KINEMATICS IN ONE DIMENSION CHAPTER 2 GIANCOLI

MECHANICS THE STUDY OF MOTION OF OBJECTS AND THE RELATED CONCEPTS OF FORCE AND ENERGY DIVIDED INTO TWO PARTS

KINEMATICS HOW OBJECTS MOVE

DYNAMICS WHY OBJECTS MOVE

TRANSLATIONAL MOTION MOTION WITHOUT ROTATION

FRAME OF REFERENCE ANY MEASUREMENT OF POSITION, VELOCITY, OR DISTANCE MUST HAVE A POINT OF REFERENCE. COORDINATE AXES DISPLACEMENT – CHANGE IN POSITION

AVERAGE VELOCITY AVERAGE SPEED = DISTANCE/TIME AVERAGE VELOCITY=DISPLACEMENT TIME

SCALAR V.S. VECTOR SCALAR – MAGNETUDE ONLY VECTOR – MAGNETUDE + DIRECTION

WHITE BOARD ACTIVITY THE POSITON OF A RUNNER AS A FUNCTION OF TIME IS PLOTTED AS MOVING ALONG THE X AXIS OF THE COORDINATE SYSTEM. DURING A 3.00 S TIME INTERVAL, THE RUNNER’S POSITON CHANGES FROM 50.0M TO 30.5M. WHAT IS THE RUNNER’S AVERAGE VELOCITY?

MOTION OF RUNNER GRAPH OF RUNNER X X 0 10 20 30 40 50 60

ANSWER -6.50 M/S WHY IS IT NEGATIVE?

PRACTICE HOW FAR CAN A CYCLIST TRAVEL IN 2.5 H ALONG A STRAIGHT ROAD IF HER AVERAGE SPEED IS 18 KM/H? 45 KM

INSTANTANEOUS VELOCITY THE AVERAGE VELOCITY OVER AN INFINTESIMALLY SHORT TIME. WHY DOES INSTANTANEOUS SPEED ALWAYS EQUAL INSTANTEOUS VELOCITY? BECAUSE DISTANCE AND DISPLACEMENT BECOME THE SAME WHEN THEY ARE INFINTESIMALLY SMALL.

ACCELERATION THE RATE OF CHANGE OF THE VELOCITY OVER A GIVEN PERIOD OF TIME. AVERAGE ACCELERATION IS THE CHANGE IN THE VELOCITY DIVIDED BY THE TIME TAKEN TO MAKE THIS CHANGE.

PRACTICE A CAR ACCELERATES ALONG A STRAIGHT RAOD FROM REST TO 75 KM/H IN 5.0 S. WHA TIS THE MAGNITUDE OF ITS AVERAGE ACCELERATION? 15 KM/H/S

QUESTION IF THE VELOCITY OF AN OBJECT IS ZERO, DOES IT MEAN THAT THE ACCELERATION IS ZERO? IF THE ACCELERATION IS ZERO, DOES THAT MEAN THE VELCITY IS ZERO?

UNIFORMLY ACCELERATED MOTION CONSTANT ACCELERATION THE MAGNETUDE DOES NOT CHANGE THE DIRECTION DOES NOT CHANGE

CONSTANT ACCELERATION EQUATIONS V=Vo + AT X = Xo + VoT + 1/2AT2 V2 = Vo2 +2A(X-Xo) V = V + Vo 2

PROBLEM SOLVING RECIPE READ AND REREAD DRAW A DIAGRAM WRITE DOWN KNOWNS THINK…WHAT PRINCIPLES APPLY EQUATION/S NEEDED CALCULATIONS DOES YOUR ANSWER SEEM REASONABLE? CHECK YOUR UNITS. THIS CAN SERVE AS A FAILSAFE FOR YOU.

FALLING OBJECTS PRIME EXAMPLE OF UNIFORMLY ACCELERATED MOTION ACCELERATION IS DUE TO GRAVITY 9.80 m/s/s

GALILEO’S HYPOTHESIS ..FREE FALL IS AT CONSTANT ACCELERATION G. …SUMMARIZE GALILEO’S CONTRIBUTION….AT A GIVEN LOCATION ON THE EARTH AND IN THE ABSENCE OF AIR RESISTANCE ALL OBJECTS FALL WITH THE SAME CONSTANT ACCELERATION. IT APPROXIMATE MAGNETUDE IS 9.80 M/S/S

PROBLEM SUPPOSE THAT A BALL IS DROPPED FROM A TOWER 70.0 M HIGH. HOW FAR WILL IT HAVE FALLEN AFTER 1.00S, 2.00S, AND 3.00S? ASSUME Y IS POSITIVE DOWNWARD. NEGLECT AIR RESISTANCE.

ANSWER Y=1/2AT2 4.90 M 19.6 M 44.1 M

PRACTICE MORE WHAT IF THE BALL IS THROWN DOWNWARD WITH AN INITIAL VELOCITY OF 3.00 M/S, INSTEAD OF BEING DROPPED. A. WHAT THEN WOULD BE ITS POSTION AFTER 1.00S, 2.00S?

ANSWER X = Xo + VoT + 1/2AT2 Y = VoT + 1/2AT2 7.90 M 25.6 M

MORE WHAT WOULD ITS SPEED BE AFTER 1.00S AND 2.00S? V=Vo + AT 12.8 M/S NOW CALCULATE THE SPEEDS OF THE DROPPED BALL FOR 1.00 S AND 2.00 S.

MORE 9.80 M/S 19.6 M/S HOW DO THESE SPEEDS COMPARE TO THE SPEEDS OF THE DROPPED BALL? THE SPEED OF THE BALL INCREASES LINEARLY WITH TIME FOR BOTH SCENERIOS, BUT THE THROWN BALL IS ALWAYS 3.0 M/S GREATER THAN THE BALL IN FREE FALL.

OBJECTS THROWN UPWARD WHAT GOES UP MUST COME DOWN IN THE SAME AMOUNT OF TIME IT TOOK TO GO UP! ACCELERATION IS G GOING UP AND DOWN V = 0 M/S AT THE ZENITH WHAT IS THE ACCELERATION AT THE ZENITH?

QUESTIONS ARE VELOCITY AND ACCELERATION ALWAYS IN THE SAME DIRECTION? WHAT IS THE ACCELERATION OF AN OBJECT AT ITS HIGHEST POINT?

QUADRATIC FORMULA THERE MAY BE TIMES YOU WILL NEED TO USE THE QUADRATIC FORMULA IN PROBLEM SOLVING. SEE EXAMPLE 2-15 ON PAGE 37 FOR A CLEAR AND CONCISE EXAMPLE.

GRAPHICAL ANALYSIS OF LINEAR MOTION SLOPE ON A POSITION/TIME GRAPH IS EQUAL TO THE VELOCITY SLOPE ON A VELOCITY/TIME GRAPH IS EQUAL TO ACCELERATION. THE AREA UNDER THE CURVE IN A VELOCITY/TIME GRAPH IS EQUAL TO THE DISPLACEMENT