Work, Energy and Power Chapter 6 – READ!

Work – When a force acts on an object to cause movement of the object, it is said that work was done upon the object. Work tells us how much a force changes the energy of a system. dot product Angle between F and d Component of force parallel to distance moved Work - a bridge between force (a vector) and energy (a scalar)

Dot Product The product of the magnitudes of 2 vectors and the angle between them. The result is a SCALAR. A B q Result is a scalar that measures how much of one vector lies along the direction of the other. Bcosq

Work SI Unit of work is Joule: J = (N)(m) Work is a SCALAR dot product Component of force parallel to the distance moved SI Unit of work is Joule: J = (N)(m) Work is a SCALAR

Force and direction of motion both matter in defining work! There is no work done by a force if it causes no movement. Forces can do positive, negative, or zero work. When an box is pushed on a flat floor, for example… The normal force and gravity do no work, since they are perpendicular to the direction of motion. The person pushing the box does positive work, since she is pushing in the direction of motion. Friction does negative work, since it points opposite the direction of motion.

Work Question Fapp Dx FG Is this bellhop doing work on the suitcases as he walks forward at constant speed? FG Fapp Dx

Work Question If a man lifts a 50 kg barbell 2 m, how much work does he do on the barbell? h FG Fapp

Example: Work done on a crate Example: Work done on a crate. A 50 kg crate is pulled 40 m along a horizontal floor by a constant force exerted by a, FP = 100 N, which acts at a 370 angle. The floor is rough and exerts a friction force fK = 50 N. Determine the work done by each force on the crate and the net work done on the crate. FG FN FP=100 fK 370 d = 40m

Example: Work done on a crate. FG FN FP fK 370 Dx = 40m

Example: Work done on a crate. FG FN FP fK 370 d = 40m

Does Earth do work on the Moon Does Earth do work on the Moon? The Moon revolves around the Earth in a circular orbit, kept there by the gravitational force exerted by the Earth. Does gravity do a) positive work, b) negative work, or c) no work at all? v FG

Question: Work on a backpack Question: Work on a backpack. a) How much work does a hiker do on a 150kg backpack to carry it up a hill of height h = 100m. Determine b) the work done by gravity on the backpack, c) the net work done on the backpack. Assume the motion is smooth and at constant velocity. FG FH Dd h=100 q

FH d h=100 FG q Question: Work on a backpack. Gravity does work only in vertical direction

Work Done by a Varying Force

Work Done by a Constant Force The force shown is a constant force. W = Fd can be used to calculate the work done by this force when it moves an object from xi to xf. The area under the curve from xi to xf can also be used to calculate the work Work = AREA under F-x curve

Work Done by a Varying Force The force shown is a variable force. W = F·d CANNOT be used to calculate the work done by this force. The area under the curve from xi to xf can STILL be used to calculate the work Work = AREA under F-x curve

How much work is done by the force shown when it Sample Problem How much work is done by the force shown when it acts on an object and pushes it from x = 0.25 m to x = 0.75 m?

Sample Problem How much work is done by the force shown when it acts on an object and pushes it from x = 2.0 m to x = 4.0 m?

More Work Done by a Varying Force SPRINGS 19

Springs When a spring is stretched or compressed from its equilibrium position, it does negative work since the spring pulls in the direction opposite the direction of motion. Hooke’s Law: The force exerted by a spring is directly proportional to the distance the spring is stretched from the equilibrium position. F = -kx F : Force (N) k : spring constant (N/m) Describes the stiffness of the spring x : displacement (m) Fsp Fpull

Springs When a spring is stretched or compressed from its equilibrium position, it does negative work since the spring pulls in the direction opposite the direction of motion. Force of a spring varies with Dx Fsp Fpull Dx x 21

Springs When a spring is stretched or compressed from its equilibrium position, it does negative work since the spring pulls in the direction opposite the direction of motion. Fsp Fpull Fsp = -kx

It takes 180 J of work to compress a certain spring 0.10 m. Sample Problem It takes 180 J of work to compress a certain spring 0.10 m. What is the spring constant of the spring? To compress the spring an additional 0.10 m, does it take 180J, more than 180 J, or less than 180J. Verify your answer with a calculation.

