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### Transcript of V avg = Δd/Δt a avg = Δv/Δt Δd = v i Δt +.5aΔt 2 v f = v i + aΔt v f 2 = v i 2 + 2aΔd.

• Slide 1
• v avg = d/t a avg = v/t d = v i t +.5at 2 v f = v i + at v f 2 = v i 2 + 2ad
• Slide 2
• Sin = Opp/Hyp Cos = Adj/Hyp Tan = Opp/Adj
• Slide 3
• Slide 4
• Kinematics
• Slide 5
• Kinematics the study of motion
• Slide 6
• Motion What does it mean for an object to be in motion? the change in position of an object as compared to a reference point *
• Slide 7
• Is the brick wall moving? Not from where shes sitting, but
• Slide 8
• from space, the earth rotates and the wall with it. So, whether or not something is moving depends on your frame of reference. *
• Slide 9
• Frame of Reference a fixed point used to determine magnitude and direction of motion Magnitude?
• Slide 10
• See Video Here
• Slide 11
• Rate a change in a given quantity over a specified period of time (examples: velocity and acceleration)
• Slide 12
• Scalar quantity a measurement specified by magnitude only. No direction implied Ex. mass, volume, density, distance, speed, temperature
• Slide 13
• Vector quantity a measurement specified by magnitude and direction Ex.: displacement, velocity, acceleration, force
• Slide 14
• Distance the length of the actual path taken by the object regardless of direction scalar quantity units include m, km
• Slide 15
• Displacement length (measured in a straight line) from the reference point to the object (implies a given direction) vector quantity units include m, km
• Slide 16
• Displacement Displacement = change in position = final position initial position Symbolically, d = d f d i *
• Slide 17
• Total Displacement Add individual displacement's indicating individual directions with +/-
• Slide 18
• Remove following slides
• Slide 19
• Reference point is origin or start position What is the distance? 70 cm What is the displacement? d = d f d i d = 80cm 10cm d = 70cm In Centimeters
• Slide 20
• Reference point is origin or start position What is the distance? 70 cm What is the displacement? d = d f d i d = 10cm 80cm d = -70cm In Centimeters
• Slide 21
• Displacement indicates direction. Convention dictates right will be considered positive and left will be considered negative
• Slide 22
• Reference point is origin or start position What is the distance? 70 m What is the displacement? d = d f d i d = 40cm -30cm d = 70cm In Centimeters -30-200-10201030405060
• Slide 23
• Reference point is origin or start position What is the distance? 70 m What is the displacement? d = d f d i d = -30cm 40cm d = -70cm In Centimeters -30-200-10201030405060
• Slide 24
• Displacement is not always equal to distance travelled! What is Clyde the Caterpillars displacement? d = d f d i d = 80m 20m = 60m
• Slide 25
• Home KCHS Gas Mall Movies 1 km 1.75 km 2.0 km 1.5 km Example A Draw this diagram and determine the following in reference to home: NORTH
• Slide 26
• Determine the distance and displacement for each scenario in reference to home 1.You drive from home to the mall. 2.You drive from home and stop at the gas station. You realize you left your wallet at home. You go back home to get it. You stop at gas station then continue on to the mall. 3.You drive from the mall to the gas station. 4.You drive from home to school.
• Slide 27
• For total displacement Add displacement vectors. Sign indicates direction.
• Slide 28
• 1.Home-mall Dist = 3.5 km Disp =3.5 km N 2.Home-gas-home-gas-mall Dist = 6.5 km Disp =3.5 km N 3.Mall-gas Dist = 2.0 km Disp =1.5 km -3.5 km =-2km (you are going south) Assuming mall is reference point 4.Home-school Dist = 1.0 km Disp =-1.0 km -0 km =-1 km (you are going south)
• Slide 29
• 9/10 Goal: Prepare for Thursdays test We will go over the trig quiz and Reading Quiz Yesterday we discussed scalar and vector quantities. We learned how trig was applied to displacement problems. While waiting for class to start, complete sample problems 1 & 2 in kinematics notes. Pick up 03 WS I. This is due tomorrow.
• Slide 30
• complete these DA problem: Your drive your car at 45 mph for a million kilometers. How many seconds will it take? (1 in= 2.54 cm) Convert 98 feet/second to nm/decade. Assume 365.25 days = 1 year 1 km = 0.621 miles
• Slide 31
• 9/10 Goal: Prepare for Thursdays test We will go over the trig quiz and Reading Quiz While waiting for class to start, complete this DA problem: Your drive your car at 45 mph for a million kilometers. How many seconds will it take? (1 in= 2.54 cm)
• Slide 32
• 9/11 We remember Goal: Prepare for tomorrows test Have last nights homework (03WS1) out to be checked. While waiting for class to start, complete this DA problem: An otter scampers down Mrs. Sauders dock for a distance of 23.0 feet. How long does it take the otter (in seconds) to get to the end of the dock if its average speed is 1.78 feet/s? What is the otters rate of speed in m/s? An otter scampers down Mrs. Sauders dock for a distance of 23.0 feet. How long does it take the otter (in seconds) to get to the end of the dock if its average speed is 1.78 feet/s? What is the otters rate of speed in m/s?
• Slide 33
• . Your drive your car at 45 mph for a million kilometers. How many seconds will it take? (1 in= 2.54 cm) 4.97 x 10 7 sec. 1 x 10 6 km 1000 m100 cm1 in 11 km1 m2.54 cm 1 ft 1 mile1hr 3600 sec 12 in5280 ft45 miles1 hr
• Slide 34
• Sine, Cosine, Tangent Sine, Cosine, Tangent http://www.mathsisfun.com/sine- cosine-tangent.html
• Slide 35
• Thursdays test 3-4 dimensional analysis problems 1 accuracy vs precision problem Solving a right triangle 2 Linear distance and displacement problem Right angle distance and displacement problem where you must determine the angle in reference to X axis!!!
