energy is the energy of a moving object this is kinetic energy = 1/2 mv 2 A second form of energy is what is called Potential Energy. This energy is the energy stored in a compressed spring or stretched elastic or in an object that is held at rest above the earths surface. When the spring or elastic or the object is released one gets kinetic energy appearing from the stored energy. In the case of a pendulum there is a continual storage and release of energy as the pendulum swings. 10/28/2020 Physics 214 summer 2015 4

Work and energy If an object initially at rest is acted on by a

Work and energy If an object initially at rest is acted on by a net force F it will accelerate and after time t will have moved a distance d + F d We define Work W = Fd units are joules Both F and d can be + of – so W can be positive or negative Now take our usual equations v = v 0 + at d = v 0 t +1/2 at 2 and F = ma Fd = ma(1/2 at 2) = ma(1/2 av 2/a 2) = 1/2 mv 2 Or v 2 – v 02 = 2 ad 1/2 mv 2 – 1/2 mv 02 = mad = Fd 10/28/2020 Physics 214 2015 F is the net force in the direction ofsummer motion 5

Negative Work F If F is in the opposite direction to the motion then

Negative Work F If F is in the opposite direction to the motion then Fd is negative. d Remember F and d have magnitude and direction and can be positive or negative. If the work is negative energy is being removed from the object Friction always opposes motion and the work Ff does is negative 10/28/2020 F Ff W = Fd - Ffd Physics 214 summer 2015 6

Net force and Work If there is more than one force acting we have

Net force and Work If there is more than one force acting we have to find the work done by each force and the work done by the net force Net force F – Ff F Ff d work = (F – Ff)d = 1/2 mv 2 The work the force F does is Fd and if we write the equation as Fd = Ffd + 1/2 mv 2 we can see that some work goes into heat and some into kinetic energy and we can account for all the work and energy 10/28/2020 Physics 214 summer 2015 7

1 M-04 Pile Driver The kinetic energy of a pendulum is transferred to a

1 M-04 Pile Driver The kinetic energy of a pendulum is transferred to a block which then slides to rest What happens to the Potential Energy of the Mass M ? The potential energy of the pendulum is turned into kinetic energy. Then if the collision is perfectly elastic all the kinetic energy is transferred to the block and then the energy is turned into heat through friction. Mgh = Ffd Ff is the average frictional force between the block and the wood. 10/28/2020 Physics 214 summer 2015 8

1 M-05 Pile Driver A Pile Driver does work on a nail What happens

1 M-05 Pile Driver A Pile Driver does work on a nail What happens to the Potential Energy of the Mass M ? Work-Energy Relationship mg(h+y) = fy f is the average friction force between the nail and the wood. POTENTIAL ENERGY CHANGES TO KINETIC ENERGY, KINETIC ENERGY CHANGES TO WORK. 10/28/2020 Physics 214 summer 2015 9

Potential energy If we raise an object a height h so that it starts

Potential energy If we raise an object a height h so that it starts and finishes at rest then the average force = mg and the work done = mgh. This energy is stored as potential energy since if the mass is allowed to fall back to it’s original point then h F = mg g v 2 = v 02 + 2 gh and mgh = 1/2 mv 2 So the original work in lifting is stored and then returned as kinetic energy Similarly for a spring stored energy = 1/2 kx 2 Where x is the distance stretched 10/28/2020 Physics 214 summer 2015 10

Potential energy Unlike kinetic energy for Potential energy we have to define where zero

Potential energy Unlike kinetic energy for Potential energy we have to define where zero is. d h A block is at a height h above the floor and d above the desk. Potential energy is mgh with respect to the floor but mgd with respect to the desk. If we dropped block it would have more kinetic energy hitting the floor than hitting the desk 10/28/2020 Physics 214 summer 2015 11

Oscillations Many simple systems oscillate with a continual transfer from KE to PE and

Oscillations Many simple systems oscillate with a continual transfer from KE to PE and PE to KE with the sum of the two remaining constant. In practice energy is lost through friction and the motion slows down. http: //www. physics. purdue. edu/class/ applets/phe/pendulum. htm http: //www. physics. purdue. edu/academic_programs/courses/phys 214/movies. php (anim 0006. mov) (anim 0007. mov) (anim 0009. mov) 10/28/2020 Physics 214 summer 2015 12

