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Chapter 3 Linear Motion

Chapter 3 Linear Motion . (Motion in a straight line, such as falling straight downward). Demo : Cracking Nuts. What’s the best way to crack open a nut?. Tools you’ll learn today. Speed and Velocity Acceleration Relationships among distance, velocity, and acceleration. Falling motion.

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Chapter 3 Linear Motion

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  1. Chapter 3Linear Motion (Motion in a straight line, such as falling straight downward) Physics 1 (Garcia) SJSU

  2. Demo: Cracking Nuts What’s the best way to crack open a nut? Physics 1 (Garcia) SJSU

  3. Tools you’ll learn today • Speed and Velocity • Acceleration • Relationships among distance, velocity, and acceleration. • Falling motion. Physics 1 (Garcia) SJSU

  4. Speed Define speed of an object as (Distance traveled) (SPEED) = (Time elapsed) For example, 30 miles per hour means object travels distance of 30 miles in an elapsed time of one hour. Write as, miles 30 miles per hour = 30 hour Physics 1 (Garcia) SJSU

  5. Speed and Distance From definition of speed, (Distance traveled) = (Speed) X (Time elapsed) Example: If speed is 30 miles per hour and time elapsed is 2 hours then distance traveled is (30)X(2) = 60 miles. Match units: This time elapsed is also 120 minutes but it’s not correct to compute distance traveled as (30)X(120) = 3600 miles {WRONG}. Physics 1 (Garcia) SJSU

  6. Check Yourself What is the average speed of a cheetah that sprints 100 meters in 4 seconds? How about if it sprints 50 meters in 2 seconds? A car has an average speed of 100 kilometers per hour. How far does it travel in 60 minutes? Physics 1 (Garcia) SJSU

  7. Average versus Instantaneous Sometimes consider average speed, other times we speak of instantaneous speed. For example, say it takes you one hour to drive the 30 miles from home to campus. Average speed is 30 miles per hour. Instantaneous speed (given by your speedometer) varies due to traffic, stop lights, morons driving in front of you, etc. Physics 1 (Garcia) SJSU

  8. Demo: Ball Races Which ball wins the race, A or B? A Finish Line B Which ball has the larger average speed? Which has the larger instantaneous speed at each point. Physics 1 (Garcia) SJSU

  9. Check Yourself A car has an average speed of 60 miles per hour. Is it possible for the instantaneous speed to always be less than 60 miles per hour? Physics 1 (Garcia) SJSU

  10. Velocity Velocity is speed and direction of object’s motion. Examples: 30 miles per hour, Northward 25 meters per second, Downward 300 miles per hour, Coming towards you 25 m/s, upward 25 m/s, downward Same speeds Different velocities Physics 1 (Garcia) SJSU

  11. Check Yourself The speedometer of a car moving east reads 100 km/h. It passes another car moving west at 100 km/h. Do they have same speed? Velocity? During a certain period of time, the speedometer of a car reads a constant 60 km/h. Does this indicate a constant speed? Constant velocity? Physics 1 (Garcia) SJSU

  12. Changes in Velocity Velocity changes if speed or direction of motion change. Velocity changes in both these cases. 10 m/s, downward 25 meters per second, 45 degrees upward 25 m/s, downward 25 meters per second, 45 degrees downward Physics 1 (Garcia) SJSU

  13. Acceleration Define acceleration as, (Change in Velocity) (ACCELERATION) = (Time interval) Note: An object accelerates anytime its velocity changes. Examples include: Object speeds up. Object slows down (speed decreases). Object speed constant but direction changes (curved path) Best example of acceleration is objects in free fall Physics 1 (Garcia) SJSU

  14. Demo: String of Falling Balls Falling objects accelerate (speed increases). Listen for the sound as balls hit the ground. Time between “clicks” gets shorter & shorter (falling faster & faster). String does not pull; no tension while falling. Physics 1 (Garcia) SJSU

  15. Velocity in Free Fall (Down) Release Zero meters per sec. How fast do objects go when they fall? Acceleration of gravity is 10 meters per second per second. With each second of fall, speed increases by 10 meters/second 1 second 10 meters per sec. 2 seconds 20 meters per sec. 3 seconds 30 meters per sec. 4 seconds Physics 1 (Garcia) SJSU 40 meters per sec.

  16. Velocity in Free Fall (Up & Down) Zero meters per sec. Moving upward, with each second the speed decreases by 10 meters/second. Going back down the motion exactly reverses itself. See Fig. 3.8 (pg. 47) 10 meters per sec. 20 meters per sec. 30 meters per sec. 40 meters per sec. Physics 1 (Garcia) SJSU

  17. Position in Free Fall Release 5 meters How far do objects go when they fall? More complicated because speed is increasing. There’s a pattern & Galileo figured it out. But it wasn’t easy. 1 second Higher than this ceiling 20 meters 2 seconds 45 meters 3 seconds Higher than King library 4 seconds 80 meters Physics 1 (Garcia) SJSU

  18. Galileo’s Inclines Galileo realized that rolling down an incline and falling were very similar. It was much easier for him to study the slower motion of an incline. Physics 1 (Garcia) SJSU

  19. Demo: Galileo’s Clicking Ramps Roll balls down notched, inclined ramps and listen for the clicks. 8 16 24 32 40 48 56 64 Start 1 4 9 16 25 36 49 64 4=2x2 9=3x3 16=4x4 25=5x5 36=6x6 49=7x7 64=8x8 Physics 1 (Garcia) SJSU

  20. Position in Free Fall (cont.) Release 5 meters Galileo realized that: 1 second 5=5x 1x1 (Distance Fallen) = ½ (Acceleration)(Time)(Time) 20 meters 2 seconds 20=5x 2x2 Gravity acceleration is 10 meters per second per second so at a time of 3 seconds, 45 meters 3 seconds 45=5x 3x3 (Distance Fallen) = ½ (10)(3)(3) = 45 meters 4 seconds 80 meters Physics 1 (Garcia) SJSU 80 =5x 4x4

  21. Lab: Acceleration of Gravity Record position of falling object using spark timer and paper tape. Physics 1 (Garcia) SJSU

  22. Demo: Dropping the Ball How long does it take a ball to fall 3 meters? Using the formula, (Distance Fallen) = ½ (Acceleration)(Time)(Time) Can check that it takes 0.77 seconds since (3) = ½ (10)(0.77)(0.77) Beauty of science: Predict, then verify by dropping balls! Note: Do similar measurement in first experiment in the Phys 1L lab. Physics 1 (Garcia) SJSU

  23. Demo: Catch a Buck Put thumb and index fingers near Washington’s head. Can you react fast enough to catch the money? Physics 1 (Garcia) SJSU

  24. Demo: Reaction Time Distance (inches) Time (sec.) 1 0.07 2 0.10 3 0.12 4 0.14 5 0.16 6 0.17 7 0.19 8 0.20 10 0.23 12 0.25 14 0.27 16 0.29 18 0.30 Release Catch Physics 1 (Garcia) SJSU

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