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# PHYS 101 Chapter 1

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• Have a pendulum demo. Adjust the length and let them count the number of cycles. Maybe also have a spring.
• Do the bucket over the head demo (maybe paper instead of water)
• Try the tape spark demo
• ### PHYS 101 Chapter 1

1. 1. Chapter 1 The Study of Motion
2. 2. Units <ul><li>We can classify almost all quantities in terms of the fundamental physical quantities : </li></ul><ul><ul><li>Length L </li></ul></ul><ul><ul><li>Mass M </li></ul></ul><ul><ul><li>Time T </li></ul></ul><ul><ul><ul><li>For example: </li></ul></ul></ul><ul><ul><ul><ul><li>Speed has units L/T (miles per hour) </li></ul></ul></ul></ul>
3. 3. Units , cont’d <ul><li>SI (Système International) Units: </li></ul><ul><ul><li>MKS: </li></ul></ul><ul><ul><ul><li>L = meters (m) </li></ul></ul></ul><ul><ul><ul><li>M = kilograms (kg) </li></ul></ul></ul><ul><ul><ul><li>T = seconds (s) </li></ul></ul></ul><ul><ul><li>CGS: </li></ul></ul><ul><ul><ul><li>L = centimeters (cm) </li></ul></ul></ul><ul><ul><ul><li>M = grams (g or gm) </li></ul></ul></ul><ul><ul><ul><li>T = seconds (s) </li></ul></ul></ul>
4. 4. Units , cont’d <ul><li>British (or Imperial) Units: </li></ul><ul><ul><ul><li>L = feet (ft) </li></ul></ul></ul><ul><ul><ul><li>M = slugs or pound-mass (lbm) </li></ul></ul></ul><ul><ul><ul><li>T = seconds (s) </li></ul></ul></ul><ul><li>We will use mostly SI but we need to know how to convert back and forth. </li></ul>
5. 5. Units , cont’d <ul><li>The back of your book provides numerous conversions. Here are some: </li></ul><ul><ul><ul><li>1 inch = 2.54 cm </li></ul></ul></ul><ul><ul><ul><li>1 m = 3.281 ft </li></ul></ul></ul><ul><ul><ul><li>1 mile = 5280 ft </li></ul></ul></ul><ul><ul><ul><li>1 km = 0.621 mi </li></ul></ul></ul>
6. 6. Units , cont’d <ul><li>We can use these to convert a compound unit: </li></ul>
7. 7. Converting units <ul><li>Look at your original units. </li></ul><ul><li>Determine the units you want to have. </li></ul><ul><li>Find the conversion you need. </li></ul><ul><li>Write the conversion as a fraction that replaces the original unit with the new unit. </li></ul>
8. 8. Example Problem 1.1 <ul><li>A yacht is 20 m long. Express this length in feet. </li></ul>
9. 9. Example <ul><li>A yacht is 20 m long. Express this length in feet. </li></ul>ANSWER:
10. 10. Example <ul><li>How many liters are in a five gallon bucket? There are four quarts in a gallon. </li></ul>
11. 11. Example <ul><li>How many liters are in a five gallon bucket? There are four quarts in a gallon. </li></ul>ANSWER:
12. 12. Metric prefixes <ul><li>Sometimes a unit is too small or too big for a particular measurement. </li></ul><ul><li>To overcome this, we use a prefix. </li></ul>
13. 13. Metric prefixes , cont’d Power of 10 Prefix Symbol 10 15 peta P 10 12 tera T 10 9 giga G 10 6 mega M 10 3 kilo k 10 -2 centi c 10 -3 milli m 10 -6 micro  10 -9 nano n 10 -12 pico p 10 -15 femto f
14. 14. Metric prefixes , cont’d <ul><li>Some examples: </li></ul><ul><ul><li>1 centimeter = 10 -2 meters = 0.01 m </li></ul></ul><ul><ul><li>1 millimeter = 10 -3 meters = 0.001 m </li></ul></ul><ul><ul><li>1 kilogram = 10 3 grams = 1,000 g </li></ul></ul>
15. 15. Frequency and period <ul><li>We define frequency as the number of events per a given amount of time. </li></ul><ul><li>When an event occurs repeatedly, we say that the event is periodic . </li></ul><ul><li>The amount of time between events is the period . </li></ul>
