Motion in our Daily Lives 04/28/2008Lecture 10 1UCSDPhysics 10Motion in Our Daily LivesMotion in Our Daily LivesEmphasis on amusement parks,Emphasis on amusement parks,circular motioncircular motionSpring 2008 2UCSDPhysics 10What kind of motions do we What kind of motions do we feelfeel??••Aside from vibrations, donAside from vibrations, don’’t feel constant velocityt feel constant velocity– Earth moves 30,000 m/s around sun• only curves 3 mm toward sun each second, so compared to the30,000 meters, you could say that our path is almost straight••But we can But we can feelfeel acceleration acceleration– It’s that “visceral” feeling…– vis·cer·al adj. 1. Relating to, situated in, or affectingthe viscera. 2. Perceived in or as if in the viscera.– vis·cer·a pl.n. 1. The soft internal organs of the body,especially those contained within the abdominal andthoracic cavities. 2. The intestines. [3. Your gut.]Spring 2008 3UCSDPhysics 10Questions:Questions:••Why do we feel acceleration? What is it about ourWhy do we feel acceleration? What is it about ourgutgut that tells us we that tells us we’’re moving? What other organsre moving? What other organsin our body tell us we are accelerating?in our body tell us we are accelerating?– Think in terms of amusement park rides, whereacceleration is extreme (or like how my sister drives).••Can you Can you feelfeel gravity when you gravity when you’’re sitting still?re sitting still?Standing? Laying down? Falling?Standing? Laying down? Falling?Spring 2008 4UCSDPhysics 10Motion in our livesMotion in our lives••WeWe’’ll ignore constant velocity: just like sitting stillll ignore constant velocity: just like sitting still– boring••But accelerating motionBut accelerating motion……– that’s where things get interesting••Direction of acceleration is the same as theDirection of acceleration is the same as thedirection of direction of net forcenet force••Acceleration perpendicular to the velocity vectorAcceleration perpendicular to the velocity vectoracts to change the acts to change the directiondirection of motion. of motion.Motion in our Daily Lives 04/28/2008Lecture 10 2Spring 2008 5UCSDPhysics 10The Amusement Park: Acceleration CentralThe Amusement Park: Acceleration Central••Zero-Zero-gg (no acceleration) motion (no acceleration) motion– Free-fall, cresting roller coaster••Linear accelerationLinear acceleration– log flume deceleration, roller coaster abrupt stop••Directional changes (bread & butter of parks)Directional changes (bread & butter of parks)– Curves of roller coaster, tilt-a-whirl, swings– Loops, crests, troughs of roller coasters– Spinning drum (pinned against wall)Spring 2008 6UCSDPhysics 10Free fallFree fall••By dropping a carriage, or by launching a car on aBy dropping a carriage, or by launching a car on aparabolic path, experience momentary zero-parabolic path, experience momentary zero-gg••You You areare accelerating downwards toward the earth, accelerating downwards toward the earth,but no longer but no longer feelfeel accelerated: don accelerated: don’’t feel weightt feel weight– only lasts a brief moment: 15-story (45 m) drop onlylasts about 3 secondsNASA conducts zero-g flights lasting 30 seconds by flyinga parabolic path in a plane that has come to be known as the “vomit comet”.www.avweb.com/articles/vcomet/Spring 2008 7UCSDPhysics 10Linear Acceleration (in velocity direction)Linear Acceleration (in velocity direction)••This is the familiar stoplight acceleration along aThis is the familiar stoplight acceleration along astraight linestraight line••Zero to Sixty-Seven (30 m/s) in 5 seconds:Zero to Sixty-Seven (30 m/s) in 5 seconds:– 30 m/s in 5 seconds means 6 m/s2 (~0.6g)••Typical car acceleration, normal driving ~0.2Typical car acceleration, normal driving ~0.2gg••Fun activity: drive with helium balloons in carFun activity: drive with helium balloons in car– They move into acceleration--counter-intuitive– They simply point the way a plumb bob hung from therear-view mirror doesn’tSpring 2008 8UCSDPhysics 10Questions:Questions:••During which part of a roller coaster ride do youDuring which part of a roller coaster ride do youfeel heaviest: at the bottom of a dip or at the crestfeel heaviest: at the bottom of a dip or at the crestof a hill? Where do you feel the lightest?of a hill? Where do you feel the lightest?••If youIf you’’re in an elevator with an upward/downwardre in an elevator with an upward/downwardacceleration rate of 1 m/sacceleration rate of 1 m/s22 and you normally and you normallyweigh 100 pounds, how much will you weighweigh 100 pounds, how much will you weighwhen the elevator accelerates upwards?when the elevator accelerates upwards?Downwards?Downwards?– Assume gravity is 10 m/s2 for numerical simplicityMotion in our Daily Lives 04/28/2008Lecture 10 3Spring 2008 9UCSDPhysics 10Curves, Centrifugal, Centripetal ForcesCurves, Centrifugal, Centripetal Forces••Going around a curve Going around a curve smushes smushes you against windowyou against window– Understand this as inertia: you want to go straightyour body wants tokeep going straightbut the car is acceleratingtowards the center of the curveCar acceleration is v2/r you think you’re being accelerated by v2/r relative to the carSpring 2008 10UCSDPhysics 10Centripetal, Centrifugal Forces, continuedCentripetal, Centrifugal Forces, continued••The car is accelerated toward the center of theThe car is accelerated toward the center of thecurve by a curve by a centripetalcentripetal (center seeking) force (center seeking) force••In your reference frame of the car, you experienceIn your reference frame of the car, you experiencea a ““fakefake””, or fictitious centrifugal , or fictitious centrifugal ““forceforce””– Not a real force, just inertia relative to car’s accelerationCentripetal Forceon carvelocity of car(and the way you’d rather go)Spring 2008 11UCSDPhysics 10Pictorial Pictorial ““DerivationDerivation”” of Centripetal Acceleration of Centripetal Accelerationv1v2a = v/tIn uniform circular motion theacceleration is constant, directedtowards the center. The velocityhas constant magnitude, and istangent to the path.Top view:aaaaaa = v2/r (r is radius of curve)Spring 2008 12UCSDPhysics 10Rotating Drum RideRotating Drum Ride••Vertical drum rotates,