• Slide 36
• Unit 03 WSI 1. 1. c = 9.63u (pythagoreans) A = 59.8 (tan) B = 30.2 2. 2.Walk 8yds east. Dist = 35 yards Disp= -5 yards or 5 yards west 3. Somersaults. Dist = 10 yards Disp = 7.62 yards at 66.8 S of W 4. 30.2 km (start with 45 min) 5. 10500 sec (start with 211 km)
• Slide 37
• Same diagram, last question. 5. You drive from home to the mall and then to the movies. Distance? 5.25 km Displacement? Use Pythagoreans: 3.91km How do you indicate direction?
• Slide 38
• Home KCHS Gas Mall Movies 1 km 1.75 km 2.0 km 1.5 km The displacement is the dotted line. This is referred to as the resultant. NORTH
• Slide 39
• Tests are graded. If you have not taken test, you will take it today during class. Missed benchmarks will be given next M, T, and W after school. You will have until the last ten minutes of class to work on test corrections. This will earn you a daily grade. Expectations: Write out givens, redo all the work. Include appropriate diagrams. For future reference, if it is not a math problem you would write out question and answer. Make sure to include name and period at top of corrections. Staple corrections to test and place in blue sorter. 9/14 Pick up vector sheet
• Slide 40
• Arrows represent vectors Length of arrow corresponds to magnitude of vector Connect the tail of one vector to the arrow tip of the other No matter what route you take from point A to point B your final displacement vector will be the same The final displacement vector is called the resultant vector Draw in the resultant vector from the tail of the first vector to the arrow head of the second Vector Diagrams
• Slide 41
• Home KCHS Gas Mall Movies 1 km 1.75 km 2.0 km 1.5 km To determine direction, view diagram on a coordinate plane. Direction is determined in reference to the x axis. This would be angle . NORTH
• Slide 42
• In reference to X tan = 3.5/1.75 tan = 2 = 63.4 North of East
• Slide 43
• N of E, E of N I am confused. Which is which?
• Slide 44
• Complete Displacement practice problems 1&2 in note packet and 1,3, & 4 on WS 01
• Slide 45
• Solving Problem Set Ups Place given information on left. Draw diagram here if applicable. show formula and substitution here. Box in answer.
• Slide 46
• Displacement Practice 1. 1.d = +2m or 2m north 2. 2.r = 17.7m at 73.6 S of W
• Slide 47
• 9/18 Power up and Go to Tablet Camp (you downloaded this yesterday) You will work through one tutorial this period. You are riding in the MS 150. Would you rather ride into the wind or have it at your back?? (BTW The MS150 benefits MS and occurs every April )
• Slide 48
• What is the difference between speed and velocity?
• Slide 49
• Speed change in distance divided by change in time (d/t ) scalar quantity units include m/sec or cm/sec.
• Slide 50
• Velocity speed in a given direction magnitude and direction included in the measurement vector quantity units include m/sec or cm/sec.
• Slide 51
• Average Velocity The average velocity of an object is defined as the displacement of an object divided by the time in which it took place. Average velocity = v avg = Change in displacement Change in time dtdt*
• Slide 52
• Abbreviations
• Slide 53
• Example B A motorcycle drives 825m east in 1.4 min. What is its average velocity in km/hr? If the biker was driving through a school zone (20 mph limit) should she be ticketed? You can solve this without any knowledge of velocity by using dimensional analysis and following the units.
• Slide 54
• Example B A motorcycle drives 825m east in 1.4 min. What is its average velocity in km/hr? If the biker was driving through a school zone (20 mph limit) should she be ticketed? 35.4 km/h 22.0 mph yes
• Slide 55
• Example C What distance (in km) does a helicopter travel in 39.7 minutes provided it moves in a direct path at 25.8 m/s? You can solve this without any knowledge of velocity by using dimensional analysis and following the units.
• Slide 56
• Example C What distance (in km) does a helicopter travel in 39.7 minutes provided it moves in a direct path at 25.8 m/s? 61.5 km
• Slide 57
• Work through examples D-F showing velocity as a vector Remember v = d t
• Slide 58
• Solving Problem Set Ups Place given information on left. Draw diagram here if applicable. show formula and substitution here. Box in answer.
• Slide 59
• A plane heading east at 632 miles per hour is directly hit by a wind measuring 25 miles per hour. The wind is blowing directly west. Without correction, what is the planes resultant velocity? Example D
• Slide 60
• +632 mph-25 mph = +607mph Indicate direction with + or East, North, or Right + West, South, or Left - +632 mph -25 mph
• Slide 61
• Example E Later in its journey, the wind shifts to the north. The plane, heading east at 632 miles per hour, is hit by this 25-mph wind. Without correction, what is the planes resultant velocity?
• Slide 62
• How do we figure out the resultant velocity? You guessed it! A triangle! The resultant velocity vector is c. Use Pythagoreans to solve just as you did with displacement. Then solve for direction in reference to the x axis. Do you know which angle? 632 mph E 25 mph N c
• Slide 63
• c = 632 mph (632.4942.) Did you really expect a measly 25 mph north wind to affect the planes eastern velocity? tan =2.27 N of E 632 mph E 25 mph N c
• Slide 64
• What if I made my diagram like this? It doesnt matter, you get all the same answers. 632 mph E 25 mph N
• Slide 65
• Example F You are on a 32 ft boat. The boat is moving northward at 0.8m/s. You walk from stern to bow at 0.2m/s. A. How long did it take you (in seconds) to walk the entire length of the boat? (1in = 2.54 cm).
