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Physics – Energy CH 5 – NOTES Kowinsky 1 of 11 UNIT Outline: 1. Work Definition Force at angles Units for work 2.Energy Types: KE, PE, Derive KE, GPE, and EPE Calorie Conversion 3.Power Equation, Units Horsepower 4.Conservation of Energy work-energy theorem Magic can and Pendulum 5.Simple Machines Types of simple Machines Efficiency Simple Machine LAB ____________________________________________________________________________________ 1. WORK Work: A measurement of the energy used to cause a force to displace an object. Key words: Force, displacement, and Cause. The force MUST cause the displacement Examples: Is work being done? Push a wall - no wall is not displaced Book falling from desk to floor – Yes, book is displaced by gravity Is my hand doing work by carrying a book across the room – No, there is a force, but that force doesn’t cause the displacement. Dragging book across room – Yes, some of the force is used to displace the book Dragging a book across room in a circle – No, no displacement. Running on a treadmill – No, no displacement Physics – Energy CH 5 – NOTES Kowinsky 2 of 11 Closer look at work: W = F x d = N x m = Energy = Joule -> J A joule is a small number. If one moves a 1N object (.1 kg ~ .2pound object) a distance of 1 m, 1 J of work is done. For example, a 100 W light bulb will give off 360,000 J of energy each hour it runs. W=Fd However, the force needs to cause the displacement. Therefore The Force and Displacement MUST be in the same direction How do we make sure it’s in the same direction? Trig… Cos Therefore, W = F x d x cos If all force is in direction of displacement, = 0, cos = 1 If no force is in direction of displacement, = 90, cos = 0 Do examples of problems with angles. Physics – Energy CH 5 – NOTES Kowinsky 3 of 11 2. Energy Since work is a measurement of energy, let’s take a closer look at energy 2 types of energy: KE and PE KE – Kinetic Energy - energy of motion PE - Potential Energy - stored energy This energy can be released to create motion (KE) Deriving KE equation: We do work on a ball by throwing it, the ball is in motion. Lets apply a constant force to the ball for a distance (x) before it leaves my hands. This will cause the motion. W = Fx As we throw it, it accelerates. According to newtons 2nd law, F = ma Therefore, a = F/m Once it leaves our hands, it will obtain its final speed. Vf2 = Vi2 + 2ax However, the ball is starting from rest, so Vi = 0 Vf2 = 2ax Let’s substitute what we know for acceleration (a = F/m) into the above equation: Vf2 = 2 (F/m)x We are talking about work, so lets solve the equation for work: move F and x to one side Fx = ½ mVf2 Fx is the work done on the ball by us. ½ mVf 2 is therefore the energy of the ball in motion. The symbol for the energy of an object in motion is KE (Kinetic Energy) Therefore, KE = ½ mV2 Physics – Energy CH 5 – NOTES Kowinsky 4 of 11 Since KE is a measure of energy, it’s units should be the Joule…. Look at units: KE = ½ mV2 kg (m/s)2 kg m2/s2 (kg m/s2)(m) N m Joule Do sample problems Introducing PE Lots of types of PE: CPE – chemical – batteries, digestion, gas, other chemical reactions (you learn this in chemistry class) EPE – electrical stored energy – capacitors (will look at this later in the year) GPE – gravitational PE – stored energy due to an objects position EPE – Elastic PE – stored energy in elastic materials due to their stretching or compressing Lets look at GPE and EPE GPE GPE = Fx = F(grav) x(height) = (m ag ) h GPE = magh Since GPE is a measure of energy, it’s unit should be a joule… GPE = magh kg m/s2 m (kg m/s2)(m) N m Joule Do sample problems Elastic PE In 1600’s a British physicist names Robert Hook studied springs. He noted a relationship. The amount by which an elastic substance is deformed is related to the force causing the deformation. This is known as Hooke’s Law Kind of common sense, the more force you apply to a spring, the more it will