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Transcript
PHY 2053 Announcements Sample exams and solutions manuals for PHY2053 are available at Target Copy Two Kinds of Forces Conservative and Non-Conservative • A force is conservative if work done on object moving between two points is independent of the path the object takes between the points – The work depends only upon the initial and final positions of the object – Any conservative force can have a potential energy function associated with it Examples of conservative forces include: Gravity (ideal) Spring force Electromagnetic forces • A force is nonconservative if the work it does on an object depends on the path taken by the object between its final and starting points. • Examples of nonconservative forces – kinetic friction and air drag •The blue path is shorter than the red path •The work required is less on the blue path than on the red path •Friction depends on the path and so is a non-conservative force Work-Kinetic Energy Theorem • When work is done by a net force on an object and the only change in the object is its speed, the work done is equal to the change in the object’s kinetic energy Wnet = KEf − KEi = ∆KE • – Speed will increase if work is positive – Speed will decrease if work is negative Work and Potential Energy Conservative force potential energy function Evaluating the difference of the function at any two points in an object’s path gives the negative of the work done by the force between those two points Example will be gravity Work and Gravitational Potential Energy • PE = mgy Won −book = PEi − PE f = mgyi − mgy f = mg ( yi − y f ) Units of Potential Energy, Work, and Kinetic Energy are same joules Work-Energy Theorem Wnc = (KEf − KEi ) +(PEf − PEi ) = 0 (if conservative) Conservation of Energy KEi + PEi = KE f + PE f Reference Levels for Gravitational Potential Energy • A location where the gravitational potential energy is zero must be chosen for each problem – The choice is arbitrary since the change in the potential energy is the important quantity – Choose a convenient location for the zero reference height • Often the Earth’s surface • May be some other point suggested by the problem – Once the position is chosen, it must remain fixed for the entire problem Reference Levels, cont • At location A, the desk may be the convenient reference level • At location B, the floor could be used • At location C, the ground would be the most logical reference level • The choice is arbitrary, though Problem Solving with Conservation of Energy • Define the system- Verify only conservative forces present • Select the location of zero gravitational potential energy Do not change this location while solving problem • Identify two points the object of interest moves between At one point information is given At other point you want to find out something • Apply the conservation of energy equation to the system HITT RF Remote Login Procedure: (If you have a really old IR remote you do not need to login.) The radio channel number for this room is “07” (zero, seven). It is STRONGLY recommended to login your remote for every class just to be sure it is on the correct radio channel and working before class. 1. 2. 3. 4. PRESS AND HOLD THE DOWN ARROW KEY until the GREEN light on the remote turns RED. PRESS THE “0” KEY and you will see the RED light flash GREEN. PRESS THE “7” KEY and you will see the RED light flash GREEN. PRESS AND RELEASE THE DOWN ARROW KEY again and you will see the red light search for the receiver, if it BLINKS GREEN MULTIPLE TIMES you are logged in. In-class quiz 9/23 Your physics professor asks you to stand against the wall and release a bowling ball hanging on a rope. As you let it go, you want to jump out of the way, but your belief in what physics law helps you repress this urge? A. B. C. D. E. Newton’s 1st Law Law of Gravity E=mc2 Conservation of Energy Physics is Bogus In-class quiz 9/23 A diver drops (does not jump) from a board 10 m above the water. If he weights 700 N, what is his speed just as he hits the water? A. 700 m/s B. 35 m/s C. 14 m/s D. 10 m/s E. 0 m/s v f = 2 gyi A skier, starting from rest, slides down a 20° frictionless slope to a flat area 20 m vertically below him. (a) Find the skiers speed at the bottom. (b) How far does he slide on the flat if the coefficient of friction between her skis and the snow on the flat is 0.25? Spring Force Hooke’s Law gives the force F=-kx k is spring constant • F is the restoring force • F is in the opposite direction of x • k depends on how the spring was formed, material from which it was made, thickness of the wire, etc. Spring Work F varies with x: F = - k x W=F*x only good if F constant. Approximate with series of steps Work is sum of areas of rectangles = area under curve. Linear spring is simple A = ½ B h W = ½ xmax Fmax = ½ k x2 = work done on spring Potential Energy in a Spring 1 2 PE s = kx 2 Elastic Potential Energy – related to the work required to compress spring from its equilibrium position to some final, arbitrary, position x Work = Potential Energy Initial and Final Kinetic Energies=0