• Slide 66
• Example F continued. You are on a 32 ft boat. The boat is moving northward at 0.8m/s. You walk from stern to bow at 0.2m/s. B. What is the magnitude and direction of your apparent resulting velocity in reference to the earth?
• Slide 67
• Example F Part A You want sec. What to start with? 32 ft: Use dimensional analysis. Ft-in-cm-m-sec! t = 48.8 sec Part B Solve for v r + 0.2m/s + + 0.8 m/s = 1.0 m/s N
• Slide 68
• Skip Example G A plane is headed 25.8 west of north at 340mi/hr when the wind is from the south at 45mi/hr. What is the apparent resultant velocity of the plane with respect to the ground?
• Slide 69
• 9/19 Today we will look at more complex motion problems. We will discuss D, E, and F if not discussed yesterday. Have a calculator and pick up Unit 03 WSIII A Begin working on WS III A while waiting for class to start. Please do on paper. Today (after school) is last for completing test corrections and retakes.
• Slide 70
• Slide 71
• 9/20 Today we will continue the girl scout problem. Have HW from yesterday ready to be checked. (Unit 03 WSIII A) Pick up WS III B and a calculator. Quiz tomorrow over resolving vectors at right angles and girl scout type problem. Yesterday (after school) was last day for completing test corrections and retakes.
• Slide 72
• ????? Maybe introduce walking across a boat as it is moving
• Slide 73
• Example H A girl scout elects to swim across the river. The river is 37.5 meters wide. A current flows downstream at a rate of 0.66 m/s. If she initially swims towards the boy scout camp (directly cross the river) at a rate of 1.73 m/s, how long will it take her to reach the far shore?
• Slide 74
• Remember what the question asks. How long does it take her to swim across? To solve for time, what do we need to know? Use velocity and displacement but only in reference to crossing the river. ] 37.5m 1.73 m/s
• Slide 75
• v = d/t t = d/v t = 37.5m1.73m/s t = 21.7 s ] 37.5m 1.73 m/s
• Slide 76
• Where exactly does the girl scout end up on the far shore? What do we need to know? To determine displacement we need velocity and time but only in reference to downstream. ] 37.5m 1.73 m/s Example I
• Slide 77
• To find where she ends up, what is the downstream velocity? 0.66m/s What is the time? 21.7 sec Time is the same for both cross stream and downstream. 14.3 m downstream 0.66m/s
• Slide 78
• When working with multiple vectors remember they are independent of one another although they have a net effect. In the case of the girl scout, her overall (think resultant) velocity and direction changed. Do you know how to solve for the apparent resultant velocity and direction?
• Slide 79
• Resultant velocity? c 2 = 1.73 2 + 0.66 2 c = 1.85 m/s Which angle for direction? tan = 1.73/0.66 = 2.62 = 69.1 = 69.1 v r = 1.85 m/s at 69.1downstream in respect to shore v r = 1.85 m/s at 69.1 downstream in respect to shore 0.66m/s 1.73 m/s c
• Slide 80
• What angle should the girl scout enter the water upstream to end up at the boy scout camp?? 69.1pstream in respect to shore 69.1 upstream in respect to shore 0.66m/s 1.73 m/s c
• Slide 81
• 9/21 Get a calculator. You must you my calculator for the quiz. Make sure it is degree mode. Have homework out to be checked We will go over problems 1 and 2. Then we will take quiz. After quiz we will discuss 3-5 ITS FRIDAY!!!!!
• Slide 82
• 9/24 Tutoring M,T, W after school Get a calculator and formula sheet The quizzes from FRIDAY are graded. See me to make up. Remember we have a test on Wed HW: kinematics WS V 1-8 (See LMS) Todays goal: apply acceleration formulas to motion. Open kinematics notes on LMS. Go to III B: Acceleration
• Slide 83
• What is the westerly component? What is the northerly component? What does c represent? What can we say about the units? A B c #5 610 km/hr East 792 km/hr North 1590 km E 2060 km N
• Slide 84
• If you are driving is your speed always the same? There are a variety of formulas that are used to calculate how the position of an object changes. Be prepared: You are going to be algebraically challenged!!!!!
• Slide 85
• How do we define average velocity? Change in displacement divided by change in time What is the formula? v avg = d/t
• Slide 86
• Algebraically we can come up with the following. v avg = (v i + v f )/2 d/t = (v i + v f )/2 2d = (v i + v f )t d = (v i + v f )t If it is yellow, it probably is important. This is the mother equation for the 3 big acceleration formulas. This is the mother equation for the 3 big acceleration formulas.
• Slide 87
• How do we define average acceleration? Change in velocity divided by change in time What is the formula? a avg = v/t
• Slide 88
• With a little algebra, this can be rewritten as a avg = v/t a avg = (v f - v i )/(t f t i ) v f = v i + at
• Slide 89
• What else can we come up with? d = (v i + v f )t d = (v i +[v i + at]t d = (2v i + at)t d = v i t + at 2
• Slide 90
• Anything else? d = (v i + v f )t 2d = (v i + v f )t t = 2d/(v i + v f ) v f =v i + at v f =v i + a[(2d)/(v i + v f )] Continuing.
