Chapter 7: Work, Power & Energy WORK My family owned at one point a Paletria in Tucson, AZ. As many already know, it is very hot in Tucson (usually have 100+ days over 100 o F or 40 o C) and therefore, the paleta business was very good. I always remember my parents putting me to work by moving boxes of fruit here, there, everywhere it seemed like the work was endless. I was always volunteered to move these boxes of fruit. Picturewise, I imagine me working moving the boxes of fruit as So work depends on two things: (i) how much force I used to move the box and (ii) how far I had to move the box. Definition The work done by a constant force is Work = Force distance = Fd Key points 1. There are two ways to do a lot of work: The way that you see these two types of work is (i) U-Haul truck ramps and using (ii) car jacks for raising car to change tires. 2. Work has an unusual feature of zero distance implies zero work. Turkey's Naim Suleymanoglu (Pocket Hercules). It takes muscle, technique and a lot of nerve to put 413 pounds of iron over your head, especially when the tonnage represents roughly three times your body weight (141 lbs). The bar bows, red and green disks like locomotive wheels sagging around your ears. Takes nerve, mostly, if you've never lifted that much before. 7-1
Is there work being done by Pocket Hercules holds the bar above his head? 3. The Meaning of a Joule of Work unit of force F = Newton Unit of work = 1 N m = 1 Joule unit of distance d = meter Another unit of work and energy is the food calorie: 1 calorie 4 J and 1000cal = 1 Cal = 4000J food calorie The work done is measured in terms of Joules, which is equivalent to lifting a cell phone a distance of 1 m: W = Fd = 1 N 1 m = 1 Joule weight of a cell phone height change To put this into an everyday type of situation, let s say that you go out and have a Baskin-Robbins Milkshake (a mere 150 Calories). After enjoying it you start feeling guilty and feel the need to work off the milkshake by bench pressing the calories off. Let s say you use 160 lbs 700 N as your bench pressing weight. How many times must you lift it to compensate for the calories in the milkshake? I raise the bar 0.50 m above my chest, and lower it the same distance. How much work is done ON the bar? Lifting and lowering phases: W = Fd = 700 N 0.50 m = + 350 J W + W = 700 J ( ) ( ) lifting lifting lowering Therefore, your body does 700 J of work since your heart applies a force and moves your blood some distance. Converting Joules into more familiar units of food calories, W 700 J 0.18 Cal body So the number of reps that are required to "burn-off" a 1500 Cal shake from Baskin- Robbins is number reps to 1500 Cal 8,500 reps burn off milk shake 0.18 Cal 7-2
POWER Review of work: let s answer the following questions on work: Which requires more work going up the stairs or coming down them? NEITHER! Since the distance and forces are the same going up or down the stairs, you do the same amount of work. Which requires more work running up or walking up the stairs? NEITHER! Our definition of work does not take time into account, to time is irrelevant for talking about work. According to our definition of work it is not a useful term to describe the amount of something that we are doing. All we do know is we are expending something at a much faster rate when we run and less of that something when we walk up the stairs. It turns out that what we are really trying to say is when we are running we are doing a fixed amount of work in a shorted time when we are walking we are doing a fixed amount of work in a longer time So what is missing from our statement is something about time. This leads us to a new definition, power. Power is a measure of how fast we do work: Power = Work time Similar to work, something can be powerful two ways: either do (i) work quickly or (ii) simply be able to do a lot of work. 1. Big power by doing work quickly: Work Power = When one says that is a powerful car we mean that the can do a certain amount of work in a short amount of time. For example, sports cars advertise how fast it can go from 0 to 60 mph. The faster a car, the more powerful the car is said to be. Powerful means the ability to do work quickly Bugatti Veyron Super Sport: 267 mph, 0-60 in 2.4 secs. Aluminum, Narrow Angle 8 Liter W16 Engine with 1200 hp, base price is $2,400,000. time 2. Big power by doing a large amount of work: another way to be powerful is doing the maximum amount of work. Power Work = time 7-3
