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Review: Friction Forces Phy 2053 Announcements Contact between bodies with a relative velocity produces friction Exam 1 1. Feb 18, 8:20 – 10:10 pm Please get there at least 10 minutes early, and preferably 20 minutes Will cover material from sections 1.1 – 5.3 of Serway/Vuille Room assignments If your last name begins with A through P, you should go to Carleton 100 If your last name begins with R through Z, you should go to Pugh 170 You be allowed one handwritten formula sheet (both sides), 8 ½” x 11” paper Exam conflicts: Anyone with exam conflicts, send email to [email protected] and [email protected] by no later than Friday, Feb 6!! Friction is proportional to the normal force Static friction: the direction of the frictional force is opposite ƒs ≤ µ n Kinetic friction: the direction of the frictional force is opposite the direction of motion the direction of the applied force, Include the reason for the conflict ƒk = µ n Prof. Chan is out of town from Feb 5 – Feb 14. His office hours are cancelled for this period, but he will be reading e-mail. I will be out of town from Feb 11 – Feb 13 and Feb 17-19. Office hours also cancelled, but I will be reading e-mail I will have special office hours on Monday Feb 9 from 10-12 am and Monday Feb 16 10-12 am Review: Energy and Work • Professors out of town: 2. Mechanical Energy •Kinetic (associated with motion) •Potential (associated with position Work: Work-Kinetic Energy Theorem Wnet = KEf − KEi = ΔKE W ≡ (F cos θ)Δx Work Can Be Positive or Negative • 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 1 2 • Kinetic Energy: KE = mv 2 • Units: 1 Joule = 1 N m = 1 kg m2/s2 • A force is conservative if work done on object moving between two points is independent of the path the object takes between the points • • units follow from above definitions Two Kinds of Forces Conservative and Non-Conservative • 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 Spring force Electromagnetic forces Speed will increase if work is positive Speed will decrease if work is negative An object’s kinetic energy can also be thought of as the amount of work the moving object could do in coming to rest 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 1 Problem 5-18 Work and Potential Energy On a frozen pond, a 10 kg sled is given a kick that imparts to it an initial speed of v0 = 2.0 m/s. The coefficient of kinetic between the sled and the ice is μk = 0.1. Use the Work-energy theorem to find the distance the sled moves before coming to rest. For every conservative force a potential energy function can be found 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 Image Credit: http://www.snowmobileforum.com/snowmobile-still-shots/8148-sled-car.html Work and Gravitational Potential Energy Conservation of Mechanical Energy PE = mgy In any isolated system of objects interacting only through conservative forces, the total mechanical energy of the system remains constant. Won −book = PEi − PE f = mgyi − mgy f = mg ( yi − y f ) Units of Potential Energy, Work, and Kinetic Energy are the same=joules Ei = E f Work-Energy Theorem KEi + PEi = KE f + PE f Wnc = (KEf − KEi ) +(PEf − PEi ) = 0 If nonconservative forces are present, then the full Work-Energy Theorem must be used instead of the equation for Conservation of Energy (conservative) Conservation of Energy KEi + PEi = KE f + PE f Wnc = (KEf − KEi ) +(PEf − PEi ) Springs: Force Problem Solving with Conservation of Energy Define the system- Verify only conservative forces present Select the location of zero gravitational potential energy ¾ Do not change this location while solving problem Identify two points the object of interest moves between ¾ At one point information is given ¾ At other point you want to find out something Apply the conservation of energy equation to the system Hooke’s Law gives the force F=-kx k is the ‘spring constant’ F is the restoring force F 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. Fapplied xmax 2 Springs: Work F varies with x: F = - k x W=Fparallel Δx is only valid if F constant. For varying forces, we can approximate with series of steps Work is sum of areas of rectangles = area under curve. Linear spring is a simple case: A=½Bh W = ½ xmax Fmax = ½ k x2 Potential Energy in a Spring 1 PE s = kx 2 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 Area unde r cu rve = work done on spring Springs and Gravity Wnc = (KEf – KEi) + (PEgf – PEgi) + (PEsf – PEsi) PEg is the gravitational potential energy PEs is the elastic potential energy associated with a spring PE will now be used to denote the total potential energy of the system Conservation of Energy: Spring + Gravity The PE of the spring is added to both sides of the conservation of energy equation (KE + PE g + PE s )i = (KE + PE g + PE s )f PEg is the gravitational potential energy PEs is the elastic potential energy associated with a spring PE will now be used to denote the total potential energy of the system The same problem-solving strategies apply 3