• Slide 91
• Continuing.. (v i - v f ) = [(2a d)/(v i + v f )] (v i - v f )(v i + v f ) = 2a d v f v i v i v f v i 2 + v f 2 = 2ad v f 2 = v i 2 + 2ad
• Slide 92
• For next year: Rewrite formulas to mimic Starr chart
• Slide 93
• What 3 major equations will we be working with? d = v f = v f 2 =
• Slide 94
• What 3 major equations will we be working with? d = v i t + at 2 v f = v i + at v f 2 = v i 2 + 2ad
• Slide 95
• v f = v i + at Solve for t v f 2 = v i 2 + 2ad Solve for d
• Slide 96
• Horizontal acceleration problems
• Slide 97
• Example J A tricycle, initially traveling at 0.15 m/s, experiences an acceleration of 0.045 m/s 2. What is the velocity of such tricycle after a period of 15 seconds?
• Slide 98
• Example J v i = 0.15 m/s a = 0.045 m/s 2 t = 15 s v f = ? What equation? v f = v i + at v f = v f = 0.15 m/s +( 0.045 m/s2)(15 s) v f = 0.83 m/s
• Slide 99
• Example K A bowling ball decelerates. If it slows from 15.3 m/s to 2.77 m/s in 14.0 seconds, what is the measure of such deceleration?
• Slide 100
• Example K v i = 15.3 m/s v f = 2.77 m/s t = 14.0 s a = ? What equation? v f = v i + at Solve for a v f = v i + at v f - v i = at (v f v i )/t = a a = (2.77 m/s a = (2.77 m/s 15.3 m/s)/(14.0 s) a= -0.895 m/s 2
• Slide 101
• Example L An arrow takes a horizontal path for a distance of 280 m. The arrow slows from 26.3 m/s to 15 m/s during flight. How long does it take for this arrow to fly this distance?
• Slide 102
• Example L v i = 26.3 m/s v f = 15 m/s d = 280 m t = ? What equation? This will need 2 different equations! We will solve for a then t v f 2 = v i 2 + 2ad Solve for a v f 2 = v i 2 + 2ad v f 2 v i 2 = 2ad (v f 2 v i 2 )/2d = a a = (15 m/s) 2 -(26.3 a = (15 m/s) 2 -(26.3m/s) 2 /(2 x 280m) a= -0.83 m/s 2
• Slide 103
• Example L part 2 v i = 26.3 m/s v f = 15 m/s x = 280 m a = 0.83 m/s 2 t = ? What is the 2 nd equation? v f = v i + at Solve for t v f - v i = at (v f v i )/a= t (v f v i )/a = t t = (15 m/s-26.3 t = (15 m/s-26.3 m/s)/-0.83 m/s 2 t = 14 s
• Slide 104
• 9/24 Tutoring M,T, W after school Get a calculator The quizzes from FRIDAY are graded. I will be passing them back today. Remember we have a test on Wed Have out HW: kinematics WS V 1-8 Todays goal: review acceleration formulas to motion. For future reference, download HW assignments in class so you dont have to worry about connectivity at home.
• Slide 105
• Write in 3 SF and proper Scientific Notation 436,70036020.000005800402,400,0020.0433333333
• Slide 106
• 436,700 4.37 x 10 5 36023.60 x 10 3 0.0000058005.80 x 10 -6 402,400,0024.02 x 10 8 0.04333333334.33 x 10 -2
• Slide 107
• Meter Stick Lab Part I DO THIS NOW : ) On new page in Lab Book, Title a page: Meter Stick Lab. There is a blue card on the desks. Determine length in cm and convert to meters. Remember to estimate one value beyond smallest interval. Thus your measurement should be xx.xx cm Record length of card in lab book DO NOT WRITE THE MEASUREMENT ON THE BLUE CARD!!!!!!!
• Slide 108
• 9/27 Tutoring M,T, W after school GET YOUR LAB BOOKS!!!! Yesterday we took the kinematics test. If you were absent, make ups are on Monday after school. Test corrections will be offered Monday and Wednesday after school next week. I will not be available next Tuesday after school. For future reference, download HW assignments in class so you dont have to worry about connectivity at home.
• Slide 109
• Meter Stick Lab Part I Dollar Bill Bet Without trying to catch the falling dollar bill, hypothesize if you can catch it before it falls through your fingers.
• Slide 110
• TEACHER NOTES Describe the bet about catching a dollar bill Have students measure a dollar bill in cm and convert to m (I have some cardboard ones)
• Slide 111
• Meter Stick Lab Part I Why do objects fall? What factors influence the rate of a falling object? Assume in the following experiment that air resistance is negligible and that objects will accelerate downward at a uniform rate of 9.8 m/s 2
• Slide 112
• Gravity in a Vacuum Gravity in a Vacuum This video is 3 min and 41 seconds If the link does not work, the name is The Mechanical Universe: The Law of Falling Bodies The Mechanical Universe: The Law of Falling BodiesThe Mechanical Universe: The Law of Falling Bodies Show segment Gravity in a vacuum
• Slide 113
• Free Fall In the absence of air resistance all objects dropped near the surface of a planet fall with the same constant acceleration. Such motion is referred to as free fall.
• Slide 114
• Acceleration due to Gravity Free fall accelerationaka called acceleration due to gravity denoted with the symbol g or a g. Down is positive since it is natural to fall down g = a g = 9.80m/s 2 g = a g = 9.80m/s 2
• Slide 115
• Meter Stick Lab Part II Objective Use acceleration of gravity to determine your reaction time. Materials Meter Stick Methods 1.Prepare a table in your lab book to record distance of catch in centimeters. Remember to give the table a title and to label columns. 2.Drop and catch the meter stick. Remember to start at zero. Perform 5 trials. 3.Average 5 individual trials. Convert average cm to meters using dimensional analysis.
