Keynote update3-20030829_1 2005-01-18 21:37:48 -0800 root East West North 1st Qtr 20.4 30.6 45.9 2nd Qtr 27.4 38.6 46.9 3rd Qtr 90.0 34.6 45.0 4th Qtr 20.4 31.6 43.9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 root East West North 1st Qtr 20.4 30.6 45.9 2nd Qtr 27.4 38.6 46.9 3rd Qtr 90.0 34.6 45.0 4th Qtr 20.4 31.6 43.9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 root East West North 1st Qtr 20.4 30.6 45.9 2nd Qtr 27.4 38.6 46.9 3rd Qtr 90.0 34.6 45.0 4th Qtr 20.4 31.6 43.9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 root East West North 1st Qtr 20.4 30.6 45.9 2nd Qtr 27.4 38.6 46.9 3rd Qtr 90.0 34.6 45.0 4th Qtr 20.4 31.6 43.9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 root East West North 1st Qtr 20.4 30.6 45.9 2nd Qtr 27.4 38.6 46.9 3rd Qtr 90.0 34.6 45.0 4th Qtr 20.4 31.6 43.9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 root East West North 1st Qtr 20.4 30.6 45.9 2nd Qtr 27.4 38.6 46.9 3rd Qtr 90.0 34.6 45.0 4th Qtr 20.4 31.6 43.9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 root East West North 1st Qtr 20.4 30.6 45.9 2nd Qtr 27.4 38.6 46.9 3rd Qtr 90.0 34.6 45.0 4th Qtr 20.4 31.6 43.9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0.501961 0.501961 1 1 1 1 0 0 0.25098 1 1 1 0.980392 0.992157 0 1 1 1 1 1 1 version 1 CPBorderColorProperty 1 1 1 CPTextProperty root East West North 1st Qtr 20.4 30.6 45.9 2nd Qtr 27.4 38.6 46.9 3rd Qtr 90.0 34.6 45.0 4th Qtr 20.4 31.6 43.9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> Physics 111: Lecture 1, Pg Body Text Second Level Third Level » Fourth Level Fifth Level – <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> Physics 111: Lecture 1 Advice Scope of this course Measurement and Units Fundamental units Systems of units Converting between systems of units Dimensional Analysis 1-D Kinematics (review) Average & instantaneous velocity and acceleration Motion with constant acceleration <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> Course Info & Advice See info on the World Wide Web (heavily used in Physics 111) Go to http://www.physics.uiuc.edu and follow “courses” link to the Physics 111 homepage Course has several components: Lecture: (me talking, demos and Active learning) Discussion sections (group problem solving) Homework sets, Web based Labs: (group exploration of physical phenomena) If you miss a lab or discussion you should always try to make it up as soon as possible The first few weeks of the course should be review, hence the pace is fast. It is important for you to keep up! <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> Lecture Organization Three main components: Lecturer discusses class material » Lecturer does as many demos as possible » » Usually three per lecture » <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> Scope of Physics 111 Classical Mechanics: Mechanics: How and why things work Classical: Not too fast (v << c) » Not too small (d >> atom) » Most everyday situations can be described in these terms. Path of baseball Orbit of planets etc... <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> Units How we measure things! All things in classical mechanics can be expressed in terms of the fundamental units: Length L Mass M Time T For example: Speed has units of L / T (i.e. miles per hour). Force has units of ML / T 2 etc... (as you will learn). <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> Length: Distance Length (m) Radius of visible universe 1 x 1026 To Andromeda Galaxy 2 x 1022 To nearest star 4 x 1016 Earth to Sun 1.5 x 1011 Radius of Earth 6.4 x 106 Sears Tower 4.5 x 102 Football field 1.0 x 102 Tall person 2 x 100 Thickness of paper 1 x 10-4 Wavelength of blue light 4 x 10-7 Diameter of hydrogen atom 1 x 10-10 Diameter of proton 1 x 10-15 <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> Time: Interval Time (s) Age of universe 5 x 1017 