Sample Problem A vertical spring (ignore its mass) with spring constant 900 N/m, is attached to a table and compressed 0.150 m with a ball. When released, what is the launch speed of the 0.30 kg ball? Fspr Fspr=kx FPush Dx With gravity

Springs - Practice You have two springs that are identical except that spring 1 is stiffer than spring 2 (k1>k2). On which spring is more work done a) if they are stretched using the same force? b) if they are stretched the same distance? Spring2, k2 smaller/looser so spring stretches farther with same force Spring1, k1 larger/stiffer so need larger F to stretch same distance

Power Power is the rate of which work is done. P = W/Dt = Fv W: work in Joules Dt: elapsed time in seconds When we run upstairs, t is small so P is big. When we walk upstairs, t is large so P is small.

Unit of Power SI unit for power is the Watt 1 W = 1 J/s W: work in Joules Dt: elapsed time in seconds Named after the Scottish engineer James Watt (1776-1819) who perfected the steam engine.

Sample problem: A record was set for stair climbing when a man ran up the 1600 steps of the Empire State Building in 10 min and 59 sec. If the height gain of each step was 0.20 m, and the man’s mass was 70.0 kg, what was his average power output during the climb? FG Fapp

Sample problem: Calculate the power output of a 1 Sample problem: Calculate the power output of a 1.0 g fly as it walks straight up a window pane at 2.5 cm/s. FG Ffly

Sample problem: Cary pushes a 15 kg lawn mower across a lawn at a constant speed by pushing with a force of 115 N along the direction of the handle which makes a 22.50 angle with the horizontal. a) If Carey develops 64.6 W for 90.0 s, what distance is the lawn mower pushed? b) What is the work done by friction? What is the coefficient of friction between the lawn mower and the lawn? If the initial speed of the lawn mower is 1 m/s and Cary then increases her pushing force so that the lawn mower speeds up to 2 m/s after 20 m, what is Cary’s new pushing force? 54.7 m -5814 J 0.56 316 N 30

Energy – has the ability to do work

Work and Energy Work changes mechanical energy! If an applied force does positive work on a system, it tries to increase mechanical energy. If an applied force does negative work, it tries to decrease mechanical energy. The two forms of mechanical energy are called potential and kinetic energy.

Kinetic Energy Energy due to motion Unit: Joule Sample: A 10.0 g bullet has a speed of 1.2 km/s. a)What is the kinetic energy of the bullet? b)What is the bullet’s kinetic energy if the speed is halved? c)What is the bullet’s kinetic energy if the speed is doubled?

The net work done on an object changes its kinetic energy. Work-Energy Theorem for Fnet The net work done on an object changes its kinetic energy.

energy of translational motion SI unit of kinetic energy: Joule If positive work done on an object, its KE increases If negative work done on object, its KE decreases SI unit of kinetic energy: Joule KE is a scalar KE of a group of objects is the algebraic sum of the KEs of the individual objects

Question: KE and work done on a baseball Question: KE and work done on a baseball. A 145 g baseball is thrown with a speed of 25 m/s. a) What is its kinetic energy? b) How much work was done on the baseball to make it reach this speed if it started from rest?

Question: Work on a car, to increase its KE Question: Work on a car, to increase its KE. How much work is required to accelerate a 1000 kg car from 20 m/s to 30 m/s?

Question: A 15 g acorn falls from a tree and lands on the ground 10 m below with a speed of 11.0 m/s. What would the speed of the acorn have been if there had been no air resistance? Did air resistance do positive, negative or zero work on the acorn? Why? How much work was done by air resistance? What was the average force of air resistance? Fa FG 10m

How We Buy Energy… The kilowatt-hour is a commonly used unit by the electrical power company. Power companies charge you by the kilowatt-hour (kWh), but this not power, it is really energy consumed. 1 kW = 1000 W 1 h = 3600 s 1 kWh = 1000J/s • 3600s = 3.6 x 106J

Energy and its Conservation

Potential Energy Energy associated with forces that depend on the position and/or configuration of an object. Eg. Wound up clock spring has PE because as it unwinds it can do work moving the clock hands. Eg. Gravitational PE. Heavy brick held high in air has PE because of its position. When released it has ability to do work.