16. 16. Frequency and period , cont’d <ul><li>The symbols we use to represent frequency are period are: </li></ul><ul><ul><li>frequency: f </li></ul></ul><ul><ul><li>period: T </li></ul></ul><ul><li>They are related by </li></ul>
17. 17. Frequency and period , cont’d <ul><li>The standard unit of frequency is the Hertz (Hz). </li></ul><ul><ul><li>It is equivalent to 1 cycle per second. </li></ul></ul>
18. 18. Example Example 1.1 <ul><li>A mechanical stopwatch uses a balance wheel that rotates back and forth 10 times in 2 seconds. What is the frequency of the balance wheel? </li></ul>
19. 19. Example Example 1.1 <ul><li>A mechanical stopwatch uses a balance wheel that rotates back and forth 10 times in 2 seconds. What is the frequency of the balance wheel? </li></ul>ANSWER:
20. 20. Speed <ul><li>Speed is the rate of change of distance from a reference point. </li></ul><ul><li>It is the rate of movement. </li></ul><ul><li>It equals the distance something travels divided by the elapsed time. </li></ul>
21. 21. Speed , cont’d <ul><li>In mathematical notation, </li></ul><ul><li>So we can write speed as </li></ul>
22. 22. Speed , cont’d <ul><li>The symbol  is the Greek letter delta and represents the change in . </li></ul><ul><li>As the time interval becomes shorter and shorter, we approach the instantaneous speed . </li></ul>
23. 23. Speed , cont’d <ul><li>If we know the average speed and how long something travels at that speed, we can find the distance it travels: </li></ul>
24. 24. Speed , cont’d <ul><li>We say that the distance is proportional to the elapsed time: </li></ul><ul><li>Using the speed gives us an equality, i.e., an equal sign, so we call v the proportionality constant . </li></ul>
25. 25. Speed , cont’d <ul><li>Note that speed is relative. </li></ul><ul><ul><li>It depends upon what you are measuring your speed against. </li></ul></ul><ul><li>Consider someone running on a ship. </li></ul>
26. 26. Speed , cont’d <ul><li>If you are on the boat, she is moving at </li></ul>
27. 27. Speed , cont’d <ul><li>If you are on the dock, she is moving at </li></ul>
28. 28. Example <ul><li>When lightning strikes, you see the flash almost immediately but the thunder typically lags behind. The speed of light is 3 × 10 8 m/s and the speed of sound is about 345 m/s. If the lightning flash is one mile away, how long does it take the light and sound to reach you? </li></ul>
29. 29. Example ANSWER: For the thunder: For the flash:
30. 30. Velocity <ul><li>Velocity is the speed in a particular direction. </li></ul><ul><li>It tells us not only “how fast” (like speed) but also how fast in “what direction.” </li></ul>
31. 31. Velocity , cont’d <ul><li>In common language, we don’t distinguish between the two. </li></ul><ul><ul><li>This sets you up for confusion in a physics class. </li></ul></ul><ul><li>During a weather report, you might be given the wind-speed is 15 mph from the west. </li></ul>
32. 32. Velocity , cont’d <ul><li>The speed of the wind is 15 mph. </li></ul><ul><li>The wind is blowing in a direction from the west to the east. </li></ul><ul><li>So you are actually given the wind velocity. </li></ul>
33. 33. Vector addition <ul><li>Quantities that convey a magnitude and a direction, like velocity, are called vectors. </li></ul><ul><li>We represent vectors by an arrow. </li></ul><ul><ul><li>The length indicates the magnitude. </li></ul></ul>
34. 34. Vector addition , cont’d <ul><li>Consider again someone running on a ship. </li></ul><ul><ul><li>If in the same directions, the vectors add. </li></ul></ul>