Age of Grand Canyon 3 x 1014 32 years 1 x 109 One year 3.2 x 107 One hour 3.6 x 103 Light travel from Earth to Moon 1.3 x 100 One cycle of guitar A string 2 x 10-3 One cycle of FM radio wave 6 x 10-8 Lifetime of neutral pi meson 1 x 10-16 Lifetime of top quark 4 x 10-25 <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> Mass: Object Mass (kg) Milky Way Galaxy 4 x 1041 Sun 2 x 1030 Earth 6 x 1024 Boeing 747 4 x 105 Car 1 x 103 Student 7 x 101 Dust particle 1 x 10-9 Top quark 3 x 10-25 Proton 2 x 10-27 Electron 9 x 10-31 Neutrino 1 x 10-38 <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> Units... SI (Système International) Units: mks: L = meters (m), M = kilograms (kg), T = seconds (s) cgs: L = centimeters (cm), M = grams (gm), T = seconds (s) British Units: Inches, feet, miles, pounds, slugs... <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> Converting between different systems of units Useful Conversion factors: 1 inch = 2.54 cm 1 m = 3.28 ft 1 mile = 5280 ft 1 mile = 1.61 km <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> Dimensional Analysis This is a very important tool to check your work Example: Doing a problem you get the answer distance d = vt 2 (velocity x time 2 ) Units on left side = L Units on right side = L / T x T 2 = L x T Left units and right units don’t match, so answer must be wrong!! <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> (a) (b) (c) Given: d has units of length ( L ) and g has units of ( L / T 2 ) . P = 2π (dg)2 Lecture 1, Act 1 Dimensional Analysis The period P of a swinging pendulum depends only on the length of the pendulum d and the acceleration of gravity g. Which of the following formulas for P could be correct ? <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> (a) (b) (c) (a) Not Right !! Lecture 1, Act 1 Solution Realize that the left hand side P has units of time (T ) Try the first equation (a) (b) (c) (b) Not Right !! <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> Lecture 1, Solution Try the second equation (a) (b) (c) (c)
This must be the answer!!
 Try the third equation <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> Lecture 1, Act 1 Solution <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> t x t1 t2 Δ x Δ t x1 x2 some particle’s trajectory
in 1-D Motion in 1 dimension In 1-D, we usually write position as x(t 1 ) . Since it’s in 1-D, all we need to indicate direction is + or − Displacement in a time Δ t = t 2 - t 1 is Δ x = x(t 2 ) - x(t 1 ) = x 2 - x 1 <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> t x t1 t2 Δ x x1 x2 trajectory Δ t Vav = slope of line connecting x 1 and x 2 . 1-D kinematics Velocity v is the “rate of change of position” Average velocity v av in the time Δ t = t 2 - t 1 is: <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> t x t1 t2 Δ x x1 x2 Δ t so v(t 2 ) = slope of line tangent to path at t 2. 1-D kinematics... Consider limit t 1 t 2 Instantaneous velocity v is defined as: <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> And instantaneous acceleration a is defined as: using 1-D kinematics... Acceleration a is the “rate of change of velocity” Average acceleration a av in the time Δ t = t 2 - t 1 is: <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> x a v t t t Recap If the position x is known as a function of time, then we can find both velocity v and acceleration a as a function of time! <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> Graphically, this is adding up lots of small rectangles: v(t) t + +...+ = displacement More 1-D kinematics We saw that v = dx / dt In “calculus” language we would write dx = v dt, which we can integrate to obtain: <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> 1-D Motion with constant acceleration Since a is constant, we can integrate this using the above rule to find: Similarly, since we can integrate again to get: <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> x a v t t t Recap So for constant acceleration we find: <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> y Lecture 1, Act 2 Motion in One Dimension v and its acceleration a at the highest point in its path? (a) Both v = 0 and a = 0. (b) v ≠ 0, but a = 0. (c) v = 0, but a ≠ 0. <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> x a v t t t