1 M-01 Bowling Ball Pendulum A bowling ball attached to a wire is released

1 M-01 Bowling Ball Pendulum A bowling ball attached to a wire is released like a pendulum Is it safe to stand here after I release the bowling ball ? mgh h 1/2 mv 2 mgh = 1/2 mv 2 NO POSITIVE WORK IS DONE ON THE BALL THUS, THERE IS NO GAIN IN TOTAL ENERGY THE BALL WILL NOT GO HIGHER THAN THE INITIAL POSITION 10/28/2020 Physics 214 summer 2015 13

1 M-03 Triple Chute Three Steel Balls travel down different Paths Each path is

1 M-03 Triple Chute Three Steel Balls travel down different Paths Each path is clearly different. Which ball will travel the farthest ? The Change in Gravitational Potential Energy does not depend on the Path Traveled EACH BALL HAS SAME KINETIC ENERGY AT BOTTOM OF RAMP, REGARDLESS OF THE PATH TAKEN AND HAS THE SAME VELOCITY EACH OF THE STEEL BALLS LANDS AT THE SAME POSITION 10/28/2020 Physics 214 summer 2015 14

Conservative forces Gravity is an example of a conservative force where total energy is

Conservative forces Gravity is an example of a conservative force where total energy is conserved and there is just an interchange between kinetic and potential energy. In real life frictional forces would cause energy to be lost as heat For a conservative force if no energy is added or taken out then E = PE + KE 10/28/2020 Physics 214 summer 2015 15

1 M-08 Galileo Track Ball travels down one ramp and up a much steeper

1 M-08 Galileo Track Ball travels down one ramp and up a much steeper ramp Will the ball travel to a lower or higher height when going up the steeper, shorter ramp ? Conservation of Energy: mgh = 1/2 mv 2 = mgh So, The Ball should return to the same height AS THE BALL OSCILLATES BACK AND FORTH, THE HEIGHT IS REDUCED BY A LITTLE. WHAT MIGHT ACCOUNT FOR THIS? FRICTION IS SMALL, BUT NOT ZERO. 10/28/2020 Physics 214 summer 2015 16

1 M-10 Loop-the-Loop Ball travels through a Loop-the-Loop From what height should the ball

1 M-10 Loop-the-Loop Ball travels through a Loop-the-Loop From what height should the ball be dropped to just clear the Loop-the. Loop ? Conservation of Energy: mgh = mg(2 R) + 1/2 mv 2 At the top of the loop N + mg = mv 2/r The minimum speed is when N = 0 Therefore h = 5/2 R (Friction means in practice H must be larger) 10/28/2020 Physics 214 summer 2015 17

Power It is not only important how much work is done but also the

Power It is not only important how much work is done but also the rate at which work is done So the quantity Power = P = W/t (unit is a watt) is very important. Generally energy supplies, motors etc are rated by power and one can determine how much work can be done by multiplying by time. W = Pt 10/28/2020 (joules) Physics 214 summer 2015 18

Watts and Joules Joule is the Unit of Energy and Energy is the fundamental

Watts and Joules Joule is the Unit of Energy and Energy is the fundamental resource that is required for all activity and for life itself. All our energy comes from the sun although there is geothermal energy which was produced by the formation of the earth and tidal motion produced by the motion of the moon. Practical The unit for electrical usage is the kilowatt –hour. A kilowatt – hour is the energy used by a 1000 watt device for 3600 seconds 1 k. WHr = 1000*3600 = 3. 6 million joules Watt is the Unit of Power and Power measures the rate at which work is done or energy is used. All appliances, motors etc are rated in Watts so that one can match to the required application. Example. In order to lift an elevator with a mass of 1000 kg to 100 meters requires 1000*9. 8*100 joules but we need to do it in say 20 seconds so the power we need is 1000*9. 8*100/20 = 49000 Watts so we need to install a motor rated at > 49000 watts 10/28/2020 Physics 214 summer 2015 19