Gravitational Potential Energy, GPE To lift an object of mass m vertically a height h (constant velocity): Hand increases the energy of ball by 10J y2 h=1m FG FH Gravity decreases the energy of ball by 10J But where did the energy that the gravitational force took from the ball go? y1 m=1kg

Gravitational Potential Energy, GPE But where did the energy that the gravitational force took from the ball go? FH FG y2 The 10 J of work done lifting the book was stored by the gravitational force and then converted to kinetic energy. The gravitational field stores POTENTIAL ENERGY mgh. Gravity is a conservative force. h=1m y1 m=1kg

Rise FG y1 y2 h Looses KE Gains GPE Gains KE Looses GPE Fall

Gravitational Potential Energy Energy associated with an objects position in the gravitational field. SI unit of PE: Joule PE is a scalar The higher an object is above the ground, the more gravitational potential energy it has Changes in gravitational PE depend ONLY on change in vertical height and NOT on the path taken.

Energy and Conservative Forces Forces such as gravity for which the work done does not depend on the path taken, but only on initial and final positions, are called conservative forces. h FG In ALL cases

What about Friction? FPush=10 fK Dx = 1m FG FN FPush=10 fK Dx = 1m Hand increases the energy of book by 10J Friction decreases the energy of ball by 10J But where did the energy that the frictional force took from the book go?

What about Friction? FPush fK Dx = 1m FG FN FPush fK Dx = 1m But where did the energy that the frictional force took from the book go? It is NOT stored as potential energy. It is converted to heat energy and dissipated. Friction is a nonconservative force.

Elastic Potential Energy xf Dx FPush Fspring=kx Fspring= - kx Spring force is variable Spring decreases the balls energy Hand increases the balls energy

Elastic Potential Energy But where did the energy that the spring force took from the ball go? Dx FPush Fspring The work done compressing the spring was stored by the spring and converted to kinetic energy. The spring stores Elastic POTENTIAL ENERGY 1/2kx2. Elastic force is conservative. Spring force is variable

Potential Energy If a conservative force does positive work on an object, potential energy is lost (KE gained) If a conservative force does negative work on an object, potential energy is gained (KE lost) In general, the change in PE associated with a particular conservative force is equal to the negative of the work done by that force if object moved from one point to another.

Nonconservative Forces Gravitational (GPE=mgh) Friction Elastic (EPE=1/2kx2) Air resistance Electric Tension in a cord Motor or rocket propulsion Push or pull by a person Path independent store energy that is available to convert to KE Path dependent do not store energy that is available to convert to KE

Conservative Forces Work is path independent. Work can be calculated from the starting and ending points only. The actual path is ignored in calculations. Work along a closed path is zero. If the starting and ending points are the same, no work is done by the force. Work changes potential energy. Examples Gravity Spring Force Conservation of mechanical energy holds!

Non-conservative Forces Work is path dependent. Knowing the starting and ending points is not sufficient to calculate the work. Work along a closed path is NOT zero. Work changes mechanical energy. Examples Friction Drag (air resistance) Conservation of mechanical energy does not hold!

How does the gravitational PE depend on the path taken to get to h? Dd FN h FH q FG Path-INDEPENDENT

Energy and Conservative Forces Q: Assume a conservative force moves an object along the various paths. Which two works are equal? A: W2 = W3 (path independence) Q: Which two works when added together, give a sum of zero? A: W1 + W2 = 0 or W1 + W3 = 0 (work along a closed path is zero)

Example: Potential energy changes for a roller coaster Example: Potential energy changes for a roller coaster. A 1000 kg roller coaster car moves from point 1 to point 2 to point 3 to point 4. a) What is the gravitational PE at 2 and 3 relative to 4 (that is set y=0 at 4)? b) What is the change in GPE when it goes from 2 to 3? Repeat but take reference point at point 2.