g = 9.81 m/s 2
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lock-aspect-ratio="true"> <styles> <shadow-style opacity="0" radius="0"/> <dash-style pattern="none"/> </styles> </image> <image opacity="1" natural-size="63.978 13.9748" transformation="2.01367 0 0 2.16071 328.75 208.625" display-name="Image-68" image-data="image33.pdf" stroke-color="g1" byte-size="5635" stroke-width="2" lock-aspect-ratio="true"> <styles> <shadow-style opacity="0" radius="0"/> <dash-style pattern="none"/> </styles> </image> <image opacity="1" natural-size="114.973 38.9764" transformation="2.34239 0 0 2.16667 137.5 259" display-name="Image-69" image-data="image34.pdf" stroke-color="g1" byte-size="12709" stroke-width="2" lock-aspect-ratio="true"> <styles> <shadow-style opacity="0" radius="0"/> <dash-style pattern="none"/> </styles> </image> <image opacity="1" natural-size="14.9953 11.9906" transformation="2.01667 0 0 2.14583 275.375 214.75" display-name="Image-70" image-data="image35.pdf" stroke-color="g1" byte-size="2027" stroke-width="2" lock-aspect-ratio="true"> <styles> <shadow-style opacity="0" radius="0"/> <dash-style pattern="none"/> </styles> </image> <image opacity="1" natural-size="14.9953 11.9906" transformation="2.01667 0 0 2.14583 115 366.125" display-name="Image-71" image-data="image35.pdf" stroke-color="g1" byte-size="2027" stroke-width="2" lock-aspect-ratio="true"> <styles> <shadow-style opacity="0" radius="0"/> <dash-style pattern="none"/> </styles> </image> <image opacity="1" natural-size="105.987 30.9827" transformation="2.01887 0 0 2.17339 155.625 343.5" display-name="Image-72" image-data="image36.pdf" stroke-color="g1" byte-size="8308" stroke-width="2" lock-aspect-ratio="true"> <styles> <shadow-style opacity="0" radius="0"/> <dash-style pattern="none"/> </styles> </image> <textbox size="230.35 27" transformation="1 0 0 1 434.075 282.725"> <content font-color="1 1 1" paragraph-spacing="-2" paragraph-head-indent="22.5" paragraph-alignment="left" tab-stops="L 22.5 L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="24" paragraph-line-spacing="1.8" font-name="TimesNewRomanMS">(a = constant)</content> <styles> <shadow-style opacity="0" radius="0"/> </styles> </textbox> </g> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="none" duration="0"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st26.tiff"/> </thumbnails> <bullets> <bullet level="0" spacing="-4.08" marker-type="none"> <content font-color="0.980392 0.992157 0" paragraph-alignment="center" tab-stops="L 0 L 72 L 144 L 216 L 288 L 360 L 432 L 504" font-size="24" paragraph-line-spacing="-2.08" font-name="Arial-BoldMS">Alternate (Calculus-based) Derivation</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-1"> <drawables> <title visibility="visible" vertical-alignment="tracks-master"/> <body visibility="visible" bullet-indentation="0 0 31.5 58.5 85.5 108" vertical-alignment="tracks-master"/> <textbox size="550.875 23" transformation="1 0 0 1 80.125 120.125"> <content font-color="0 1 0" paragraph-spacing="-2" paragraph-head-indent="0.635" paragraph-alignment="left" paragraph-first-line-indent="0.635" tab-stops="L 22.5 L 72 L 144 L 216 L 288 L 360 L 432 L 504" font-size="20" paragraph-line-spacing="-1.4" font-name="MonotypeSorts"><span font-name="LucidaGrande"> <![CDATA[ ]]> </span> <span font-color="1 1 1" font-name="ArialMS">For constant acceleration:</span> </content> <styles> <shadow-style opacity="0" radius="0"/> </styles> </textbox> <image