FrictionHolding in PlaceInequalityCoefficient of FrictionSlippery SlopeSlidingStatic vs. KineticDownhill SkiingForce DiagramMinimum SlidingNormal Force and FrictionFrictionFrictionHolding in PlaceHolding in PlaceObjects on an incline will often stay put.Objects on an incline will often stay put.There must be a force that holds the object in place.There must be a force that holds the object in place.Static frictionStatic friction is from the contact of resting objects. is from the contact of resting objects.•Force holds up to a certain pointForce holds up to a certain point•Force is based on the type of contact (rough, smooth)Force is based on the type of contact (rough, smooth)•Maximum force is proportional to the pressing force of the Maximum force is proportional to the pressing force of the object (normal force)object (normal force)InequalityInequalityThe approximate formula for static friction is:The approximate formula for static friction is:ss is the coefficient of static friction is the coefficient of static frictionThis is an This is an inequalityinequality..•The force of static friction is generally less than the The force of static friction is generally less than the coefficient times the normal forcecoefficient times the normal forceNsfrFFCoefficient of FrictionCoefficient of Frictionm1FTmgFsfr(max)Use rope and measure the Use rope and measure the force when movement force when movement begins.begins.•Measure weightMeasure weight•Measure force at slipping Measure force at slipping point.point.WFmgFFmgTTsTs// Slippery SlopeSlippery SlopeIf If FFfrfr < < ssFFNN = = ssmgmg cos cos then the block will hold.then the block will hold.At equality the block just At equality the block just begins to move.begins to move.NFmmgFgcosmgsinmgsin(max)mgFfrtancossinssNsfrmgmgFFSlidingSlidingSliding objects also have a frictional force exerted on Sliding objects also have a frictional force exerted on them.them.This frictional force is kinetic friction.This frictional force is kinetic friction.An approximate formula:An approximate formula:kk is the coefficient of kinetic friction is the coefficient of kinetic friction NkfrFFStatic vs. KineticStatic vs. KineticStatic and kinetic friction are Static and kinetic friction are similar.similar.•Force in opposite direction Force in opposite direction to motionto motion•Proportional to normal forceProportional to normal force•Coefficient of friction Coefficient of friction depends on materialsdepends on materialsStatic and kinetic friction are Static and kinetic friction are different.different.•Static friction is an inequality Static friction is an inequality up to a maximumup to a maximum•Coefficient of friction is Coefficient of friction is typically greater for static typically greater for static friction at the same surfacefriction at the same surface•Wood on wood (0.4 vs. 0.2)Wood on wood (0.4 vs. 0.2)Downhill SkiingDownhill SkiingA TV station has invited you A TV station has invited you to be the science to be the science commentator for an commentator for an upcoming ski race. You upcoming ski race. You observe that a skier needs at observe that a skier needs at least 3least 3°° of slope to move of slope to move forward at a constant forward at a constant velocity.velocity.What is the coefficient of What is the coefficient of friction on the skis?friction on the skis?°Force DiagramForce DiagramAt constant velocity the At constant velocity the forces must all balance.forces must all balance.Friction doesn’t act in the Friction doesn’t act in the direction of the normal force.direction of the normal force.The normal force cancels the The normal force cancels the component of gravity.component of gravity.Fg = -mgFgy = -mg cosFN = mg coscosmgFNFfr = -kFNMinimum SlidingMinimum SlidingWhen the skier is sliding When the skier is sliding slowly we can neglect air slowly we can neglect air resistance.resistance.Kinetic friction balances the Kinetic friction balances the component of gravity pulling component of gravity pulling forward.forward.°Fgx = mg sinFN = mg cosFfr = -kFN05.0tancossin0kkfrgxmgmgFFNormal Force and FrictionNormal Force and FrictionFriction depends on both the normal force and on the Friction depends on both the normal force and on the coefficient of friction.coefficient of friction.To reduce friction requires reducing one of those To reduce friction requires reducing one of those factors.factors.•Reduce normal force by lightening the loadReduce normal force by lightening the load•Reduce normal force by adding additional upward forceReduce normal force by adding additional upward force•Add a lubricant to reduce the coefficient of frictionAdd a lubricant to reduce the coefficient of
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