Mechanical Advantage Very often we are limited by the maximum force we can apply

Mechanical Advantage Very often we are limited by the maximum force we can apply and the power we can supply. This is also true of electric motors. One can design simple arrangements so that for example one can lift a large weight by using a lever or a pulley system that reduces the force. The total work done is the same as lifting the weight directly but for example using a force which is half the weight but pulling it for twice the distance http: //www. physics. purdue. edu/class/applets/phe/ pulleysystem. htm 10/28/2020 Physics 214 summer 2015 20

Where do we get energy? v Power comes from the sun 1. 35 kilowatts/m

Where do we get energy? v Power comes from the sun 1. 35 kilowatts/m 2 on the atmosphere and a maximum of about 1 kilowatt/m 2 on earth. In one hour 1 kilowatt = 3600 x 103 joules. A toaster is usually 1 to 2 kilowatts. v. Burning fossil fuels and making new molecules carbon plus oxygen gives CO 2 plus energy v Nuclear power plants breaking heavy nuclei into lighter nuclei 10/28/2020 Physics 214 summer 2015 21

The heat of the earth First we have to define what heat is. Heat

The heat of the earth First we have to define what heat is. Heat is the internal energy stored in an object by the motion of it’s constituent particles (e. g. atoms) How do we get heat in our everyday life? We can transfer mechanical energy of an object into heat. For example if drop a brick the kinetic energy just before impact is turned into heat. An object can also be heated by bombarding it with particles of which photons from the sun is a common example. That is why snow and ice can melt even if the temperature is below freezing About 60% of the heat in the earth comes from the original formation due to loss of potential energy and impact of the material that makes up the earth. About 40% comes from energy emitted in radioactive decays 10/28/2020 Physics 214 summer 2015 22

Escape velocity Suppose we want to propel an object to a height of 1

Escape velocity Suppose we want to propel an object to a height of 1 kilometer. If we assume that g is 9. 8 m/s 2 and no friction then 1/2 mvi 2 = mgh so vi 2 = 19600 and v = 140 m/s this is about 315 mph. To fire an object so that it never returns requires a speed of 11200 m/s or 25000 mph. The highest projectile ever fired was from a 16 inch gun with a barrel length of 176 feet and it reached an altitude of 112 miles or 180 km. 10/28/2020 Physics 214 summer 2015 HARP Project, Barbados 23

Summary of Chapter 6 W = Fd joules and can be + or –

Summary of Chapter 6 W = Fd joules and can be + or – Power = W/t KE = 1/2 mv 2 F watts F joules PE = mgh or 1/2 kx 2 joules d d Conservative E = KE + PE Gravity, oscillations such as a pendulum or mass on a spring and KE and PE just keep interchanging http: //www. physics. purdue. edu/class/applets/p he/springpendulum. htm 10/28/2020 Physics 214 summer 2015 24

Questions Chapter 6 Q 1 Equal forces are used to move blocks A and

Questions Chapter 6 Q 1 Equal forces are used to move blocks A and B across the floor. Block A has twice the mass of block B, but block B moves twice the distance moved by block A. Which block, if either, has the greater amount of work done on it? Explain. Work is Force times distance so the most work is done on B Q 3 A string is used to pull a wooden block across the floor without accelerating the block. The string makes an angle to the horizontal. A. Does the force applied via the string do work on the block? F d B. Is the total force involved in doing work or just a portion of the force? A. Yes B. just the horizontal component 10/28/2020 Physics 214 summer 2015 25

Q 4 In the situation pictured in question 3, if there is a frictional

Q 4 In the situation pictured in question 3, if there is a frictional force opposing the motion of the block, does this frictional force do work on the block? Explain. Yes it does negative work since force is opposite the motion Q 8 A woman uses a pulley, arrangement to lift a heavy crate. She applies a force that is one-fourth the weight of the crate, but moves the rope a distance four times the height that the crate is lifted. Is the work done by the woman greater than, equal to, or less than the work done by the rope on the crate? Explain. The product Fd is the same for both and the work is equal 10/28/2020 Physics 214 summer 2015 26