byte-size="3760" display-name="Image-73" transformation="0.996053 0 0 0.946429 270.375 215.75" lock-aspect-ratio="true" image-data="image37.pdf" opacity="1" stroke-width="2" stroke-color="g1"> <styles> <shadow-style opacity="0" radius="0"/> <dash-style pattern="none"/> </styles> </image> <image byte-size="5643" display-name="Image-74" transformation="0.997832 0 0 0.989796 267.375 168.375" lock-aspect-ratio="true" image-data="image38.pdf" opacity="1" stroke-width="2" stroke-color="g1"> <styles> <shadow-style opacity="0" radius="0"/> <dash-style pattern="none"/> </styles> </image> <image opacity="1" natural-size="188.617 34.611" transformation="0.994709 0 0 0.971429 268 255" display-name="Image-75" image-data="image25.pdf" stroke-color="g1" byte-size="4793" stroke-width="2" lock-aspect-ratio="true"> <styles> <shadow-style opacity="0" radius="0"/> <dash-style pattern="none"/> </styles> </image> <g transformation="1 0 0 1 244.25 154.625"> <shape path="M 0 0 L 100 0 L 100 100 L 0 100 Z M 0 0" transformation="2.29 0 0 1.24625 253 162.5" opacity="1" stroke-color="0 1 0" stroke-width="1"> <styles> <fill-style fill-type="none"/> <dash-style pattern="solid"/> <shadow-style opacity="0" radius="0"/> </styles> </shape> <shape path="M 0 0 L 100 0 L 100 100 L 0 100 Z M 0 0" transformation="2.45625 0 0 1.4125 244.25 154.625" opacity="1" stroke-color="0 1 0" stroke-width="1"> <styles> <fill-style fill-type="none"/> <dash-style pattern="solid"/> <shadow-style opacity="0" radius="0"/> </styles> </shape> <line stroke-color="0 1 0" head="244.25 154.625" opacity="1" stroke-width="1" tail="253 162.5"> <styles> <dash-style pattern="solid"/> <shadow-style opacity="0" radius="0"/> <line-head-style is-filled="false"/> <line-tail-style is-filled="false"/> </styles> </line> <line stroke-color="0 1 0" head="244.25 295.875" opacity="1" stroke-width="1" tail="253 287.125"> <styles> <dash-style pattern="solid"/> <shadow-style opacity="0" radius="0"/> <line-head-style is-filled="false"/> <line-tail-style is-filled="false"/> </styles> </line> <line stroke-color="0 1 0" head="482 287.125" opacity="1" stroke-width="1" tail="489.75 295.875"> <styles> <dash-style pattern="solid"/> <shadow-style opacity="0" radius="0"/> <line-head-style is-filled="false"/> <line-tail-style is-filled="false"/> </styles> </line> <line stroke-color="0 1 0" head="482 162.5" opacity="1" stroke-width="1" tail="489.75 154.625"> <styles> <dash-style pattern="solid"/> <shadow-style opacity="0" radius="0"/> <line-head-style is-filled="false"/> <line-tail-style is-filled="false"/> </styles> </line> </g> <textbox size="550.875 23" transformation="1 0 0 1 80.125 312.125"> <content font-color="0 1 0" paragraph-spacing="-2" paragraph-head-indent="0.635" paragraph-alignment="left" paragraph-first-line-indent="0.635" tab-stops="L 22.5 L 72 L 144 L 216 L 288 L 360 L 432 L 504" font-size="20" paragraph-line-spacing="-1.4" font-name="MonotypeSorts"><span font-name="LucidaGrande"> <![CDATA[ ]]> </span> <span font-color="1 1 1" font-name="ArialMS">From which we know:</span> </content> <styles> <shadow-style opacity="0" radius="0"/> </styles> </textbox> <image byte-size="8750" display-name="Image-76" transformation="0.997159 0 0 0.994048 284.375 373.875" lock-aspect-ratio="true" image-data="image39.pdf" opacity="1" stroke-width="2" stroke-color="g1"> <styles> <shadow-style opacity="0" radius="0"/> <dash-style pattern="none"/> </styles> </image> <g 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pattern="solid"/> <shadow-style opacity="0" radius="0"/> <line-head-style is-filled="false"/> <line-tail-style is-filled="false"/> </styles> </line> <line stroke-color="0 1 0" head="472.749 473.843" opacity="1" stroke-width="1" tail="479.639 481.625"> <styles> <dash-style pattern="solid"/> <shadow-style opacity="0" radius="0"/> <line-head-style is-filled="false"/> <line-tail-style is-filled="false"/> </styles> </line> <line