• Slide 116
• Meter Stick Lab Part II 4. Reevaluate your hypothesis concerning the dollar bill. Would you win the bet? Make a statement and justify your answer. 5. Refer to your acceleration formulas and use your data to calculate your reaction time. Hint: list your knowns (d-v-v-a-t) 5. Refer to your acceleration formulas and use your data to calculate your reaction time. Hint: list your knowns (d-v-v-a-t) 6. Show formula used, rearranged, substitution, and answer beneath your data table. 7. d = v i t + at 2 What is the value for v i t ? What is the value for v i t ? Record your reaction time in 3 SF Record your reaction time in 3 SF
• Slide 117
• What is your reaction time related to?
• Slide 118
• Meter Stick Lab Part III Objective Use your reaction time to determine motor nerve conduction speed. What 2 values do you need for speed? What 2 values do you need for speed? Assume that the impulse in the motor neuron traveled from the back of your head to the tip of your index finger. Thus, measure this distance to find d. What units should you use to record this distance? Assume that the impulse in the motor neuron traveled from the back of your head to the tip of your index finger. Thus, measure this distance to find d. What units should you use to record this distance? Solve for velocity of the impulse using your reaction time and distance from index finger to back of head. Show formula, substitution, and answer. Solve for velocity of the impulse using your reaction time and distance from index finger to back of head. Show formula, substitution, and answer.
• Slide 119
• MY DATA Dollar bill 15.50 cm =.155m Average of 5 catches 32.40 cm =.324 m Time to catch 0.257 sec Distance from finger tip to base of skull 84.50 cm 84.50 cm
• Slide 120
• 9/28 Goals: Apply acceleration formulas to vertical problems Yesterday we performed the meter stick lab. You can make this up today after school, next Monday or Tuesday morning, or Monday or Wednesday afternoon. Have kinematics notes open to Example M. HW: Unit 03WS VI. We will start this in class today. Upload it now. This will be due Tuesday. Work on #1 and #2 while waiting for class to start.
• Slide 121
• A boy is spinning on a merry-go-round at constant speed of 0.5 m/s. Describe his velocity. Describe his acceleration.
• Slide 122
• v=d/t or the big 3?? Only use v=d/t when you have an average velocity given or asked for If objects are starting, stopping, or changing speed, then you must use the big 3 #1 3.3 s #2 -5 m/s 2
• Slide 123
• Example M A villain from a 007 movie is dropped from a plane flying 0.470 km above the ground. A. Without the antagonistic effects of a parachute and air resistance, determine the acceleration of this individual as he plummets to the ground. B.With what velocity does this person hit the ground? C.How long will it take for this person to meet his demise?
• Slide 124
• Example M Determine the acceleration 9.80m/s 2 The acceleration = 9.80m/s 2
• Slide 125
• Example M Determine the Example M Determine the v f List your knowns: d = 0.470 km v i = 0 m/s v f = ? 9.80m/s 2 a = 9.80m/s 2 t = ? Choose the appropriate formula and Solve for v f
• Slide 126
• Example M Determine the Example M Determine the v f v f 2 = v i 2 + 2ad v f 2 = ( + [(2)(9.80m/s 2 )(470m)] v f 2 = (0 m/s) 2 + [(2)(9.80m/s 2 )(470m)] v f 2 v f 2 = 9212 m 2 /s 2 v f = 96.0 m/s d = 0.470 km v i = 0 m/s v f = ? a = 9.80m/s 2 t = ?
• Slide 127
• Example M Determine the Example M Determine the t v i t +.5at 2 d = v i t +.5at 2 +.5at 2 d = 0 +.5at 2 d/.5a = t 2 t 2 470m/[(.5)(9.80m/s 2 ) t 2 = 470m/[(.5)(9.80m/s 2 ) t = 9.79 s d = 0.470 km v i = 0 m/s v f = 96.0 m/s a = 9.80m/s 2 t = ?
• Slide 128
• Complete 9 and 10 on WS V 9. To calculate the depth of a well a physics student drops a rock into the well. 4.5 seconds after the rock is dropped the student sees it hit the bottom. The rock accelerates downwards at 9.80 m/s 2. a. How deep is the well? b. How fast is the rock traveling the instant before it hits the bottom? 10. Flossy Fletcher was curling her hair when she dropped the curling iron. The curling iron fell 1.651m to the floor. a. How fast was the iron traveling when it hit the floor? a. How fast was the iron traveling when it hit the floor? b. How long was it in the air? b. How long was it in the air?
• Slide 129
• Complete 9 and 10 on WS V 5. To calculate the depth of a well a physics student drops a rock into the well. 4.5 seconds after the rock is dropped the student sees it hit the bottom. The rock accelerates downwards at 9.80 m/s 2. a. How deep is the well? 99.2m b. How fast is the rock traveling the instant before it hits the bottom? 44.1 m/s 6. Flossy Fletcher was curling her hair when she dropped the curling iron. The curling iron fell 1.651m to the floor. a. How fast was the iron traveling when it hit the floor? 5.69 m/s a. How fast was the iron traveling when it hit the floor? 5.69 m/s b. How long was it in the air? 0.581 s b. How long was it in the air? 0.581 s
• Slide 130
• Example N Example N A ball is shot upwards with a velocity of 114 m/s. A.How high will it rise? B.How long will it take for the ball to return to the earth? Determine your knowns first!! Why is v f 0 m/s? It stops and begins to fall. d = ? v i = -114 m/s v f = 0m/s a = 9.80m/s 2 t = ?
