1MotionChapter 1: Pages 14-31Review Questions 3-8, 10, 22, 24, 26-28Study of Motion• Aristotle 4thcentury BC– Student of Plato– Tutor of Alexander– Motion ceased when objects in their proper place– Thought speed depended on weight– Ignored friction, air resistance– Influential for 2000 yearsAristotle, marble portrait bust, Roman copy (2nd century BC) of a Greek original (c. 325 BC); in the Museo NazionaleRomano, RomeGalileohttp://airandspace.si.edu/etp/discovery/disc_galileo.html• Studied Copernicus’work of 1543• Speed not dependent on weight, only on amount of time for fallingGalileo’s investigation of motion• Examined motion by experiment rather than logic• Used inclined planes to slow the descent of objects, because he didn’t have a precise timerStudy of Motion• Speed not dependent on weight, only on amount of time for falling• Noted that gravity increased speed of falling objects, decrease speed of rising objects• Defined ‘inertia’: keep moving in same direction and speed without outside influences—resistance to change of motionGalileo’s inclined planes• Balls roll down faster and faster• Roll up slower and slower• Weight not a factor2• Rises to same height as it is released• Height not dependent on inclineGalileo’s inclined planes Mass• Measure of inertia• How much matter is there• Corresponds to weight—the influence of the acceleration of gravity on the mass• They are proportionalMass• Measured in kilograms• Influence of gravity gives weight– Pounds lb.– Newtons N• 1 kg = 9.8 N• Not a measure of volumeInertia vs. weight• Weight is the force, due to gravity—pulling iron ball down• Inertia is resistance to change of movement—ball is not moving• Pull slowly, you increase force and break string that is holding the ball up• Rapid jerk will break string below ball, because it has large mass that is not moving—has inertiaForce• Weight is a force due to gravity • Force is VECTOR QUANTITY• Vectors have magnitude and direction• Multiple vectors add up Applied forces3Objects not moving• Force of weight is equal to force of string holding it up• The sum of the forces is zero• There is mechanical equilibrium Objects not movingSupport Force• Weight acts downward• Atoms push back upwardDynamic Equilibrium• Can be moving• At a constant speed in a straight line• Net forces are zeroFriction• Force that acts to resist motion• Always in opposite direction to applied force• When you are pushing something, and it moves at a constant speed, the frictional force is the same as the pushing force• Speed—how fast • Velocity—how fast and what direction• Acceleration—how fast it is changing how fastStudy of Motion4Speedtimespeeddistance==hkm4320h80kmCommon units of speed• Miles per hour mph mi./h• Kilometers per hour km/h• Meters per second m/sSpeed of cheetahsm4100sm25=sm/25Distance equationdistance timeRate =ו Keep units with numbers, so you know you have set up the problems correctlyExample of speed calculationkmhhkm320480=•• Notice that hours cancels because it is above and below the fraction barCar traveling• 60 km/h for 4 h• 60 km/h for 10 h=• hhkm460=• hhkm1060km240km6005Speed and VelocityAccelerationinterval Timeyin velocit ChangeonAccelerati• =CHANGE of speed over time, not the RATE of speed• RATE OF CHANGEDelta Δ• Δ is the fourth letter in the Greek alphabet• Used in equations to represent change• Δv = change in velocity– Find final velocity, find initial velocity, and subtract• Δt = change in time, or time interval from beginning to end• Units of time appear twice in denominatorExamples of acceleration• Driving on Monmouth Avenue at 20 mi./h• Increase to 45 mi./h in 25 seconds—change in speed is:• Divide change of speed by timeand=−hmihmi .20.45smhmi 2.11.25=shmishmia ⋅== /.125/.25hmi.25How to Convert to s2smmimhhmi 2.11.1610minsec60min601.25=•••244.025/2.11smssma ==Change Δ v to m/sfrom mi./h by using unit fractionsThen divide by amount of time over which the change occursAccelerationNotice that time units appear in denominator twiceBecause it is an amount of time over which the change of speed occursshmishmia ⋅== /.125/.25244.025/2.11smssma ==6Acceleration• Car can go from stopped to 90 km/h in 10 seconds• Be sure to REDUCEto lowest termsshkm10/90shkm⋅= /9smhrkm 2590=25.210/25smssm=Acceleration• Car goes from 60 km/h to 80 km/h in 10 seconds• First find amount of change of speed• Then divide by timeshkmshkm⋅= /210/20smhrkm 5.520=255.010/5.5smssm=hkmhkmhkmv206080=−=ΔAcceleration• Bicycle goes from rest to 5 km/h in 2.5 secondsshkmshkm⋅= /25.2/5255.05.2/39.1smssm=smhrkm 39.15=Acceleration of gravity•9.81 m/s2 at sea level• Round off to 10 m/s2for ease of calculation• …unless you are trying to launch a rocket to space, etc.Acceleration of Gravity• Acceleration same for each second of travel• Free falling objects Acceleration of Gravity• Free fall of object• Speed increases 10 m/s for every second of fall• 10 m/s= 10mss2Time elapsed(seconds)Speed (meters/ second)00 1102203304407Acceleration of Gravity• Upward throw 30 m/s• Gravity acts against it• Slows to stop at 10 m/s2• Falls and gains speed at 10 m/s2• Neglecting air resistance• Surface area changes air resistance• Objects reach terminal velocity due to air resistance• In vacuum, this is not a factorGalileo’s investigation of motionAcceleration• Neglect air resistance for these equationsa= Δv/ Δt Æ v=at• acceleration is velocity divided by time• velocity acquired is acceleration multiplied by timeHang time for basketball player• Spud Webb slam dunk contest• He can jump 1.25 m. How long is he in the air?→to go up, so double for time in the airgdt2=• http://www.youtube.com/watch?v=BUu7drj9hPw221gtd =ssmmgdt
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