Example: Potential energy changes for a roller coaster. Reference: at point 4, y=0 Reference: at point 2, y=0

Is This Possible? Why or why not? Roadrunner Clip Rolling Boulder http://www.lghs.net/ourpages/users/dburns/RRPhysics/Road_Runner_Physics/Movie.html

Work-Energy Theorem General form: Nonconservative forces change mechanical energy. If nonconservative work is negative, as it often is, the mechanical energy of the system will drop.

Total Mechanical Energy is conserved Conservation of Mechanical Energy If only conservative forces act on a system: Total Mechanical Energy is conserved If only conservative forces are acting, the total mechanical energy of a system neither increases or decreases.

Conservation of Mechanical Energy In any isolated system, the total energy remains constant. Energy can neither be created nor destroyed, but can only be transformed from one type of energy to another.

Conservation of Mechanical Energy Only gravity acts on the rock and FG is conservative. at any point http://www.batesville.k12.in.us/physics/phynet/Mechanics/Energy/EnergyIntro.html

Falling Rock: If the original height of the stone is 3 Falling Rock: If the original height of the stone is 3.0 m, calculate the stone’s speed when it has fallen to 1.0 m above the ground.

Roller coaster: If a 200 kg roller coaster car is pulled up to point 1, starts from rest and coasts down the track, What will be its energy at point 1 and point 4? What will its speed be at point 4? Draw energy bar diagrams at point 1 and 4. Assume no friction between the car and track and no air drag. A) B)

Roller coaster: d) What would the total and kinetic energy be at point 4 if there was friction between point 3 and 4? The average frictional force between the car and the track is 400 N and the distance between point 3 and 4 is 25m. E1 = E2 = E3 = 68,600J Energy loss due to friction C)

Roller coaster: E1 = E2 = E3 = 68,600J Energy loss of 10,000J due to friction

slope flat

Kingda Ka How fast do you have to go here… … to get here? (h = 456ft = 139m) (0.0006214 mi/m) h=456 feet (139 m) Speed 128mph (0.0006214 mi/m)

Pendulums and Energy Conservation Energy goes back and forth between KE and GPE. At highest point, all energy is GPE. As it drops, GPE goes to KE. At the bottom , energy is all KE.

Example: Pendulum. What is the speed of the pendulum bob at point B if it is released from rest at point A? vB = 2.62 m/s 400 1.5m x A h B

Springs and Energy Conservation Energy goes back and forth between KE and PE. When fully stretched or compressed, all energy is PE. When passing through equilibrium, energy is all KE. At other points in cycle, energy is a mix of PE and KE.

Spring Energy For any two points 1 and 2: all EPE all KE X=0 all EPE all KE For max and min displacement from equilibrium: all EPE

http://www.science-animations.com/support-files/energy.swf Great animations of conservation of energy

Example A dart of mass 0.100 kg is loaded in a toy dart gun. The spring in the gun has a spring constant of 250 N/m. The spring is compressed 6.0 cm and then released. What speed does the dart leave the gun with? vB = 3.0 m/s

Spring example: A 1. 60 kg block slides with a speed of 0 Spring example: A 1.60 kg block slides with a speed of 0.950 m/s on a frictionless, horizontal surface until it encounters a spring with a force constant of 902 N/m. The block comes to rest after compressing the spring 4.00 cm. Find the spring potential energy, U, the kinetic energy of the block, K, and the total mechanical energy of the system, E, for the following compressions: 0 cm, 2.00 cm, 4.00 cm. x v = 0.95 m/s

Spring example: A 1.60 kg block slides with a speed of 0.950 m/s … v = 0.95 m/s

Work Done by Nonconservative Forces Nonconservative forces change mechanical energy. They add or remove energy to the system. If nonconservative work is negative, as it is for friction, the mechanical energy of the system will drop and the amount of energy lost is equivalent to the work done by the non conservative force.