• Slide 131
• Example N Determine the Example N Determine the d v f 2 = v i 2 + 2ad (v f 2 - v i 2 ) /(2a) = d d =[(0m/s) 2 - (-114m/s) 2 ]/[(2)(9.80m/s 2 )] d = -663m ( upward displacement) d = ? v i = -114 m/s v f = 0 m/s a = 9.80m/s 2 t = ?
• Slide 132
• Example N Determine the Example N Determine the t v f = v i + at (v f v i )/a = t t = (0 m/s - - 114m/s)/9.80m/s 2 t = 11.6 s ARE YOU SURE? What goes up must come down!!!!! The question was how long it will take to return to earth. This is only half the time! x =- 663 m v i = -114 m/s v f = 0 m/s a = 9.80m/s 2 t = ?
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• Example N Determine the Example N Determine the t Total time in the air = 2(11.6 s) = 23.2s d = -663 m v i = -114 m/s v f = a = 9.80m/s 2 t = ?
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• Questions like this: A ball is thrown straight up. At the top of its path its acceleration is? About 10 m/s2
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• 9/21 Today we will review motion graphs, then we will delve into advanced kinematic equations. (James Bond!) Have your Moving Man lab out as well as your Summary of graphs. I will not be here after school: Physics meeting.
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• Demo Dropping ball into moving box
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• 10/5 Open kinematic notes to Example O Remember moving man lab is due Monday. We will have a quiz Monday over graphing. 6 week test make ups Monday after school. Monday after school. Last day! Last day!
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• Example O James Bond is standing on a bridge 15 meters above the river below. He needs to escape his pursuers. He sees a speed boat in the distance coming toward him. The boat is moving at constant velocity of 2.5 m/s. How far away should the boat be when 007 jumps off the bridge if he wants to land in the boat? Neglect air resistance.
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• Example O What do you know about 007? d = 15 m v i = 0 a = 9.8 m/s 2 What do you know the boat? v = 2.5 m/s What do we want them to have in common? Time!!!! What determines the time? 007 fall
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• Example O Determine time with data from 007. What formula? d = v i t + at 2 t = 1.75 seconds Use the time it takes 007 to fall to determine distance of boat when he jumps. What formula? v avg = d/t d = 4.38 m
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• Example P A truck is traveling at 80km/h in a school zone. A police car starts from rest just as the speeder passes it and accelerates at a constant rate of 3.24m/s 2. When does the police car catch the speeding truck? What distance does the police car cover to catch the speeder?
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• Example P What do you know about the truck? v = 80km/h What do you know about the police? v i = 0 m/s a = 3.24m/s 2 What do we want them to have in common? Distance from where the truck passed the police to where the police catches up.
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• Example P Would you agree that this distance occurs in the same amount of time for both vehicles? What formula can you use to determine distance about the truck? d = vt What formula can you use to determine distance about the police? d = v i t + at 2 Set the two formulas equal to each other!
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• Example P v i t + at 2 vt = v i t + at 2 If we substitute the values for the truck on the left and the police on the right, what are we solving for? TIME!! Truck: v = 80km/h Police: v i = 0 m/s a = 3.24m/s 2 What is the next step? Change 80km/h to m/s with DA Truck: v = 22.2 m/s
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• Example P Now substitute v i t + at 2 vt = v i t + at 2 Truck: v = 22.2 m/s Police: v i = 0 m/s a = 3.24m/s 2 v i t for police equals? 0 (22.2 m/s)t = (.5)(3.24m/s 2 )t 2 (22.2 m/s)t = (1.62m/s 2 )t 2 22.2 m/s = (1.62m/s 2 )t t = 13.7 sec
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• Example P t = 13.7 sec Now we can solve for distance using information from truck or the police. It is the same! Which one would you do? I would choose the truck! Easier formula. d = vt d = (22.2 m/s)(13.7 s) = 304 m Summary: It will take 13.7 seconds for police to catch up over a distance of 304 m
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• 9/20 Goal: Self guided inquiry to determine the differences between position time graphs and velocity time graphs. Pick up Moving Man WS and Graph Summary Sheet Log on to a laptop and go to my webpage via KCHS. You may have to share. Wednesday we will discuss special problems such as 11 & 12 on Unit 03 WS VI. You should try to see if you can answer them. All of WS VI is due on Thursday except #3. Kinematics test on Friday.