35. 35. Vector addition , cont’d <ul><li>Consider again someone running on a ship. </li></ul><ul><ul><li>If in the opposite directions, the vectors subtract. </li></ul></ul>
36. 36. Vector addition , cont’d <ul><li>What if the vectors are in different directions? </li></ul>
37. 37. Vector addition , cont’d <ul><li>The resulting velocity of the bird (from the bird’s velocity and the wind) is a combination of the magnitude and direction of each velocity. </li></ul>
38. 38. Vector addition , cont’d <ul><li>We can find the resulting magnitude of the Pythagorean theorem . </li></ul>b a c
39. 39. Vector addition , cont’d <ul><li>Let’s find the net speed of the bird? </li></ul><ul><li>(Why didn’t I say net velocity?) </li></ul>10 8 6
40. 40. Vector addition , cont’d <ul><li>Here are more examples, illustrating that even if the bird flies with the same velocity, the effect of the wind can be constructive or destructive. </li></ul>
41. 41. Acceleration <ul><li>Acceleration is the change in velocity divided by the elapsed time. </li></ul><ul><li>It measures the rate of change of velocity. </li></ul><ul><li>Mathematically, </li></ul>
42. 42. Acceleration , cont’d <ul><li>The units are </li></ul><ul><li>In SI units, we might use m/s 2 . </li></ul><ul><li>For cars, we might see mph/s. </li></ul>
43. 43. Acceleration , cont’d <ul><li>A common way to express acceleration is in terms of g ’s. </li></ul><ul><li>One g is the acceleration an object experiences as it falls near the Earth’s surface: g = 9.8 m/s 2 . </li></ul><ul><ul><li>So if you experience 2 g during a collision, your acceleration was 19.6 m/s 2 . </li></ul></ul>
44. 44. Acceleration , cont’d <ul><li>There is an important point to realize about acceleration: </li></ul><ul><li>It is the change in velocity. </li></ul>
45. 45. Acceleration , cont’d <ul><li>Since velocity is speed and direction, there are three ways it can change: </li></ul><ul><ul><li>change in speed, </li></ul></ul><ul><ul><li>change in direction, or </li></ul></ul><ul><ul><li>change in both speed & direction. </li></ul></ul><ul><li>The change in direction is an important case often misunderstood. </li></ul>
46. 46. Acceleration , cont’d <ul><li>If you drive through a curve with the cruise control set to 65 mph, you are accelerating. </li></ul><ul><ul><li>Not because your speed changes. </li></ul></ul><ul><ul><li>But because your direction is changing. </li></ul></ul><ul><ul><ul><li>There must be an acceleration because items on your dash go sliding around. </li></ul></ul></ul><ul><ul><ul><li>More on this in chapter 2. </li></ul></ul></ul>
47. 47. Example Example 1.3 <ul><li>A car accelerates from 20 to 25 m/s in 4 seconds as it passes a truck. What is its acceleration? </li></ul>
48. 48. Example Example 1.3 ANSWER: The problem gives us The acceleration is:
49. 49. Example Example 1.3 CHECK: Does this make sense? The car needs to increase its speed 5 m/s in 4 seconds. If it increased 1 m/s every second, it would only reach 24 m/s. So we should expect an answer slightly more than 1 m/s every second.
50. 50. Example Example 1.4 <ul><li>After a race, a runner takes 5 seconds to come to a stop from a speed of 9 m/s. Find her acceleration. </li></ul>
51. 51. Example Example 1.3 ANSWER: The problem gives us The acceleration is:
52. 52. Example Example 1.3 CHECK: Does this make sense? If she was traveling at 10 m/s, reducing her speed 2 m/s every second would stop her in 5 seconds. What’s up with the minus sign?