Typically this is talked about in the ability of a truck to haul a very large load. So how quickly work is done is not important, but moving the very large load is. http://www.youtube.com/watch?v=pe8xbjv2bqq&feature=related UNITS of Measurement of Power unit of work W = Joule Joule Unit of power = = 1 Watt unit of time t = sec sec PGE charges you by kilowatt-hr which is a form of energy. Example Suppose that two people (a heavy and a thin) are going up a hill. Which person does more work if they walk side-by-side? Which person has a higher output of power? In order for both to person to have the same power, what must happen? There are two answers. Energy and Conservation of Energy (Energy nrg) DEMO Use the bowling ball pendulum to talk about the transfer of energy between PE and KE. This transfer of something is what physicist likes to call ENERGY and there are two kinds: Potential Energy energy that is stored due to changes in position Kinetic Energy energy that is associated with a moving object Heat energy and frictional energy What is energy? Energy is the measure of a system s capacity to do work. That is, it is what is transferred when work is done. The more work done on something, the more energy it gains. We might say that energy is stored work. Work-Energy Theorem Need to do work in order to produce energy (or the work done results in a change of energy): PE Work = change in energy = E KE Efriction = Ef There are many kinds of work (heat, light, sound, electrical, ). In mechanics, there are three main forms of energy: potential, kinetic, and friction. 1. POTENTIAL ENERGY PE Energy that is stored due to changes in position Work done to Work is "stored energy" in change in PE change the height the Earth's gravitational field Equationwise, we write PE in terms of work done by gravity: WorkΔPE = (force = of gravity) (height change ) = F g h smaller height change smaller PE less work stored in the g-field larger height change larger PE more work stored in the g-field 7-4
Note that PE only depends on the height change Other Kinds of PE: spring, elastic, chemical, Larger stretch more PE is stored in the rubber band or spring Smaller stretch more PE is stored in the rubber band or spring 2. KINETIC ENERGY = KE Energy that is stored due to motion and depends on mass and velocity: KE = mass (velocity) = mv 1 2 1 2 2 2 Remarks i. Only changes in KE are meaningful. That is, it is meaningless to speak about KE at a single point. There must be a reference KE to measure from. ii. KE depends on mass & velocity, however, the meaning of KE is the amount of work required to change the KE of an object. v-dependence: a slow car has a small KE whereas a fast car has a large KE m-dependence: a car and a large truck moving at the same velocity have different KE values iii. Car s driving at different speeds require more work to stop: What force does the work in stopping the car? Friction a car moving twice as fast leave a skid mark 4 times longer whereas a car traveling three times faster leaves a skid mark 9 times longer. Question: which requires more work to catch a bowling ball or a baseball with the same KE? Neither! In catching either ball, the final KE is zero and depends only on the initial KE values. According to the work-nrg theorem, they require the same amount of work and therefore, equally safe: 1 2 1 2 K = 0 mv 2 0 = 0 mv 2 0 = W 3. HEAT & FRICTION ENERGY 7-5
Friction is an example of negative work being done on an object. In other words, negative work reduces the overall energy available to a system or object. DEMO Bowling ball Pendulum Explain the various types of energy (PE, KE, friction and heat energies) Conservation of Energy 1. Energy cannot be created or destroyed only transformed from one form into another form (KE, PE, Heat energy, mass, ) 2. Key point: the total amount of energy never changes as given by the conservation of energy equation: total energy = constant = KE + PE Remarks 1. What is important about conservation of energy is that it is a bookkeeping method to track how energy is transferred from one form into another. The total energy amount is not important as well will see. 2. Because the total energy of the system is a constant, equation wise the energies are inversely proportional to each other. In other words, as one increases, the other must decreases. We will use energy diagrams to keep track of these changes. KE PE constant = + PE = KE + = KE + PE For example, we can use a simple method of keeping track of energy using ENERGY DIAGRAMS. PE KE PE + = + KE = decreases increases increases decreases constant energy state-1 = energy state-2 = = constant Examples 1. Ball rolling down an incline 2. Dropping a ball 3. Roller coaster It is clear that a ball moves faster as it moves down an incline. What is an energy measurement that tells us about speed? KE. So if we keep track of KE using conservation of energy, it will tell us about the speed of the ball. 7-6
Applet Roller Coaster http://surendranath.tripod.com/applets/dynamics/coaster/coasterapplet.html 7-7