1Phy 2053 Announcements1. Exam 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] [email protected] by no later than Friday, Feb 6!! Include the reason for the conflict2. Professors out of town: 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 amReview: Friction ForcesContact between bodies with a relative velocity produces friction Friction is proportional to the normal force Static friction: the direction of the frictional force is oppositethe direction of the applied force, ƒs≤ µ n Kinetic friction: the direction of the frictional force is oppositethe direction of motionƒk=µnReview: Energy and WorkMechanical Energy•Kinetic (associated with motion)•Potential (associated with position• Work:•Work Can Be Positive or Negative• Kinetic Energy:• Units: 1 Joule = 1 N m = 1 kg m2/s2• units follow from above definitionsx)cosF(W Δθ≡2mv21KE =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• 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 restnet f iWKEKEKE=−=ΔTwo Kinds of ForcesConservative 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 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 force2Problem 5-18On a frozen pond, a 10 kg sled is given a kick that impartsto it an initial speed of v0= 2.0 m/s. The coefficient ofkinetic between the sled and the ice is μk= 0.1. Use the Work-energy theorem to find the distance the sled movesbefore coming to rest. Image Credit: http://www.snowmobileforum.com/snowmobile-still-shots/8148-sled-car.htmlWork and Potential Energy 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 gravityWork and Gravitational Potential Energy PE = mgyUnits of Potential Energy, Work, and Kinetic Energyare the same=joules()on book i f i f i fWPEPEmgymgymgyy−=− = − = −=−()nc f iWKEKEWork-Energy Theorem+− =()0fiPE PEii f fKEPEKE PE+= +Conservation of Energy(conservative)Conservation of Mechanical EnergyIn any isolated system of objects interacting only through conservative forces, the total mechanical energy of the system remains constant. ffiifiPEKEPEKEEE+=+=If nonconservative forces are present, then the full Work-Energy Theorem must be used instead of the equation for Conservation of Energy=−()nc f iWKEKE+−()fiPE PEProblem Solving with Conservation of Energy Define the system- Verify only conservative forces present Select the location of zero gravitational potential energy¾ Do not change this location while solving problem Identify two points the object of interest moves between¾ At one point information is given¾ At other point you want to find out something Apply the conservation of energy equation to the systemSprings: ForceHooke’s Law gives the forceF = - k xk 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.Fappliedxmax3Springs: WorkF varies with x: F = - k xLinear spring is a simple case:A = ½ B h W = ½ xmaxFmax= ½ k x2= work done on springW=FparallelΔx is only valid if F constant.For varying forces, we can approximate with series of stepsWork is sum of areas of rectangles = area under curve.Potential Energy in a SpringElastic Potential Energy related to the work required to compress spring from its equilibrium position to some final, arbitrary, position xWork = Potential EnergyInitial and Final Kinetic Energies=02skx21PE =Area under curveSprings and Gravity Wnc= (KEf–KEi) + (PEgf–PEgi) + (PEsf–PEsi)  PEgis the gravitational potential energy PEsis the elastic potential energy associated with a spring PE will now be used to denote the total potential energy of the systemConservation of Energy: Spring + Gravity The PE of the spring is added to both sides of the conservation of energy equation PEgis the gravitational potential energy PEsis 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 fsgisg)PEPEKE()PEPEKE(