53. 53. Centripetal acceleration <ul><li>Remember that acceleration can result from a change in the velocity’s direction. </li></ul><ul><li>Imagine a car rounding a curve. </li></ul><ul><li>The car’s velocity must keep changing toward the center of the curve in order to stay on the road. </li></ul>
54. 54. Centripetal acceleration <ul><li>Remember that acceleration can result from a change in the velocity’s direction. </li></ul><ul><li>Imagine a car rounding a curve. </li></ul><ul><li>The car’s velocity must keep changing toward the center of the curve in order to stay on the road. </li></ul>
55. 55. Centripetal acceleration , cont’d <ul><li>So there is an acceleration toward the center of the curve. </li></ul><ul><li>Centripetal acceleration is the acceleration associated with an object moving in a circular path. </li></ul><ul><ul><li>Centripetal means “center-seeking.” </li></ul></ul>
56. 56. Centripetal acceleration , cont’d <ul><li>For an object traveling with speed v on a circle of radius r , then its centripetal acceleration is </li></ul>
57. 57. Centripetal acceleration , cont’d <ul><li>Note that the centripetal acceleration is: </li></ul><ul><ul><li>proportional to the speed-squared </li></ul></ul><ul><ul><li>inversely proportional to the radius </li></ul></ul>
58. 58. Example Example 1.5 <ul><li>Let’s estimate the acceleration of a car as it goes around a curve. The radius of a segment of a typical cloverleaf is 20 meters, and a car might take the curve with a constant speed of 10 m/s. </li></ul>
59. 59. Example Example 1.5 ANSWER: The problem gives us The acceleration is:
60. 60. Example Problem 1.18 <ul><li>An insect sits on the edge of a spinning record that has a radius of 0.15 m. The insect’s speed is about 0.5 m/s when the record is turning at 33- 1 / 3 rpm. What is the insect’s acceleration? </li></ul>
61. 61. Example Problem 1.18 ANSWER: The problem gives us The acceleration is:
62. 62. Simple types of motion — zero velocity <ul><li>The simplest type of motion is obviously no motion . </li></ul><ul><li>The object has no velocity. </li></ul><ul><li>So it never moves. </li></ul><ul><li>The position of the object, relative to some reference, is constant. </li></ul>
63. 63. Simple types of motion — constant velocity <ul><li>The next simplest type of motion is uniform motion . </li></ul><ul><ul><li>In physics, uniform means constant. </li></ul></ul><ul><li>The object’s velocity does not change. </li></ul><ul><li>So its position, relative to some reference, is proportional to time. </li></ul>
64. 64. Simple types of motion — constant velocity , cont’d <ul><li>If we plot the object’s distance versus time, we get this graph. </li></ul><ul><ul><li>Notice that if we double the time interval, then we double the object’s distance. </li></ul></ul>
65. 65. Simple types of motion — constant velocity , cont’d <ul><li>The slope of the line gives us the speed. </li></ul>
66. 66. Simple types of motion — constant velocity , cont’d <ul><li>If an object moves faster, then the line has a larger speed. </li></ul><ul><li>So the graph has a steeper slope. </li></ul>
67. 67. Simple types of motion — constant acceleration <ul><li>The next type of motion is uniform acceleration in a straight line . </li></ul><ul><li>The acceleration does not change. </li></ul><ul><li>So the object’s speed is proportional to the elapsed time. </li></ul>
68. 68. Simple types of motion — constant acceleration , cont’d <ul><li>A common example is free fall. </li></ul><ul><ul><li>Free fall means gravity is the only thing changing an object’s motion. </li></ul></ul><ul><li>The speed is: </li></ul>
69. 69. Simple types of motion — constant acceleration , cont’d <ul><li>If we plot speed versus time, the slope is the acceleration: </li></ul>
70. 70. Simple types of motion — constant acceleration , cont’d <ul><li>For an object starting from rest, v = 0, then the average speed is </li></ul>
71. 71. Simple types of motion — constant acceleration , cont’d <ul><li>The distance is the average speed multiplied by the elapsed time: </li></ul>
72. 72. Simple types of motion — constant acceleration , cont’d <ul><li>If we graph the distance versus time, the curve is not a straight line. </li></ul><ul><ul><li>The distance is proportional to the square of the time. </li></ul></ul>