Q 12 A child pulls a block across the floor with force applied by

Q 12 A child pulls a block across the floor with force applied by a horizontally held string. A smaller frictional force also acts upon the block, yielding a net force on the block that is smaller than the force applied by the string. Does the work done by the force applied by the string equal the change in kinetic energy in this situation? No energy because is lost to friction. Fd – Ffd = 1/2 mv 2 Q 18 Suppose that work is done on a large crate to tilt the crate so that it is balanced on one edge, as shown in the diagram, rather than sitting squarely on the floor as it was at first. Has the potential energy of the crate increased in this process? Yes. Work has been put in and the center of mass is now higher 10/28/2020 Physics 214 summer 2015 27

Q 22 A pendulum is pulled back from its equilibrium (center) position and then

Q 22 A pendulum is pulled back from its equilibrium (center) position and then released. A. What form of energy is added to the system prior to its release? B. At what points in the motion of the pendulum after release is its kinetic energy the greatest? C. At what point is the potential energy the greatest? A. Potential B. at it’s lowest point C. At the highest points where it stops Q 28 Suppose that a mass is hanging vertically at the end of a spring. The mass is pulled downward and released to set it into oscillation. Is the potential energy of the system increased or decreased when the mass is lowered? The potential energy is increased 10/28/2020 Physics 214 summer 2015 28

Ch 6 E 2 Woman does 160 J of work to move table 4

Ch 6 E 2 Woman does 160 J of work to move table 4 m horizontally. What is the magnitude of horizontal force applied? F d Force & displacement in SAME direction W = Fd, 160 J = F(4 m) F = 40 N 10/28/2020 Physics 214 summer 2015 29

Ch 6 E 8 5. 0 kg box lifted (without acceleration) thru height of

Ch 6 E 8 5. 0 kg box lifted (without acceleration) thru height of 2. 0 m a) What is increase in potential energy? b) How much work was required to lift box? a) PE = mgh PE = PEfinal – PEinitial = mg(ho+2. 0 m) – mgho = mg(2. 0 m) = (5. 0 kg)(9. 8 m/s 2)(2. 0 m) = 98 J b) F = ma = 0 = Flift – mg Flift = mg = (5. 0 kg)(9. 8 m/s 2) = 49 N W = Fd = (49 N)(2. 0 m) = 98 J 10/28/2020 Physics 214 summer 2015 M ho+2. 0 m M g Flift M mg 30

Ch 6 E 10 To stretch a spring a distance of 0. 70 m,

Ch 6 E 10 To stretch a spring a distance of 0. 70 m, 40 J of work is done. What is the increase in potential energy? b) What is the value of the spring constant k? x=0 a) PE = 40 J x=0. 70 m equilibrium b) PE = ½ kx 2 k = 2 PE/x 2 = 80/(0. 7)2 - = 296. 8 n/m 10/28/2020 Physics 214 summer 2015 31

Ch 6 E 18 The frequency of oscillation of a pendulum is 8 cycles/s.

Ch 6 E 18 The frequency of oscillation of a pendulum is 8 cycles/s. What is its period? x T f = 1/T T = 1/f = 1/(8 cycles/s) T = 0. 125 seconds 10/28/2020 Physics 214 summer 2015 t 32

Ch 6 CP 2 100 kg crate accelerated by net force = 50 N

Ch 6 CP 2 100 kg crate accelerated by net force = 50 N applied for 4 s. a) Use Newton’s 2 nd Law to find acceleration? b) If it starts from rest, how far does it travel in 4 s? c) How much work is done if the net force = 50 N? a) F = ma a = F/m = 50 N/100 kg = 0/5 m/s 2 M Fnet b) d = v 0 t + ½at 2 = ½(0. 5)(4)2 = 4 m c) W = Fd = (50 N)(4 m) = 200 J d) v = v 0 + at = 0 + (0. 5 m/s 2)(4 s) = 2 m/s e) KE = ½mv 2 = ½(100 kg)(2 m/s)2 = 200 J work done equals the kinetic energy. 10/28/2020 Physics 214 summer 2015 33