stroke-color="0 1 0" head="472.749 363.004" opacity="1" stroke-width="1" tail="479.639 356"> <styles> <dash-style pattern="solid"/> <shadow-style opacity="0" radius="0"/> <line-head-style is-filled="false"/> <line-tail-style is-filled="false"/> </styles> </line> </g> <image opacity="1" natural-size="181.616 249.874" transformation="0.215659 0 0 0.216 560.75 52.875" display-name="Image-77" image-data="image.pdf" stroke-color="g1" byte-size="5967" stroke-width="2" lock-aspect-ratio="true"> <styles> <shadow-style opacity="0" radius="0"/> <dash-style pattern="none"/> </styles> </image> <shape path="M 0 0 L 100 0 L 100 100 L 0 100 Z M 0 0" transformation="0.865 0 0 0.29875 549.5 112.625" opacity="1" stroke-color="1 0 1" stroke-width="1"> <styles> <fill-style fill-type="none"/> <dash-style pattern="solid"/> <shadow-style opacity="0" radius="0"/> </styles> </shape> <textbox grow-horizontally="true" size="81 21" transformation="1 0 0 1 551.75 116.225"> <content font-color="1 1 1" paragraph-spacing="-2" paragraph-head-indent="22.5" paragraph-alignment="center" tab-stops="L 22.5 L 28 L 56 L 84 L 112 L 140 L 168 L 196 L 224 L 252 L 280 L 308 L 336" font-size="18" paragraph-line-spacing="0.6" font-name="ArialMS">Washers</content> <styles> <shadow-style opacity="0" radius="0"/> </styles> </textbox> </drawables> <transition-style type="none" duration="0"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st27.tiff"/> </thumbnails> <bullets> <bullet level="0" spacing="-4.08" marker-type="none"> <content font-color="0.980392 0.992157 0" paragraph-alignment="center" tab-stops="L 0 L 72 L 144 L 216 L 288 L 360 L 432 L 504" font-size="24" paragraph-line-spacing="-2.08" font-name="Arial-BoldMS">Recap:</content> </bullet> <bullet level="1" marker-type="none"> <content font-color="1 1 1" paragraph-spacing="5.2" paragraph-head-indent="0.635" paragraph-alignment="left" paragraph-first-line-indent="0.635" tab-stops="L 22.5 L 72 L 144 L 216 L 288 L 360 L 432 L 504" font-size="20" paragraph-line-spacing="-1.4" font-name="ArialMS"/> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-1"> <drawables> <title visibility="visible" stroke-width="1" vertical-alignment="middle"> <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> x = 0, t = 0 ab vo Problem 1 A car is traveling with an initial velocity v 0. At t = 0, the driver puts on the brakes, which slows the car at a rate of a b <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> x = xf , t = tf v = 0 x = 0, t = 0 ab v0 Problem 1... A car is traveling with an initial velocity v 0. At t = 0, the driver puts on the brakes, which slows the car at a rate of a b. At what time t f does the car stop, and how much farther x f does it travel? <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> Problem 1... Above, we derived: v = v 0 + at Realize that a = -a b Also realizing that v = 0 at t = t f : find 0 = v 0 - a b t f or t f = v 0 /a b <body bullet-indentation="0 0 31.5 58.5 85.5 108" size="558.75 226" visibility="visible" vertical-alignment="tracks-master" location="80.125 140.5" stroke-color="1 1 1" stroke-width="1"> <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> </body> <textbox size="558.75 54.8" transformation="1 0 0 1 80.125 255.5"> <content font-color="0 1 0" paragraph-spacing="5.2" paragraph-head-indent="0.635" paragraph-alignment="left" paragraph-first-line-indent="0.635" tab-stops="L 22.5 L 72 L 144 L 216 L 288 L 360 L 432 L 504" font-size="20" paragraph-line-spacing="-1.4" font-name="MonotypeSorts"><span font-name="LucidaGrande"> <![CDATA[ ]]> </span> <span font-color="1 1 1" font-name="ArialMS">In this case </span> <span font-color="0.980392 0.992157 0" font-name="Arial-ItalicMS">v = v</span> <span font-color="0.980392 0.992157 0" font-name="Arial-ItalicMS" font-baseline-offset="-5">f</span> <span font-color="0.980392 0.992157 0" font-name="Arial-ItalicMS"> = 