Intro to Mechanics: The Sudy of Motion
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Speed is the rate of change of position with time. It is a scalar quantity while velocity includes both speed and direction, making it a vector quantity. Motion can be described using graphs of distance versus time or displacement versus time. The slope of these graphs gives the speed or velocity. Speed is calculated as distance divided by time, while velocity considers both speed and direction of motion.
Intro to Mechanics: The Sudy of Motion
- 1. Speed & VelocitySpeed & Velocity Intro to Mechanics - The Study of MotionIntro to Mechanics - The Study of Motion
- 2. In your lab notebook, please answer as best you can: 1. What direction should the decimal point be moved when converting from mm to km? • Left (6 places) 2. How many decibels is 0.0385 hectobels? • 38.5 dB 3. Convert 30 meters into feet. (1 m≈ 3.3 ft) • 99 ft 4. Convert 150 lb into kg. (1kg ≈ 2.2 lb) • 68.2 lb 4. What speed is 45 m/s in miles per hour? (1 km ≈ 0.6 mi) • 97.2 mph Bonus Question: What is “DIMENSIONAL ANALYSIS” and what is it used for? Dimensional analysis is a method of using equivalent fractions to convert units of measurement.. Review Quiz 23
- 3. What is Motion?What is Motion? Motion = a change in positionMotion = a change in position An eagle flies from its nest to a tree branchAn eagle flies from its nest to a tree branch A man pushes a box of cookies across his deskA man pushes a box of cookies across his desk An elevator moves from the lobby to 25An elevator moves from the lobby to 25thth floorfloor
- 4. All Motion is RelativeAll Motion is Relative Reference pointReference point Change in position depends on an object thatChange in position depends on an object that is referred to:is referred to: man is moving relative to ground but NOT relativeman is moving relative to ground but NOT relative to train carto train car
- 5. SpeedSpeed Speed measures the rate at which aSpeed measures the rate at which a change in position occurschange in position occurs Speed =Speed = distancedistance timetime Banana Slugs: 0.75 inches/hour Average Highway Speed: 65 mph Eye Blinks: 0.005 centimeter/millisecond Earth’s Orbit: 30 km/s Speed of Light: 300,000,000 meters/second
- 6. Rates & RatiosRates & Ratios What does 65 mph mean?What does 65 mph mean? 65 miles65 miles 1 hour1 hour How far will I travel with a speed of 25 m/s if IHow far will I travel with a speed of 25 m/s if I go for 2 hours?go for 2 hours? 25 meters25 meters x 7,200 s = 180,000 mx 7,200 s = 180,000 m (180 km)(180 km) 1 second1 second * The line in any fraction or ratio means DIVIDE!* The line in any fraction or ratio means DIVIDE! 65 miles Speed x time = distanceSpeed x time = distance
- 7. SpeedSpeed Constant speedConstant speed: speed remains the same for: speed remains the same for entire distance travelledentire distance travelled Instantaneous speedInstantaneous speed: speed at one given instant: speed at one given instant Average speedAverage speed: total distance/total time: total distance/total time 15 meters in 145 seconds = .1 m/s15 meters in 145 seconds = .1 m/s 1 meter in 5 seconds = .2 m/s 2 meters in 8 seconds = .25 m/s 1 meter in 10 seconds = .1 m/s 2 meters in 30 seconds = .07 m/s 3 meters in 17 seconds = .18 m/s 3 meters in 60 seconds = .05 m/s 3 meters in 15 seconds = .2 m/s
- 8. Displacement vs. DistanceDisplacement vs. Distance DistanceDistance: how far something moved: how far something moved 8.2km + 1.8km + 4.5km = 14.5 kilometers8.2km + 1.8km + 4.5km = 14.5 kilometers DisplacementDisplacement: shortest distance between: shortest distance between starting point and ending pointstarting point and ending point 2.7 km North2.7 km North *includes direction**includes direction* DistanceDistance is ais a scalarscalar measuremeasure DisplacementDisplacement is ais a vectorvector measuremeasure because it includes directionbecause it includes direction
- 9. Graphing SpeedGraphing Speed Time in Seconds DistanceinMeters 1 meter in 5 seconds = .2 m/s 2 meters in 8 seconds = .25 m/s 1 meter in 10 seconds = .1 m/s 2 meters in 30 seconds = .07 m/s 3 meters in 17 seconds = .18 m/s 3 meters in 60 seconds = .05 m/s 3 meters in 15 seconds = .2 m/s Average speed = .1 m/s
- 10. Slope = SpeedSlope = Speed Time in Seconds DistanceinMeters
- 11. Experiment 24 Distance-Time Graphs Distance Time Calculated Speed Trial 1 Trial 2 Trial 3 1)Design your experiment to minimize variables. 2)Measure the distance traveled and time traveled. RECORD THE VALUES IN A TABLE. 1)Calculate the speed in each trial using: 2)Graph your data with distance on the y-axis and time on the x-axis. Include all trials on the same graph
- 13. Displacement – Time GraphsDisplacement – Time Graphs 1) Where did the runner start? 2) At what position did the runner stop? (relative to what?) 3) Does the graph show distance or displacement? 4) How long did it take the runner to get to their final position? 5) What can you tell about the speed of the runner? 6) What does a negative slope indicate? 7) How would this graph change if the y-axis showed total distance instead of displacement?
- 14. VelocityVelocity Velocity = Speed + DirectionVelocity = Speed + Direction A vector quantityA vector quantity SpeedSpeed: 32 m/s: 32 m/s VelocityVelocity: 32 m/s: 32 m/s SoutheastSoutheast Why does direction matter?Why does direction matter?
- 15. Transportation QuandaryTransportation Quandary You must get from Kyoto to Nagano forYou must get from Kyoto to Nagano for watchwatch the world figure skating championships.the world figure skating championships. The Bullet Train travels East & West at speeds over 350 km/hr.The Bullet Train travels East & West at speeds over 350 km/hr. A personal tachikoma can go up to 85 km/hr in any direction.A personal tachikoma can go up to 85 km/hr in any direction. Solar cell buses move North & South at 60 km/hr.Solar cell buses move North & South at 60 km/hr. A hired Pivo taxi will take you 105 km/hr NE or 125 km/hr SW.A hired Pivo taxi will take you 105 km/hr NE or 125 km/hr SW. Which mode of transportation should you take?Which mode of transportation should you take?
Editor's Notes
- #3: 1 Coulomb = 6.25 x 1018 electrons
- #8: What does the line mean? DIVIDE! If we plotted these points on a graph, what would they look like?
- #9: Example: walk across room and back. Forward/backward motion.
- #10: Average of speeds = 0.15 m/s 15 m ÷ 145 s = 0.10344
- #11: Who ran the greatest distance? (Conner) Who had the greatest (fastest) instantaneous speed? (Gracie) Who had the fastest average speed? (Connor) Why is Ankush’s graph a straight line? (his speed is continually the same) What is happening with Gracie after 1 minute? (she stops running)
- #12: Materials: matchbox cars, train cars/tracks, tennis/bouncy balls, toy cars, nerf guns/darts, wind-up moving toys Procedures: Push or drop item Time and measure distance traveled (record data in chart) Calculate average speed Graph data
- #16: Answer: the taxi and tachikoma are the only vehicles that will travel NE, the direction Nagano is from Tokyo. Since the taxi is much faster, it is the best choice.