PHYS 1441 – Section 002 Lecture #10AnnouncementsSlide 3Reminder: Special Project for Extra CreditSlide 5Friction ForceStatic FrictionMagnitude of the Static FrictionSlide 9Kinetic FrictionCoefficient of FrictionForces of Friction SummarySlide 13Example of Using Newton’s LawsExample w/o FrictionExample w/ FrictionMonday, Oct. 11, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu1PHYS 1441 – Section 002Lecture #10Monday, Oct. 11, 2010Dr. Jaehoon Yu•Force of Friction•Application of Newton’s Laws•Example for applications of Newton’s Laws–Example for Motion without friction–Example for Motion with friction•Uniform Circular MotionToday’s homework is homework #6, due 10pm, Tuesday, Oct. 19!!Announcements•Quiz #2 Results –Class average: 17/30•Equivalent to: 57/100–Top score: 30/30•Evaluation policy–Homework: 30%–Comprehensive final exam: 25%–One better of the two non-comprehensive term exam: 20%–Lab: 15%–Quiz:10%–Extra credit: 10%•Colloquium this weekMonday, Oct. 11, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu2Monday, Oct. 11, 2010 3PHYS 1441-002, Fall 2010 Dr. Jaehoon YuMonday, Oct. 11, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu4Reminder: Special Project for Extra CreditA large man and a small boy stand facing each other on frictionless ice. They put their hands together and push against each other so that they move apart. a) Who moves away with the higher speed and by how much? b) Who moves farther in the same elapsed time?•Derive fomulae for the two problems above in much more detail than what is shown in this lecture note.•Be sure to clearly define each variables used in your derivation.•Each problem is 10 points each.•Due is this Wednesday, Oct. 13.Monday, Oct. 11, 2010 5Applications of Newton’s LawsMSuppose you are pulling a box on frictionless ice, using a rope.TWhat are the forces being exerted on the box?Gravitational force: FgNormal force: nTension force: Tn= -FgTFree-body diagramFg=MgTotal force: F=Fg+n+T=TxFIf T is a constant force, ax, is constantxfvyFMTax0yaxn= -FgFg=MgTTMax−Fg+ n =yMa0vxi+axt =vxi+TM⎛⎝⎜⎞⎠⎟txf−xi=vxit +12TM⎛⎝⎜⎞⎠⎟t2What happened to the motion in y-direction?PHYS 1441-002, Fall 2010 Dr. Jaehoon YuMonday, Oct. 11, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon YuWhen an object is in contact with a surface there is a force acting on that object. The component of this force that is parallel to the surface is called the friction force. Friction ForceThis resistive force is exerted on a moving object due toAlways opposite to the movement!!viscosity or other types of frictional property of the medium in or surface on which the object moves. 6Monday, Oct. 11, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon YuWhen the two surfaces are not sliding across one anotherthe friction is called static friction. Static Friction7The resistive The resistive force exertedforce exertedon the object up to the time just before on the object up to the time just before the object starts moving.the object starts moving.Monday, Oct. 11, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon YuThe magnitude of the static friction force can have any value from zero up to the maximum value.MAXs sf f�MAXsf =0 1sm< <is called the coefficient of static friction.Magnitude of the Static FrictionKinetic friction applies during the move!!s NFmWhat is the unit?Once the object starts moving, there is NO MORE static friction!! None8Monday, Oct. 11, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon YuNote that the magnitude of the frictional force does not depend on the contact area of the surfaces.MAXsf =s NFm9Monday, Oct. 11, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon YuStatic friction opposes the impending relative motion betweentwo objects.kf =0 1km< <is called the coefficient of kinetic friction.Kinetic FrictionKinetic friction opposes the relative sliding motions that is happening. The resistive force exerted on the object during its movement.k NFmWhat is the direction of friction forces?opposite to the movement10Normally much smaller than static friction!!Monday, Oct. 11, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon YuCoefficient of FrictionWhat are these?11Monday, Oct. 11, 2010Forces of Friction Summary furs≤μsFurNResistive force exerted on a moving object due to viscosity or other types frictional property of the medium in or surface on which the object moves.Force of static friction, fs:Force of kinetic friction, fkThe resistive force exerted on the object until just before the beginning of its movementThe resistive force exerted on the object during its movementNkkf Fm=ur urThese forces are either proportional to the velocity or the normal force.Empirical Formula What does this formula tell you? Frictional force increases till it reaches the limit!!Beyond the limit, the object moves, and there is NO MORE static friction but kinetic friction takes it over.Which direction does kinetic friction apply?Opposite to the motion!PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu12Monday, Oct. 11, 2010 13Look at this problem again…MSuppose you are pulling a box on a rough surfice, using a rope.TWhat are the forces being exerted on the box?Gravitational force: FgNormal force: nTension force: Tn= -FgTFree-body diagramFg=MgTotal force: F=Fg+n+T+FfxFIf T is a constant force, ax, is constantxfvyFax=T −FfM0yaxn= -FgFg=MgTT −Ff=Max−Fg+ n =yMa0vxi+axt =vxi+T −FfM⎛⎝⎜⎞⎠⎟txf−xi=vxit +12T −FfM⎛⎝⎜⎞⎠⎟t2PHYS 1441-002, Fall 2010 Dr. Jaehoon YuFriction force: FfFfFfn =FgMonday, Oct. 11, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu14Example of Using Newton’s LawsA traffic light weighing 125 N hangs from the cable tied to two other cables fastened to a support. The upper cables make angles of 37.0o and 53.0o with the horizontal plane. Find the magnitudes of the tensions in the three cables. F =urFree-bodyDiagram53o37oxyT137oT253oT3 T1sin 37o( )+T2sin 53o( )−mg = −T1cos 37o( )+ T2cos 53o( )= 01T\ = T2sin 53o( )+0.754×sin 37o( )⎡⎣⎤⎦=1.25T2=125N T2=100N; 031iiixxTF031iiiyyTFNewton’s 2nd lawx-comp. of net forcey-comp. of net force0( )( )2cos 53cos 37T =oo20.754 T T1=0.754T2=75.4N Tur1+Tur2+Tur3= mar=0Monday, Oct. 11, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu15Example w/o FrictionA crate of mass M is placed on a frictionless inclined plane of angle θ. a) Determine the acceleration of the crate after it is
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