stretch. Hooke’s Law is quantified as: F = -Kx X is the deformation (amount the spring is compressed or stretched) K is the spring constant. This depends on the material the spring is made of, and how the spring is built. K is measured in force per length (N/m) (-) sign denoted the force is opposite the direction of displacement. Ex, if you pull a spring apart, it will want to fly back together. EPE = ½ KX2 Physics – Energy CH 5 – NOTES Kowinsky 5 of 11 Again, EPE is a measure of energy, so the units will be Joules. Any energy is measured in joules. Show different springs: Lab springs, Rubber bands, garage door spring, car shocks Do spring example, Bungee cord Putting it together: Work is a measure of energy. Therefore, work equals energy, so you can set it = to KE or PE. W = KE Fx = ½ mV2 W = PE Fx = m ag h Or Work can measure the change in energy: W = KEf – KEi Do sample problems: 3 kg hammer hits a nail at 3 m/s. The nail goes .5 cm into the board. What is the average force on the nail? m = 3 kg x = .005 m F=? V = 3 m/s W = KE Fx = .5mV2 Solve for F, convert weight to mass F = (.5mV2) / x = (.5 3 32) / .005 = 2700 N The hammer hits with a force of 2700 N, which is a large number – a few hundred pounds of force. seems reasonable, since if you hit your thumb with a hammer it will smash it. This One last note: Another common unit for energy instead of the Joule is the Calorie. 1 Dietary Calorie = 1000 Calories 1000 cal = 4200 J or 1 cal = 4.2 j On the dietary list on foods, in the United states we use Dietary Calories. Most other countries use regular Calories. This similar to how we use the English system, everyone else uses the metric system… Disclaimer: The types of food we eat Digest differently, some digest more efficiently than others. For example, Calorie for calorie, fat, carbohydrates, and protein, give you slightly different amounts of energy. Calorie Example: How much energy will eating a 200 calorie cereal bar give an 80 kg person? 200 dietary calories = 200,000 cal. 200,000 cal x 4.2 = 840,000 j Sounds like allot, but a 100 W light bulb used 360,000 j per hour. The unit Joule is a small number. Physics – Energy CH 5 – NOTES Kowinsky 6 of 11 If 30% of that energy is used for motion, and the 80 kg person climbs up a 1 km tall mountain side, will this cereal bar give him enough energy? 30% of 840,000 j = 252,000 j PE = M ag h = 80 9.8 1000 = 784, 000 j No, the person will be short on energy. 3 Power Sometimes it is not convenient to analyze the amount of work done. Why? What is “Work” missing?? TIME Often it is more convenient to express work in terms of time. Physicists use Work/Time POWER = Work/Time (P = W/t) Units is J/s = Watt (James Watt) Ex, Light bulbs are measured in watts Sample1: 2 students lift 75 kg weights. They both lift it 2 m into the air. However student A takes 2 seconds to lift it, while student B takes 5 seconds to lift it. Which student does more work? Which student is more powerful? P = w / t student A: (75)(9.8) (2) / 2 = 735 W Student B: (75)(9.8) (2) / 5 = 294 W Sample2: You are helping design a theater stage. A 193 kg curtain on the stage needs to be raised 7.5 m at a constant speed in about 5 s. There are 3 motors available for purchase. A 3.5kW, a 5.5 kW, and a 1 kW motor. Which motor should you choose to install on the stage? P = W / t = (193) (9.8) (7.5) / 5 = 2837 W = 2.8 kW So, the 3.5 kW will work the best. ______________________________________________________________________________ If we play with units, we can get a convenient equation: P = W/t = F x / t = F v Therefore, P = W/t = F v So if one knows the force applied and the velocity of the object, on can determine the power output. This is VERY convenient for finding the power of engines in cars, planes, boats, etc… Physics – Energy CH 5 – NOTES 7 of 11 Kowinsky ___________________________________________________________________________ HORSE POWER One last thing with power: When dealing with engines, we rarely use W or