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WORK, POWER, ENERGY QOTD: Write a list of 10 examples your idea of work. Demo : create a work equation using a spring scale, string and a book. WHAT IS WORK? Work is done only when a force moves an object A force acting on an object and causing it to move a distance is work Not every force is work..if you push against the wall it does not move..that is not work! Work = force X distance Work is measured in Joules If you pick up a bag of groceries and walk across the room the work is picking up the groceries not the walking. The object must move some distance as a result of your force The force you exert must be in the same direction as the objects motion. Ie: the groceries You walk WHAT’S WORK? A scientist delivers a speech to an audience of his peers. A body builder lifts 350 pounds above his head. A mother carries her baby from room to room. A father pushes a baby in a carriage. A woman carries a 20 kg grocery bag to her car? 5 WHAT’S WORK? A scientist delivers a speech to an audience of his peers. No A body builder lifts 350 pounds above his head. Yes A mother carries her baby from room to room. No A father pushes a baby in a carriage. Yes A woman carries a 20 kg grocery bag to her car? No 6 Work can be determined by calculating Force used x distance moved = amount of work Therefore what is the formula for work? Work = force x distance Joule – is the SI unit for work. Newton = force Meters = distance Therefore if you exert: 1 Newton of force for 1 meter of distance = 1 joule of work or 1N/m Work is done when a force is exerted through a distance. A student lifts a bag of books that weighs 135 N. If the bag is lifted .75 m, how much work does the student do? F = 135 N d = .75 m W = Fd W = (135 N)( .75 m) W = 101.25 J Negative Work If the object moves in the direction opposite the direction of the force (for instance if force and displacement are in opposite directions) then the work is negative: W < 0. The energy of the system is reduced. A +24 N force is applied to an object that moves 10 m in the same direction during the time that the force is applied. How much work is done to the object? http://www2.franciscan.edu/academic/mathsci/ mathscienceintegation/MathScienceIntegation1011.htm#item1015 Find the equation for POWER 1. Attach a string and spring scale to a large book. 2. Pull the book .5m slowly. Use a stopwatch to determine time . 3. Record the time and distance on a data table. 4. Repeat 1- 3 – but this time pull the book faster. 5. Repeat 1-3 even faster. Force-N distance -m time- s POWER Power tells you how fast something is happening..how fast the work is being done Power = work/time or Power = Force X Distance Time Power is measured in watts (W) One watt is equal to 1 joule per second of work divide joules/seconds Power – the rate at which energy is transferred. P=W t 1 Watt (W) = 1 J/s P = power W = work t = time Watts Joules seconds HOW MUCH POWER MUST A MOTOR HAVE TO OPERATE A PUMP THAT RAISES 1500 KG OF WATER EVERY MINUTE A DISTANCE OF 12 M? 1. m = 1500 kg t = 60 s d = 12 m 2. Equations P = W/t W = Fd F = mg 3. Plug and chug F = mg = (1500 kg)(9.8 m/s2) = 14,700 N W = Fd = (14,700 N)(12 m) = 1.76 x 105 J P = W/t = (1.76 x 105 J)/(60 s) = 2940 W http://www.physicsclassroom.com What is Energy? It turns out that energy is so fundamental, like space and time, that there is no good answer to this question. However, just like space and time, that doesn't stop us from doing very useful calculations with Energy We may not be able to define energy, but because it is a conserved property of nature, it's a very useful idea. POTENTIAL ENERGY Potential Energy (PE): Stored energy due to position Examples: rock on a cliff, battery, food, gasoline, stretched rubber band, apple hanging in a tree Gravitational Potential Energy A barbell of mass "m" is lifted vertically upwards a distance "h" by an outside force. How much work does that outside force do on the barbell? Fapp mg W = Fdparallel Since a = 0, Fapp = mg W = (mg) dparallel Since F and d are in