Sample problem: Catching a wave, a 72-kg surfer starts with a speed of 1.3 m/s, drops through a height of 1.75 m, and ends with a speed of 8.2 m/s. How much non-conservative work was done on the surfer? The surfer GAINS energy due to the work added by the water

Does Earth do work on the Moon Does Earth do work on the Moon? The Moon revolves around the Earth in a circular orbit, kept there by the gravitational force exerted by the Earth. Does gravity do a) positive work, b) negative work, or c) no work at all? v FG Centripetal force never does work ( does not add or remove energy)

Fwater (Nonconservative) Sample problem: A 1.75-kg rock is released from rest at the surface of a pond 1.00 m deep. As the rock falls, a constant upward force of 4.10 N is exerted on it by water resistance. Calculate the nonconservative work, WNC, done by the water resistance on the rock, the gravitational PE of the system, GPE, the kinetic energy of the rock, KE, and the total mechanical energy of the system, E, for the following depths below the water’s surface: d = 0 m, d = 0.500 m, d = 1.00 m. Let GPE be zero at the bottom of the pond. h=0 d=0 d=0.5 d=1 Fg (conservative) Fwater (Nonconservative) E0 E0.5 E1 As the rock sinks, it looses energy since the water resistance force is doing negative work. The amount of energy lost is equal to the work done by the force of the water.

Sample problem: A 1.75-kg rock is released from rest at the surface of a pond 1.00 m deep. As the rock falls, a constant upward force of 4.10 N is exerted on it by water resistance. Calculate the nonconservative work, Wnc, done by the water resistance on the rock, the gravitational potential energy of the system, U, the kinetic energy of the rock, K, and the total mechanical energy of the system, E, for the following depths below the water’s surface: d = 0.00 m, d = 0.500 m, d = 1.00 m. Let potential energy be zero at the bottom of the pond.

2. The bar graph shows the energy of the Skater, where could she be on the track?

4. If the ball is at point 4, which chart could represent the ball’s energy? KE PE A. B. C. D. 2 1 3 4

5. If a heavier ball is at point 4, how would the pie chart change? KE No changes The pie would be larger The PE part would be larger The KE part would be larger PE 2 1 3 4

6. As the ball rolls from point 4, the KE bar gets taller 6. As the ball rolls from point 4, the KE bar gets taller. Which way is the ball rolling? At 4 Next step 2 1 3 4 Up Down not enough info

Discovery of the Higgs Particle, 2013

1. Higgs video 1 (3 min) CBS with Mishio http://www.youtube.com/watch?v=uCMuInLYVr4 2. Cern Higgs BG (5min) 2. Cern LHC (6min) https://mediastream.cern.ch/MediaArchive/Video/Public/Movies/2008/CERN-MOVIE-2008-084/CERN-MOVIE-2008-084-0600-kbps-maxH-360-25-fps-audio-128-kbps-48-kHz-stereo.mp4 http://www.youtube.com/watch?v=PJ2q8WUire0 3. Binghamton U Prof video 1 (15 min) talk very well explained https://www.youtube.com/watch?feature=player_detailpage&v=Pv_DtHuj5Ds http://angelsanddemons.web.cern.ch/video/higgs-boson Higgs video 2 Collision Course(5 min) http://www.nytimes.com/video/2013/03/04/science/100000002094542/higgs-boson-a-cern-collision-course.html Joe Incandela talk(21 min) talk very well explained https://www.youtube.com/watch?v=D8Oj_hcFE5c Nova announcement(4 min) Nova higgs clip from (5 min) https://www.youtube.com/watch?v=-WdQZqtdgqg https://www.youtube.com/watch?v=bQeougqqt_M News announcement (4 min) Vivek sharma https://www.youtube.com/watch?v=dfoq8kFC6xc http://www.youtube.com/watch?v=nBNjqVbnrYo https://www.youtube.com/watch?v=KQZyQF0AL34

Tony hawk half pipe video (12-13 min) http://vimeo.com/60300881