kW. What do we usually hear? HorsePower Interestingly enough, James Watt coined the unit Horsepower. James Watt fine tuned the Steam Engine, the first types of engines invented in the 1700’s. He obviously wanted to make money by selling his steam engines. The best market for his steam engines were farms and mines, where horses would lift coal out of mines, or spin wheels in order to pump water or grind wheat corn, etc.. Farmer Joe knew nothing of the Watt unit. So James Watt would have a tough time selling them engines to replace their horses if he used unfamiliar terms. Watt decided to study workhorses. He determined that 1 horse on average could lift 330 pounds of coal per minute. OR 1000 lbs of coal 33 feet in 1 minute.(Watt was British). So he said 1 Horsepower = 33000 foot-lbs per minute Now, Watt looked at his engines and did some calculations. 1 HP = 746 Watts So, now James could go to the farmers and mine owners and say, If you buy my 1500 W engine, can replace 2 of your horses. My engines don’t need stables, food, sleep, etc. Just ethanol to run and a little oil now and then. Although almost no one uses horses today, the unit HP stuck. It’s on our cars, lawnmowers, vacuum cleaners, etc… Just imaging, a ford commercial, where instead of the truck driving in Montana with a herd of horses, it’s driving through light bulbs. For marketing reasons, companies love the term Horsepower. Change the name of a Ford Mustang to a Ford Bulb. Not going to happen. Example of using Horsepower. Ex: What is the horsepower of a 1200kg car that can go from 25 km/hr to 100 km/hr in 6 s? First, convert to standard units! 25 km/hr = 6.9 m/s 100 km/hr = 27.8 m/s Power = W / t, so find W first: Find change in energy: W = Kef – KEi = (½ 1200 6.92) - (½ 1200 27.82 ) = ½ 1200 (47.6-772.8) = ½ 1200 725.2 = 435,144 j Now find Power: P = W/t = 435144 J / 6s P = 72.5 kW Convert to HP 1 hp = 746 W 72.5 kW = 97 HP So, this car engine produces 97 HP assignments: Work&Power I wksht , WorkKE wksht Physics – Energy CH 5 – NOTES 8 of 11 Kowinsky _____________________________________________________________________________ 3. Conservation of Mechanical energy: Total energy of a system remains constant ENERGYtot = KEtot + PEtot Or ENERGY in = ENERGY out + waste Therefore: KEin + PEin = KEout + PEout + waste Total energy is conserved. There is always wasted energy. Sound produced, heating, deformation, light, etc… all of this produces waste energy. Energy can change forms, but always remains constant in a system. Bouncing a ball, if a rubber ball is dropped, it will never reach the origional height. Energy is lost. “magic can” demo Pendulum Demo Diving board diagram on chalkboard Do examples: Skier going down slope. What is skiers final V at bottom of slope (don’t use kinematics). Lets ignore friction for now, so no waste energy Lets say the ski slope is 20 m tall. Kein + PE in = Kef + Pef 0 + mag h = 1/2mv2 + 0 0 + m 9.8 20 = ½ m v2 + 0 Clean it up a bit… mass cancels: (9.8)(20) = 1/2v2 solve for v v = sqrt( (9.8)(20)(2) ) = 19.7 m/s In reality, there would be waste energy… friction, so the answer would be smaller. Sliding Board: Physics – Energy CH 5 – NOTES Kowinsky 9 of 11 Person slides down a slide. It is 3 m tall. The person however, takes a running start down the slide at a speed of 2 m/s. What is the persons final velocity at the bottom? Kei + Pei = Kef + Pef 1/2m22 + m(9.8)(3) = 1/2mv2 + 0 Mass cancels… (½)22 + (9.8)(3) = 1/2v2 2 + 29.4 = .5v2 31.4 = .5v2 v = sqrt((31.4)(2)) = 7.9 m/s Bungee jumper example: Bungee Jumping minitopic You are designing a Bungee jump. You are on a 70 m tall bridge, and, at the fullest stretch, want to land 4 m from the ground. (4 m safety cushion). M = 60 kg. K = 25 N/m , How long of a cord do you need? Initial Conditions: KE = 0, at rest, EPE = 0, not stretched, GPE = 100% Final Conditions: KE = 0, at rest again, EPE = some % stretched, GPE = some number Equation: GPE = GPE + EPE m 9.8 hi = m 9.8 hf + ½ K X2 (60)(9.8)(70) = (60)(9.8)(4) + ½ 25 X2 41160 = 2352 + ½ 25 X2 41160 – 2352 = 12.5X2 38808/12.5 = X2 X X = sqrt(3104.6) = 55.7 m Therefore, the cord stretches 55.7m. This is not the answer. The bridge is 70 m tall, and you want to stay 4 m from the ground…. 