the same direction ...and dparallel = h W = (mg) h W = mgh Gravitational Potential Energy But we know that in general, Eo + W = Ef. If our barbell had no energy to begin with, Eo = 0, then W = Ef But we just showed that we did W=mgh to lift the barbell... so mgh=Ef The energy of a mass is increased by an amount mgh when it is raised by a height "h". Gravitational Potential Energy The name for this form of energy is Gravitational Potential Energy (GPE). GPE = mgh One important thing to note is that while changes in gravitational potential energy are important, their absolute value is not. Gravitational Potential Energy You can define any height to be the zero for height...and therefore the zero for GPE. 0.5 m But whichever height you choose to call zero, changes in heights will result in changes of GPE. For example, the floor level can be considered zero energy or the ladder level can be zero. 0m 0.5 m 0m GRAVITATIONAL PE Gravitational PE (GPE): Energy stored by objects that are above the earth’s surface (objects that can fall) Depends on mass, acceleration and height GPE increases with height GRAVITATIONAL PE GPE = mass gravity height GPE = m g h = weight height GPE = m (kg) 9.8 m/s2 h (m) j = 1 Nm What is the change of GPE for a 5.0 kg object which is raised from the floor to a final height of 2.0m above the floor? answer 9 As an object falls, its GPE always _____. A increases B decreases C stays the same answer 10 What is the change of GPE for a 8.0 kg object which is lowered from an initial height of 2.0 m above the floor to a final height of 1.5m above the floor? answer 11 What is the change in height of a 2.0 kg object which gained 16 J of GPE? answer 12 GPE=mg h = GPE h = 16/(2 h = 0.82m KINETIC ENERGY Kinetic Energy (KE): Energy in the form of motion Depends on mass and velocity of moving object. Object in motion has ability to do work http://www.youtube.com/watch?featur e=player_detailpage&v=0ASLLiuejAo Kinetic Energy The energy an object has by virtue of its motion is called its kinetic energy. The symbol we will be using for kinetic energy is KE. Like all forms of energy, it is measured in Joules (J). The amount of KE an object has is given by: KE = 1/2 mv2 KINETIC ENERGY KE = ½ mass velocity2 KE = m V2 2 (j) = (kg) (m/s) 1 j = 1 kg m/s As an object falls, its KE always _____. A decreases B increases C stays the same. answer 13 A ball falls from the top of a building to the ground below. How does the kinetic energy (KE) compare to the potential energy (PE) at the top of the building? A KE = PE B KE > PE C KE < PE D It is impossible to tell. answer 14 What is the kinetic energy of a 12 kg object with a velocity of 10 m/s? answer 15 What is the mass of an object which has 2400 J of KE when traveling at 6.0 m/s? answer 16 17 A 3 kg object has 45 J of kinetic energy. What is its velocity? If the speed of a car is doubled, the KE of the car is: A quadrupled B quartered C halved D doubled answer 18 Which graph best represents the relationship between the KE and the velocity of an object accelerating in a straight line? C A KE KE v v B D KE KE v v answer 19 20 The data table below lists mass and speed for 4 objects. Which 2 have the same KE? A B B and D C A and C D B and C answer A and D Elastic Potential Energy Energy can be stored in a spring, this energy is called Elastic Potential Energy. Robert Hooke first observed the relationship between the force necessary to compress a spring and how much the spring was compressed. Hooke's Law Fspring = -kx k represents the spring constant and is measured in N/m. x represents how much the spring is compressed and is measured as you would expect, in meters. The - sign tells us that this is a restorative force. (if you let the spring go once it is compressed, it will go back to its original position) Elastic Potential Energy (F= -kx) The work needed to compress a spring is equal to the area under its force vs. distance curve. Area of a triangle = 1/2 b h W = 1/2 (x)(F) W = 1/2 (x)(kx) W = 1/2kx2 Elastic Potential Energy The energy imparted to the spring by this