Understanding Motion and Speed: Kinematics Explained

1. Set - 3 Motion & Speed Start Kinematics HW: Read Chapter 2. Watch for New WebAssign

2. Check the website for evil clicker information. • In the left hand column of the website there is a list of clickers that appear to be unregistered. • If you find your clicker number there, please register. • If you find it there and you HAVE registered, send me you PID and full name along with your clicker number and I will manually enter it. Click it! It’s the LAW!

3. Motion & Speed

4. When lightening strikes, you see a flash of light. Some seconds later, you hear the thunder. The thunder is SOUND arising from the sudden expansion of the air at the time of the flash. How do we explain the delay? Remember the lightning?

5. Science Measures So what can we measure? • We know how to measure distance (meter stick). • We know how to measure time (clock). • We know that the lightening strikes at a particular point, but we can’t PREDICT where it will hit. • We can’t do much with this experiment. • Let’s think about a new one.

6. Definition • If something takes a time (Dt) to travel a distance (Dx), we can define the speed (s) as For the moment, the object is assumed to be traveling in a straight line

7. (From the textbook)Average Speed (defined) • Average speed is defined as the total distance traveled divided by the time it took to cover this distance. (A bar is often used over a symbol to indicate its average value.)

8. d=s x t

9. So.. • The distance traveled during this interval of time is simply the speed multiplied by the time. • Example: • You are traveling at 80 miles an hour. How far would you travel in 30 minutes? • Distance=speed x time • . And about $2.00 in gasoline And a traffic ticket!

10. A historical experiment • Cannon • Guy with stop watch • Light … start watch • Boom … stop watch D

11. In 1635 • The philosopher Pierre Gassendi did this experiment. He got 478 m/s and did not own a Rolex. (50% high) • A few years later Mersenne did the experiment and got 450 m/s • In 1738 a team from the Paris Academie des Sciences got 344 m/s • Accepted value: 343 m/s or 1125 ft/sec • The big mistake that Gassendi and Mersenne made seems to be having ignored the effect of the wind.

12. Speed of sound We will take it as 1100 ft/sec This is about 1/5th of a mile

13. Knowing that the speed of sound is about 1/5th of a mile/second … • When you see lightening, start counting off the seconds … one and two and three and … etc. • When you hear the thunder, stop counting. • Divide the number you stopped at by 5. (d=s x t) • s=1/5 mils/sec. • That is how far the lightening strike was from where you are standing. (in miles.)

14. Ponder If you hear the thunder at the same time that you see the lightening, how dead are you?

15. Measuring Speed • To measure speed, we used a device for measuring distance, • such as a ruler, and one for measuring time, • such as a clock. These mile markers and your wristwatchgive you all the information you need todetermine average speeds.

16. Images of Speed • A blurred painting or photograph such as that in the figure is one way to “see” motion.

17. Images of Speed • A multiple-exposure photograph is a method that also provides a way of measuring the speed of an object. • These photographs are made in a totally dark room with a strobe and a camera with an open shutter. A strobe is a light source that flashes at a constant, controllable rate—about 10 millionths of a second—producing a still image of the moving object. Demo??

18. What’s Happening Here?

19. Images of Speed • If the strobe flashes 10 times per second, the resulting photograph will show the position of the object at time intervals of 0.1 second. Thus, we can “freeze” the motion of the object into a sequence of individual events and use this representation to measure its average speed within each time interval.

20. Images of Speed • As an example of measuring average speed, let’s determine the average speed of the puck in the figure below.

21. Images of Speed • The puck travels from a position near the 4-cm mark to one near the 76-cm mark: • a total distance of 72 centimeters. • Because there are seven images, there are six intervals. • The total time taken is six times the time between flashes—that is, 0.6 second. • Therefore, the average speed is:

22. Working It Out: Average Speed • If you know the average speed, you can determine other information about the motion. • You plan to drive 60 miles with the cruise control set at 50 mph. How long will it take to get there? • You plan to maintain an average speed of 50 mph on an upcoming trip. How far can you travel if you drive an 8-h day?

23. Average Speed vs. Instantaneous Speed • Suppose you live 40 miles from school and it takes you 2 hours to drive home. Your average speed during the trip is: This means that, on the average, you travel a distance of 20 miles during each hour of travel. Still: • You may have stopped at traffic lights (0 mph); • You may have traveled at 50 mph at some point. • The use of average speed disregards the details of the trip.

24. Average Speed vs. Instantaneous Speed • Actually, the definitions of average and instantaneous speeds are quite similar. They differ only in the size of the time interval involved. • If you want to know how fast you are going at a given instant, try studying the motion during a very small time interval. The instantaneous speed is equal to the average speed over a time interval that is very, very small.

25. Note: Instantaneous speed, rather than the average speed, plays an important role in the analysis of nearly all realistic motions.

26. Definition of Instantaneous Speed • This more complete description of motion tells us how fast you were traveling at any instant during your trip. A speedometer tells you the car’s instantaneous speed.

27. Some Definitions • If you travel a total distance D in time “t”, the average speed is: • <speed>=<s>= s =D/t • We use the Greek letter “D” to indicate very SMALL changes. • If you travel a tiny distance Dx in miniscule time “Dt”, the instantaneous speed s is: • instantaneous speed:

28. Measure This! • The fastest things you might ever try to measure: • Light: 186,000 mps (miles / sec) • Planet Earth: 67,000 mph • The sound of music: 1100 ft/sec • The slowest things you might try to measure: • The giant sloth: 0.07 mph • Continents: 1 cm / year

29. Let’s take a trip … • Travel from A to B at 50 miles per hour. • How long does it take to make this trip if A and B are 50 miles apart?

30. Do you want to reconsider? A A B We need to specify the PATH!

31. Volunteer • Come to the front of the room • Take three steps • Stop • You are wrong! What about DIRECTION ??

32. Vectors

33. Speed with Direction • Objects do more than speed up and slow down. They can also change direction, • while maintaining their speed, • or changing both speed and direction at once. • Either the average speed or the instantaneous speed tells us how fast an object is moving, but neither tells us the direction of motion.

34. Vector • The magnitude of a quantity is represented by the LENGTH of an arrow (vector) • The direction is specified by the direction of the arrow.

35. Example • 10 steps to the right: • 10 Steps up

36. 10 steps to the right and 10 Steps up Sum A+B B A

37. More Definitions • Speed is a scalar quantity. No direction. • Velocity is a speed and a direction of that speed together. It is a vector

38. Ponder: A woman jogs from A to B to C to D in 30 minutes • What was the average speed of the woman? • What was the average velocity of the woman? • Is she fast? Which of these two quantities addresses this question? 1.0 miles B C Rectangle 0.5 m A D

39. Let’s move on …