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• Moving Man Inquiry Lesson Goals: Plot data appropriately in a position time or velocity time graph What does the slope in a position time graph indicate? What does the slope in a velocity time graph indicate? Compare and contrast the following types of motion in a position time and velocity time graph: No motion Constant motion (uniform velocity) Constant motion (uniform acceleration) Understand how + and is used to indicate direction
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• Open the following link and choose run now! The Moving Man - Motion, Velocity, Acceleration PhET http://phet.colorado.edu/en/simulati on/moving-man
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• Motion Graphing Distance, Velocity, and Acceleration Motion Graphing Reference Motion Graphing Reference
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• Wed 9/1 Pick up 3 pages at front Turn in WS II to the blue sorter Turn in Yahtzee Graph to blue sorter Goal: Apply understanding of graphing to D vs T, V vs T, and A vs T Graphs
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• 10/2 Yesterday we did test corrections and made up tests and Meter Stick Lab I will be not available today after school Wednesday after school is last day for retakes. See me today if you plan on doing this. Please have grade slip signed and returned by Wednesday. Have HW VI out and ready to go over Download Motion Graphs now. Print to one note
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• d vs t graph Slope of line is velocity Linear line represents a constant velocity Horizontal line represents no motion Curved line represents acceleration Steeper slope represents greater velocity Slope = d /t = velocity Distance from detector CAN be indicated
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• v vs t graph Slope of line is acceleration Linear line represents uniform acceleration Horizontal line represents constant velocity, a=o Curved line represents changing acceleration Steeper slope represents greater acceleration Slope = v /t = acceleration Distance from detector cannot be indicated, only direction: away is positive and towards is negative
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• a vs t graph Linear line acceleration is changing at a constant rate Horizontal line uniform acceleration(the acceleration stays the same) Curved line acceleration is changing non-uniformly Steeper slope-- greater change in a Slope = a /t
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• Obj 15: Comparing graphs No motion (v=0)
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• Constant Velocity (a=0) positive direction
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• Constant velocity (a=0) negative direction
• Slide 160
• Begin Linear Motion Calculations A young science student named Earl N. Meyer walks 150 meters due east and then turns around and walks 30 meters due west. What is the total distance? What is the displacement ? Which is scalar? Which is a vector?
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• A Tiger Belle walks straight south for 12.6m then walks due east for 19.4m. What is the total distance walked by the Tiger Belle? What is the Tiger Belles displacement? How to describe direction quantitatively?
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• A picture is worth a 1000 words.. Free Body Diagrams
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• Arrows represent vectors Length of arrow corresponds to magnitude of vector Connect the tail of one vector to the arrow tip of the other No matter what route you take from point A to point B your final displacement vector will be the same The final displacement vector is called the resultant vector Draw in the resultant vector from the tail of the first vector to the arrow head of the second Free Body Diagrams
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• Adding Vectors If two vectors are at right angles to each other the resultant can be calculated with A 2 + B 2 = C 2
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• SOH CAH TOA This is a good time to review SOH CAH TOA Sine = opposite / hypotenuse Cosine = adjacent / hypotenuse Tangent = opposite / adjacent These only work for right triangles!
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• Remember S H O C H A T A O SOH-CAH-TOA
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• Naming the sides A right angled triangle The angle we are interested in. H This is the longest side the hypotenuse. O This side is opposite our angle. A This side is adjacent to our angle.
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• Naming the sides H = Hypotenuse O = Opposite A = Adjacent H O A O H A H O A H O A H O A
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• Remember S H O C H A T A O SOH-CAH-TOA
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• Whats this SOHCAHTOA? Ever wondered what the sin, cos and tan keys on your calculator are for? sin=sine cos=cosine tan=tangent Sin, cos and tan are the link between the angles and sides in a right angled triangle.
• Slide 171
• Sine 30 4cm 8cm H = O = SH O Here we know the Hypotenuse and the Opposite side. So we use the SOH triangle. This tells us that sin 30 = 4/8 = 0.5. You can check with a calculator that sin 30 is 0.5.
• Slide 172
• What happens when you dont know the angle? We can find the usable number mentioned previously using the ratios. The problem is we know need to convert it back into the original angle. The Buttons on your calculator are SinCosTan The opposite of these are SHIFT then Sin -1 Cos -1 Tan -1
• Slide 173
• Work sample problems: solving right triangles
• Slide 174
• If two vectors are not at right angles to each other then we must use the Law of Cosines: C 2 = A 2 + B 2 2AB cos or Theta, is any unknown angle but in this case it is the angle between the two vectors
• Slide 175
• The Swimmer A swimmer attempts to swim due north to the pier 2.00 miles away but the current takes him at a bearing of 40. After a while he notices he is due east of the pier. How far has he travelled? Step 1. Draw a diagram. pier 2.00 miles 40 ?
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• The Swimmer ? 2 40 Step 2. Identify the sides. Here we have the Adjacent side and want to find the Hypotenuse. So we use the CAH triangle. C H A Putting our finger on H shows that H = A/C = 2.00 (cos 40) = 2.00 0.766 = 2.61 miles
• Slide 177
• The Church Steeple Eric decides to find the height of the steeple of his local church. He measures a distance of 50. m along the ground. The angle of elevation of the top of the steeple is 35. How high is the steeple? Step 1. Draw a diagram. 50.m 35 ?
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• The Church Steeple ? 50 35 Step 2. Identify the sides. Here we have the Adjacent side and want to find the Opposite. So, we use the TOA triangle. Putting our finger on O shows that O = T A = (tan 35) 50. = 0.70 50. = 35 m T A O
• Slide 179
• Finding An Angle (1) At Heathwick airport there is a forest just 500. m from the end of the runway. The trees can be as tall as 30. m. What is the minimum angle of climb if aircraft are to avoid the trees? Step 1. Draw a diagram. 30.m 500.m ?