work must be stored in the Elastic Potential Energy (EPE) of the spring: EPE = 1/2 k x2 Like all forms of energy, it is measured in Joules (J). Determine the elastic potential energy stored in a spring whose spring constant is 250 N/m and which is compressed 8 cm. EPE = 0.5 kx2 EPE = 0.5 (250)(0.082) answer 21 EPE = 0.8 J What is the spring constant of a spring that is compressed 5 cm and has 0.65 J of elastic potential energy stored in it? answer 22 EPE = 0.5 kx2 k = EPE/0.5x2 k = 0.65 / 0.5 (0.052) k = 520 N/m How much does a spring with a spring constant of 500 N/m need to be compressed in order to store 1.75 J of elastic potential energy? answer 23 A 3 kg mass compresses a spring 2.5 cm. What is the spring constant? answer 24 F F F k k = 1176 N/m The same 3 kg mass compresses the same spring 2.5 cm. How much elastic potential energy is stored in the spring? answer 25 LAW OF CONSERVATION OF ENERGY The law of Conservation of Energy: Energy cannot be created or destroyed. It may be transformed from one form into another; however, the total amount of energy in the universe remains constant. (Transformers) LAW OF CONSERVATION OF ENERGY Energy conversions occur without a gain or loss in energy Energy into a system = energy out of a system Due to friction, energy might seem to be lost, but it has changed into thermal energy. . ENERGY ANALOGY When energy is transferred, it can transform (change form) but it still remains energy. Analogy: How is energy like money? When money is transferred from one person or place to another it can change form (transform) but it still remains money. ENERGY TRANSFORMATIONS (BALL) Demonstrate: how bounce height of ball becomes lower and lower each time it bounces. Have students infer why this happens. Each time the ball bounces, part of its energy is transformed into other forms of energy, such as thermal (heat) energy, sound energy and vibrations in the ground. In addition, some energy is absorbed by the ball. Therefore, it will never bounce as high as the initial drop height. ENERGY TRANSFORMATIONS Ex: A light bulb is a device that transforms electrical energy into electromagnetic (light) energy and thermal energy Chemical energy (coal) heat energy (burn to create steam) mechanical energy (steam is used to turn turbines) Electromagnetic energy (generates electricity) heat energy (blow drier, oven) ROLLER COASTER PE: 354kJ KE: 0kJ V: 0m/s h=70m PE: 0kJ KE: 354kJ V: 37.1m/S PE: 0kJ KE: 354kJ V: 37.1m/S Potential energy becomes Kinetic energy. Kinetic energy can become Potential 177kJ energy. PE: KE: 177kJ h=35 V: 26.2m/S m Conservation of Energy A roller coaster is at the top of a track that is 80 m high. How fast will it be going at the bottom of the hill? Eo + W = Ef Eo = Ef W=0 GPE = KE E0 = GPE, Ef = KE mgh = 0.5mv2 Substitute GPE and KE equations v2 = 2gh Solving for v yields v2 = 2 (9.8) 80 v =39.6 m/s answer A spring gun with a spring constant of 250 N/m is compressed 5 cm. How fast will a 0.025 kg dart go when it leaves the gun? answer A student uses a spring (with a spring constant of 180 N/m) to launch a marble vertically into the air. The mass of the marble is 0.004 kg and the spring is compressed 0.03 m. How high will the marble go? A student uses a spring gun (with a spring constant of 120 N/m) to launch a marble vertically into the air. The mass of the marble is 0.002 kg and the spring is compressed 0.04 m. a)How high will the marble go? answer b)How fast will it be going when it leaves the gun? answer A roller coaster has a velocity of 25 m/s at the bottom of the first hill. How high was the hill? answer A student uses the lab apparatus shown above. A 5 kg block compresses a spring 6 cm. The spring constant is 300 N/m. What will the block's velocity be when released? answer A 5 kg rock is dropped a distance of 1 m onto a spring. It compresses the spring 2 cm. What is the spring constant? answer How much work is done in stopping a 5 kg bowling ball rolling with velocity of 10 m/s? answer How much work is done compressing a spring with a 450 N/m spring constant 2 cm?