Ch 6 CP 4 A 0. 20 kg mass is oscillating horizontally on a

Ch 6 CP 4 A 0. 20 kg mass is oscillating horizontally on a friction -free table on a spring with a constant of k=240 N/m. The spring is originally stretched to 0. 12 m from equilibrium and released. a) What is its initial potential energy? b) What is the maximum velocity of the mass? Where does it reach this maximum velocity? c) What are values of PE, KE and velocity of mass when the mass is 0. 06 m from equilibrium. d) What is the ratio of velocity in (c) to velocity in (b) 10/28/2020 Physics 214 summer 2015 34

Ch 6 CP 4 (con‘t) a) PE = 1/2 kx 2 = ½(240)(0. 12)2

Ch 6 CP 4 (con‘t) a) PE = 1/2 kx 2 = ½(240)(0. 12)2 = 1. 73 J x=0 b) No friction so energy is conserved E=PE+KE, maximum KE when PE=0 KEmax = 1/2 mv 2 v = 4. 16 m/s. This occurs at the equilibrium position x=0. 12 m M c) PE = 1/2 kx 2 = ½(240)(0. 06)2 = 0. 432 J Since total energy = 1. 73 J then the kinetic energy = 1. 73 – 0. 432 = 1. 3 J KE = 1/2 mv 2 = 1. 3 then v = 3. 6 m/s d) vc/vb = 3. 6/4. 16 = 0. 86 10/28/2020 Physics 214 summer 2015 35

Review Chapters 1 - 6 - d + x Units----Length, mass, time SI units

Review Chapters 1 - 6 - d + x Units----Length, mass, time SI units m, kg, second Coordinate systems Average speed = distance/time = d/t Instantaneous speed = d/Δt Vector quantities---magnitude and direction Magnitude is always positive Velocity----magnitude is speed Acceleration = change in velocity/time =Δv/Δt Force = ma Newtons 10/28/2020 Physics 214 summer 2015 36

Conversions, prefixes and scientific notation giga 1, 000, 000 109 billion 1 in 2.

Conversions, prefixes and scientific notation giga 1, 000, 000 109 billion 1 in 2. 54 cm mega 1, 000 106 million 1 cm 0. 394 in kilo 1, 000 103 thousand 1 ft 30. 5 cm centi 1/100 0. 01 10 -2 hundredth 1 m 39. 4 in milli 1/1000 0. 001 10 -3 thousandth 1 km 0. 621 mi 5280 ft 1. 609 km 1 lb 0. 4536 kg g =9. 8 1 kg 2. 205 lbs g=9. 8 micro 1/1, 000 1/106 10 -6 millionth nano 1/1, 000, 000 1/109 10 -9 billionth 10/28/2020 Physics 214 summer 2015 3. 281 ft 37

Speed, velocity and acceleration v = Δd/Δt a = Δv/Δt v. The magnitude of

Speed, velocity and acceleration v = Δd/Δt a = Δv/Δt v. The magnitude of a is not related to the magnitude of v 2 3 4 1 vthe direction of a is not related to the direction of v v = v 0 + at constant acceleration d = v 0 t + 1/2 at 2 d = 1/2(v + v 0) t d, v 0 v, a can be + or – independently v 2 = v 02 + 2 ad 10/28/2020 Physics 214 summer 2015 38

One dimensional motion and gravity v = v 0 + at d = v

One dimensional motion and gravity v = v 0 + at d = v 0 t + 1/2 at 2 v 2 = v 02 + 2 ad d = ½(v + v 0)t + g = -9. 8 m/s 2 + 10/28/2020 At the top v = 0 and t = v 0/9. 8 At the bottom t = 2 v 0/9. 8 Physics 214 summer 2015 39

Equations v = v 0 + at d = v 0 t + 1/2

Equations v = v 0 + at d = v 0 t + 1/2 at 2 d = ½(v + v 0)t v 2 = v 02 + 2 ad Sometimes you have to use two equations. ` 10/28/2020 h v 0 = 15 m/s v = 50 m/s What is h? v = v 0 + at v 0 50 = 15 + 9. 8 t t = 3. 57 s h = v 0 t + 1/2 at 2 g h = 15 x 3. 57 + 1/2 x 9. 8 x 3. 572 = 116 m v h = ½(15 + 50) x 3. 57 = 116 m Physics 214 summer 2015 40