0</span> <span font-color="1 1 1" font-name="ArialMS">, </span> <span font-color="0.980392 0.992157 0" font-name="Arial-ItalicMS">x</span> <span font-color="0.980392 0.992157 0" font-name="Arial-ItalicMS" font-baseline-offset="-5">0</span> <span font-color="0.980392 0.992157 0" font-name="Arial-ItalicMS"> = 0 </span> <span font-color="1 1 1" font-name="ArialMS">and</span> <span font-color="0.980392 0.992157 0" font-name="Arial-ItalicMS"> x = x</span> <span font-color="0.980392 0.992157 0" font-name="Arial-ItalicMS" font-baseline-offset="-5">f</span> <span font-color="0.980392 0.992157 0" font-name="Arial-ItalicMS"> <![CDATA[ ]]> </span> </content> <styles> <shadow-style opacity="0" radius="0"/> </styles> </textbox> <image byte-size="5580" display-name="Image-81" transformation="1 0 0 0.983333 269.75 335" lock-aspect-ratio="true" image-data="image41.pdf" opacity="1" stroke-width="2" stroke-color="g1"> <styles> <shadow-style opacity="0" radius="0"/> <dash-style pattern="none"/> </styles> </image> <image byte-size="5229" display-name="Image-82" transformation="1 0 0 0.982456 302.75 401" lock-aspect-ratio="true" image-data="image42.pdf" opacity="1" stroke-width="2" stroke-color="g1"> <styles> <shadow-style opacity="0" radius="0"/> <dash-style pattern="none"/> </styles> </image> <shape path="M 13.7167 0 L 86.2833 0 C 93.8588 0 100 13.1123 100 29.287 L 100 70.713 C 100 86.8877 93.8588 100 86.2833 100 L 13.7167 100 C 6.14117 100 0 86.8877 0 70.713 L 0 29.287 C 0 13.1123 6.14117 0 13.7167 0 Z M 13.7167 0" transformation="1.54 0 0 0.72125 270.75 394.5" opacity="1" stroke-color="0.980392 0.992157 0" stroke-width="1"> <styles> <fill-style fill-type="none"/> <dash-style pattern="solid"/> <shadow-style opacity="0" radius="0"/> </styles> </shape> <image byte-size="5974" display-name="Image-83" transformation="0.997159 0 0 0.993952 272.875 192.625" lock-aspect-ratio="true" image-data="image43.pdf" opacity="1" stroke-width="2" stroke-color="g1"> <styles> <shadow-style opacity="0" radius="0"/> <dash-style pattern="none"/> </styles> </image> </drawables> <transition-style type="none" duration="0"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st31.tiff"/> </thumbnails> <bullets> <bullet level="0" spacing="-4.08" marker-type="none"> <content font-color="0.980392 0.992157 0" paragraph-alignment="center" tab-stops="L 0 L 72 L 144 L 216 L 288 L 360 L 432 L 504" font-size="24" paragraph-line-spacing="-2.08" font-name="Arial-BoldMS">Problem 1...</content> </bullet> <bullet level="1" spacing="3.8" marker-type="character"> <content font-color="1 1 1" paragraph-head-indent="0.635" paragraph-alignment="left" paragraph-first-line-indent="0.635" tab-stops="L 47 L 119 L 191 L 263 L 335 L 407 L 479" font-size="20" paragraph-line-spacing="-1.4" font-name="ArialMS">To find stopping distance we use:</content> <character-bullet-style size-technique="relative" size="0.75"> <bullet-characters font-color="0 1 0" font-name="MonotypeSorts" font-size="20"></bullet-characters> </character-bullet-style> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-1"> <drawables> <title visibility="visible" stroke-width="1" vertical-alignment="middle"> <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> Problem 1... So we found that Suppose that v o = 65 mi/hr = 29 m/s Suppose also that ab = g = 9.81 m/s2 Find that t f = 3 s and x f = 43 m <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> Tips: Read ! Watch your units ! Understand the limits ! <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> Recap of today’s lecture Scope of this course Measurement and Units (Chapter 1) Systems of units (Text: 1-1) Converting between systems of units (Text: 1-2) Dimensional Analysis (Text: 1-3) 1-D Kinematics (Chapter 2) (Text: 2-1, 2-2) Motion with constant acceleration (Text: 2-3) Example car problem Look at Text problems Chapter 2: # 49, 54, 71, 122 0 {0, 0}