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General Physics I: Day 15 Power & Gravitational Potential Energy Make sure your iClicker is registered at UserID! Worked-Example: Sailboat • What is the speed of the boat after it has travelled 200 m under the action of this force? 2 Worked-Example: Sailboat 3 Worked-Example: Sailboat 4 Springs & Hooke’s Law 5 Hooke was a contemporary of Newton’s who was very critical of Newton’s work. Hooke’s law: A spring exerts a force that is directly proportional to the Fsp rin g k L amount by which the spring is stretched or compressed. Fsp rin g kx If we assume that is measured relative the relaxed position then is called the spring constant, it measures the stiffness of the spring in units of N/m. 6 Spring Work So lets apply our general form for work to find the b work done against a spring: W F ds a F=kx F x W o n sp r. dx kx 0 x Again is measured from the relaxed position. W o n sp r. 1 2 W by spr. kx 1 2 2 kx 2 WarmUp: Kinetic Energy Race 7 Two cars, one four times as heavy as the other, are at rest on a frictionless horizontal track. Equal forces act on each of these cars for a distance of exactly 5 m. The kinetic energy of the lighter car will be _______ the kinetic energy of the heavier car. ~45% → one-quarter ~11% → one-half ~28% → equal to ~9% ~9% → twice → four times 8 Two cars, one four times as heavy as the other, are at rest on a frictionless horizontal track. Equal forces act on each of these cars for a distance of exactly 5 m. The kinetic energy of the lighter car will be _______ the kinetic energy of the heavier car. A) one-quarter B) one-half C) equal to D) twice E) four times 9 On Monday you run up the stairs to the top floor of a tall building, running at constant speed. On Tuesday you walk to the top, also at constant speed. On Wednesday you take a constant speed elevator. Call the work you do to get to the top of the building M, T and W respectively. Rank these works. A) M = T = W B) M > T > W C) M = T > W D) T > M = W WarmUp: Sustained Power 10 Some athletes can put out as much as 700 watts in short bursts. Assuming you could sustain such an energy output for 1 hour(!), estimate how fast would you be traveling at the end of that time period. ~25% → Used power → work → kinetic → speed ~8% → Realized they were stuck ~42% → Went ahead with ideas that didn’t work ~25% → Talked a bit, but gave no estimate WarmUp: Sustained Power 11 “In my exercise physiology class we learned about the Running Anaerobic Sprint Test that is used to evaluate power output for runners. I figured the mass of an athlete to be around 72.6kg The formula used is Power=(bodymass*distance^2)/time^3. But then I thought about the Kinetic energy equation which is K=1/2m*v^2 So, I used 700=1/2*72.6(v)^2 I solved for V and I ended up with 4.39m” WarmUp: Sustained Power “Using P=W/t, with flipping it around to P*t=W you would get 700watts/hour is the speed of the runner.” “watts=power=work/time work=3600[s]*700[w]=2520000[J] 2520000=.5mv^2 mv^2=5040000 v^2=5040000/94.1kg(usain bolt's mass)=53560 v=231.43m/s (518 mph!!)” 12 WarmUp: Sustained Power 13 “Honestly Im not sure how to answer this question. I understand that 700 watts equals the power, then 1 hr or 3600 seconds is the time, and my mass is about 45 kg. And since Work is equal to the change in kinetic energy, I found my work or KE to be 2.52*10^6, then plugging that into .5*m*v^2, I found v to be 335 m/s which seems utterly inhuman....” 14 Power Notice that time is not part of defining work. The amount of work it takes to lift your book is independent of the time the process takes. But we definitely care… We define power as the rate at which work is done: P dW dt For a microwave, we care about power, not total work done. Units of Power Units for power are watts, named after James Watt (steam engine!) Watt coined the term “horsepower”, (an alternative unit for power). 1 hp = 760 W. A car engine’s horsepower tells you the rate at which the engine can do work. 15 16 Power Ratings Appliances offer a great example comparison between power and energy. We care about how much energy each one transforms (uses) in a given amount of time. So appliances have power Appliance Power (W) ratings in watts. (1 W = 1 J/s) Stovetop 12,000 So each second you use a hairdryer, it converts 1000 J of EEM into K and Eth. Microwave 1,400 Hair Dryer 1,000 TV, color 350 Instantaneous Power 17 As an object moves, the power expended on it depends on: • The strength of the force • How far the object moves • How much time the movement takes The result is that we can calculate the instantaneous power due to a particular force simply with: P F v Potential Energy 18 Associated with certain forces. Potential energy is associated with a particular configuration of 2 or more objects (a system). Reference point: • When using potential energy you must always define your reference point. • Arbitrary (usually), but some choices are easier. • Regardless of your reference point, the change in potential energy from one configuration to another will always be the same! Conservative vs. Non-Conservative 19 Conservative forces defined in a couple ways: • Conceptually a conservative force is one which will “store” energy that can be released later. • Technically a conservative force is one for which the work done by that force is independent of the path taken by the object. ALL forces conserve energy, but conservative forces are special… they also conserve mechanical energy. Coming up… Tuesday (10/14) → 7.2 – 7.3 Homework 6 due Sunday by 11:59 PM Warm-Up due Monday by 10:00 PM Come pick up Worked-Examples Journal Part II if you don’t have one yet… Make sure your iClicker is registered at UserID! Exam 1… 20 Exam I Average: 48/80, 60% (middle D on my scale) My part: In my gradebook I have added 7 points (out of the 80) to everyone’s score. Adjusted average (with extra credit): 70% (mid C) This is worth 15% of your total grade. Come talk! Exams 2 is worth 20% and the final is 25%. 21