Projectile Motion axis 1 axis 2 v 1 = constant and d 1 =

Projectile Motion axis 1 axis 2 v 1 = constant and d 1 = v 1 t vv = v 0 v + at and d = v 0 vt + 1/2 at 2 v 1 g 9. 8 m/s 2 h v R Use + down so g is + and h is + v 0 v = 0, 10/28/2020 t 2 = 2 h/a R = v 1 t h = v 0 vt + 1/2 at 2 v = v 0 v + at Physics 214 summer 2015 41

Complete Projectile v 0 v v 1 9. 8 m/s 2 v 1 v

Complete Projectile v 0 v v 1 9. 8 m/s 2 v 1 v 0 v highest point the vertical velocity is zero vv = v 0 v + at so t = v 0 v/9. 8 h = v 0 vt + 1/2 at 2 end t = 2 v 0 v/9. 8 and R = v 1 x 2 v 0 v/9. 8 and the vertical velocity is minus v 0 v 10/28/2020 Physics 214 summer 2015 42

Newton’s Second and First Law Second Law F = ma unit is a Newton

Newton’s Second and First Law Second Law F = ma unit is a Newton (or pound) First Law F = 0 a = 0 so v = constant Third law For every force there is an equal and opposite reaction force N Weight = mg mg Ff F F Ff F = ma 10/28/2020 v = v 0 + at d = v 0 t + ½ at 2 d = ½(v + v 0)t v 2 = v 02 + 2 ad Physics 214 summer 2015 43

Examples + T N g 30 – 8 – T = 4 a T

Examples + T N g 30 – 8 – T = 4 a T – 6 = 2 a 30 – 8 – 6 = 6 a mg N – mg = ma a + N > mg a – N < mg 10/28/2020 Physics 214 summer 2015 44

Forces v. Forces are responsible for all physical phenomena v. Gravitation and the electromagnetic

Forces v. Forces are responsible for all physical phenomena v. Gravitation and the electromagnetic force are responsible for all the phenomena we normally observe in our everyday life. v. Newton’s laws v = v 0 + at F = ma where F is net force d = v 0 t + ½ at 2 d = ½(v + v 0)t v 2 = v 02 + 2 ad v. Every force produces an equal and opposite reaction v. Weight = mg where g = 9. 8 m/s 2 locally v. Apparent weight in an elevator depends on the acceleration a up weight is higher a down weight is lower If your weight becomes zero it’s time to worry because you are in free fall!! 10/28/2020 Physics 214 summer 2015 45

Circular motion, gravitation Ferris wheel N Ff F = ma = mv 2/r v

Circular motion, gravitation Ferris wheel N Ff F = ma = mv 2/r v Rear Ff = mv 2/r Gravitation W = mg Bottom N - mg = mv 2/r top Mg – N = mv 2/r Mg –N = mv 2/r Gm. M/r 2 = mv 2/r v 2 = GM/r T = 2πr/v T 2 = 4π2 r 2/v 2 = 4π2 r 3/GMs T 2/r 3 = 4π2/GMs 10/28/2020 Physics 214 summer 2015 46

Examples of circular motion Vertical motion Looking down N N v v W =

Examples of circular motion Vertical motion Looking down N N v v W = mg mg – N = mv 2/r Side N mg N - mg = mv 2/r 10/28/2020 Ff mg mg = Ff Physics 214 summer 2015 v T mg mg + T = mv 2/r top T - mg = mv 2/r bottom 47

Work energy and Power Kinetic energy = 1/2 mv 2 W = Fd and

Work energy and Power Kinetic energy = 1/2 mv 2 W = Fd and can be + or – F is net force parallel to d. Units are joules Power = W/t watts F v d Potential energy = mgh Spring = 1/2 kx 2 h Oscillations Transfer of KE F = mg g PE Conservative force Transfer of KE PE 10/28/2020 Physics 214 summer 2015 48