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• Finding An Angle (2) 30 500 Step 2. Identify the sides Here we have the Adjacent and Opposite sides and want to find an angle. So, we use the TOA triangle. Putting our finger on T shows that tan = O/A = 30. 500. = 0.060 T A O Now we can use the inverse tan to find the angle. = tan -1 0.060 = 3.4
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• Remember S H O C H A T A O SOH-CAH-TOA
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• 30 ? cm 8 cm H = O = SH O Sin Finding the Opposite SOH-CAH-TOA ?? Opp= Sin Hyp = (Sin 30) 8 = 4 cm
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• 27 ? km 12.3 km H = A = CH A Cos Finding the Adjacent SOH-CAH-TOA ?? Adj= Cos Hyp = (Cos 27) 12.3 = 0.891 12.3 = 11.0 km
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• 53 ? cm TA O Tan Finding the Opposite O = A = 16 cm SOH-CAH-TOA ?? Opp= Tan Adj = (Tan 53) 16 = 1.327 16 = 21 cm
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• 36 87 m ? m H = O = SH O Sin Finding the Hypotenuse SOH-CAH-TOA ?? Hyp= Opp Sin = 87 (Sin 36) = 87 0.5878 = 150 m
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• 0.80 cm ? cm H = A = CH A Cos Finding the Hypotenuse 60 SOH-CAH-TOA ?? Hyp= Adj Cos = 0.80 (Cos 60.) = 0.80 0.50 = 1.6 cm
• Slide 187
• 30 3.1 cm TA O Tan Finding the Adjacent O = A = ? cm SOH-CAH-TOA ?? Adj= Opp Tan = 3.1 (Tan 30.) = 3.1 0.5773 = 5.4 cm
• Slide 188
• What happens when you dont know the angle? We can find the usable number mentioned previously using the ratios. The problem is we know need to convert it back into the original angle. The Buttons on your calculator are SinCosTan The opposite of these are SHIFT then Sin -1 Cos -1 Tan -1
• Slide 189
• 3.0 km 7.0 km H = O = SH O Sin Finding the Angle SOH-CAH-TOA ? ? ? Sin = Opp Hyp Sin = 3.0 7.0 Sin = 0.4285 = Sin -1 (0.4285) = 25
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• 12.1 cm 14.5cm H = A = CH A Cos Finding the Angle SOH-CAH-TOA ? ? ? Cos = Adj Hyp Cos = 12.1 14.5 Cos = 0.834 = Cos -1 (0.834) = 33.4
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• 67.0 cm TA O Tan Finding the Angle O = A = 187 cm SOH-CAH-TOA ? ? ? Tan = Opp Adj Tan = 67.0 187 Tan = 0.358 = Tan -1 (0.358) = 19.7
• Slide 192
• Adding Vectors Graphically Make a scale drawing (eg. 1cm = 1km) Connect the tail of one vector to the arrow tip of the other Draw in the resultant vector from the tail of the first vector to the arrow head of the second.
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• Usually the Y axis points due north and the X axis points due east When describing the angle determine direction of adjacent side, then describe direction in relation to adjacent side. Use a protractor to measure the number of degrees the resultant is from a cardinal direction. e.g. 4 degrees south of west
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• Instantaneous Velocity or v the rate of motion (speed) at any given moment ex. Radar gun v= d t
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• Average Velocity=v the change in position divided by the time interval ex. Average speed for a trip v= d = d f d 0 t t f -t 0 t t f -t 0 Units m/s
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• Acceleration A change in velocity in a unit of time a= v = v f v o t t f -t o t t f -t o Units m/s 2
• Slide 197
• Acceleration due to gravity on earth this is a change in velocity caused by the force of attraction between the object and the earth. The acceleration due to gravity on earth is relatively constant everywhere on earth although there are slight variations due to the earth not being perfectly round.
• Slide 198
• COPY THIS DOWN BEFORE CLASS STARTS Pick up WS I & get a calculator We had a quiz yesterday on triangles The accepted value for the acceleration due to gravity on earth are: 9.80 m/sec/sec or 9.80 m/sec 2 9.80 m/sec/sec or 9.80 m/sec 2
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• Below is a ticker tape diagram. What is the explanation for the spacing of the dots? start end
• Slide 200
• Great Website for Linear Motion Great Website for Linear Motion http://www.glenbrook.k12.il.us/gbssci /phys/class/1DKin/U1L1a.html http://www.glenbrook.k12.il.us/gbssci /phys/class/1DKin/U1L1a.html Homework: go to this website, click on Lesson 2 and read Ticker Tape Diagrams. Answer the 2 questions at end of this section.
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• Slide 202
• Galileos Kinematics Lab Report Purpose Statement Construct your own data tables for Hypothesis A, B, and C. Make sure each table has a title and all columns are labeled. This requires a ruler! Graph for Hypothesis A, B, and C. Make sure each graph has a title and axes are labeled with magnitude and unit. This requires a ruler! Answer Questions for Hypothesis A, B, and C in complete sentences. To justify your answer means you reference the supporting data.
• Slide 203
• Galileos Kinematics Lab Report Purpose Statement Construct your own data tables for Hypothesis A, B, and C. Make sure each table has a title and all columns are labeled. This requires a ruler! Graph for Hypothesis A, B, and C. Make sure each graph has a title and axes are labeled with magnitude and unit. This requires a ruler! Answer Questions for Hypothesis A, B, and C in complete sentences. To justify your answer means you reference the supporting data.
• Slide 204
• Galileos Kinematics Lab Report Purpose Statement Construct your own data tables for Hypothesis A, B, and C. Make sure each table has a title and all columns are labeled. This requires a ruler! Graph for Hypothesis A, B, and C. Make sure each graph has a title and axes are labeled with magnitude and unit. This requires a ruler! Answer Questions for Hypothesis A, B, and C in complete sentences. To justify your answer means you reference the supporting data.
• Slide 205
• Galileos Kinematics Lab Report Purpose Statement Construct your own data tables for Hypothesis A, B, and C. Make sure each table has a title and all columns are labeled. This requires a ruler! Graph for Hypothesis A, B, and C. Make sure each graph has a title and axes are labeled with magnitude and unit. This requires a ruler! Answer Questions for Hypothesis A, B, and C in complete sentences. To justify your answer means you reference the supporting data.