Kinetic FrictionSlidingContinuing MotionStatic vs. KineticDragTerminal VelocityDownhill SkiingForce DiagramMinimum SlidingDownhill RunKinetic FrictionKinetic FrictionSlidingSlidingSliding 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 NkfrFFContinuing MotionContinuing MotionFFfrfr = = kkFFNN = = kkmgmg cos cosCompare to the downslope Compare to the downslope component of gravitycomponent of gravity•FFgxgx = mg = mg sin sin..•Block increases or Block increases or decreases speed depending decreases speed depending on which is greater.on which is greater.If equal there is constant If equal there is constant velocity.velocity.cosmgFNmmgFgcosmgsinmgcosmgFkfrtancossinkkmgmgStatic vs. KineticStatic vs. KineticStatic 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 materialsStatic 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)DragDragKinetic friction is a constant force.Kinetic friction is a constant force.•If there is a net force an object would accelerate foreverIf there is a net force an object would accelerate foreverAir resistance causes a friction called drag.Air resistance causes a friction called drag.•At low velocity drag is proportional to velocity, At low velocity drag is proportional to velocity, FFdd = - = -bvbv•At higher velocity drag goes as velocity squared, At higher velocity drag goes as velocity squared, FFdd = - = -cvcv22Because it depends on velocity the force increases Because it depends on velocity the force increases as an object speeds up.as an object speeds up.Terminal VelocityTerminal VelocityAn object may fall through An object may fall through the air at constant velocity.the air at constant velocity.By the law of inertia the net By the law of inertia the net force is zero.force is zero.The force of drag must The force of drag must balance the force of gravity.balance the force of gravity.This velocity is called the This velocity is called the terminal velocity.terminal velocity.Fg = mgFd = cv2cmgvmgcvFFttgd002Downhill SkiingDownhill SkiingCBS Sports has invited you to be the special science CBS Sports has invited you to be the special science commentator for the Winter Olympics downhill ski commentator for the Winter Olympics downhill ski race.race.You observe the following:You observe the following:•The downhill course is 2.5 km long with a drop of 800 mThe downhill course is 2.5 km long with a drop of 800 m•A downhill skier needs at least 3A downhill skier needs at least 3°° of slope to move forward of slope to move forward•The speed gun clocks the skier at a maximum of 130 km/hThe speed gun clocks the skier at a maximum of 130 km/h•An average skier is about 90 kgAn average skier is about 90 kgWhat is the coefficient of kinetic friction and drag What is the coefficient of kinetic friction and drag coefficient for a skier?coefficient for a skier?Force DiagramForce DiagramAt 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 cosFN = mg coscosmgFNFd = -cv2Ffr = -kFNMinimum SlidingMinimum SlidingWhen the skier is sliding to a When the skier is sliding to a halt we can neglect drag.halt we can neglect drag.Kinetic friction balances the Kinetic friction balances the component of gravity pulling component of gravity pulling forward.forward.°Fgx = mg sinFN = mg cosFfr = -kFN052.0tancossin0kkfrgxmgmgFFDownhill RunDownhill RunThe slope of the downhill The slope of the downhill course is course is •sinsin = 800 m / 2500 m = 800 m / 2500 m = 19= 19°°Drag force balances the Drag force balances the force of gravity and kinetic force of gravity and kinetic friction.friction.°kg/m 0.19cossin0cossin022cvmgmgccvmgmgFFFkkdfrgxFN = mg cosFd = -cv2Ffr = -kFNFgx = mg