66 m – 55.7 m = 10.3 m You would need a 10.3 m bungee cord with a spring constant of 25 N/m What if the person had a mass of 70 kg. What length of cord would this person need for the same distance? Do the math again, replace mass by 70 kg… 5.8 m cord. Assignment: Conservation wksht QUIZ Physics – Energy CH 5 – NOTES 10 of 11 Kowinsky __________________________________________________________________________ 4. Efficiency and Simple Machines: A machine is a device that decreases the amount of force needed to displace an object. !It does not decrees the amount of work! Examples of simple machines: Pulley Do pulley demo Inclined Plane Zig zag road going up a mountain, a wedge, a wheelchair ramp Screw Create screw from inclined plane Wheel and Axel Show wheel and axel, wrench, gear on bycicle Fulcrum (Lever) Crow bar, Human arm, door handle, The power delivered by a machine of any kind is always less than the power supplied to it. This is due to friction and waste energy. You can never get more energy out of a machine than what you put into it. Efficiency is the ratio between power out and power in or work out and work in Eff = Pout / P in Or Eff = Wout / W in Efficiency can never be over 100%. This means energy cannot be created. Also, in real life, Efficiency is not 100%, it is always lower since there is always waste energy. In real life situations, efficiency is often MUCH lower than 100% Example: Car: 7% 93% is lost in mostly heat . Now, most of that 7% is used to physically move the car. To physically move a passenger (the point of a car), the efficiency drops to 0.3%. Hybrid car is about ~10% efficient Electric Car ~40-50% efficient Water Heater ~ 50% efficient (very rough estimate) Tankless water heater ~ 80% efficient A human: Walking ~ 25% efficient Running ~50% efficient (Because muscles act as springs, you get elastic energy conversion) Mice: 3% efficient at running – they are not designed to run they scamper! Compound machines are composed of many simple machines put together. Physics – Energy CH 5 – NOTES Kowinsky 11 of 11 Sample Problems Dealing with Efficiency: When doing efficiency problems, students often confuse the output and the input. Output is what the actual machine does – the energy given off by the machine. Input is what the person, or motor, must do – the energy put into the machine. Ex1: Pulley sample: A compound pulley is used to raise a 50 kg object a vertical displacement of 3 m. For this to occur, a person must pull a rope with a force of 100N a displacement of 15 m. Calculate the efficiency of this pulley. Fout = 50 x 9.8 = 490 N Xout = 3 m Fin = 150N Xin = 15 m Eff = Wout / Win = (Fo Xo) / (Fi Xi) = (490N) (3m) / (120N) (15m) = 1470 j / 1800 j = .82 The pulley is 82% efficient Ex2: A crane whose motor has a power input of 5 Kw raises a 1200 kg beam through a hight of 30 m in 90 s. Calculate the efficiency of the crane. Pin = 5000 W , x = 30 m, t = 90 s, m = 1200 kg Eff = Pout / Pin Find Pout, and plug into above equation: Pout = W / t = (F X) / t = ((1200 9.8)(30)) / (90) = 3920 W Plug into Eff equation: Eff = Pout / Pin = (3920 W) / (5000 W) = .784 = 78% The crane has an efficiency of 78%, that means 22% of it’s energy is wasted. Ex3: A trash compactor has a .25 HP motor. It can apply 4500 N of force (1 ton crushing force). The machine is 80% efficient. How fast does the compactor move? Eff = .80 Pin = .25 HP x 746 W = 186.5 W Fout = 4500 N Vout = ? Eff = Pout/Pin However, P = F v - so, solve for v. Eff = F v / Pin v = (Eff) (Pin) / (F) v = (.80) (186.5W) / (4500 N) = .03 m/s This is a slow velocity, but it’s a trash compactor, they move slow. The power is used in the force, not the velocity. Simple Machine Lab Assignment: Review sheet EXAM