2015 WHS 02 LectureSlides

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9/26/2015Chapter 2 Motion in One DimensionLecturePresentationChapter 2Motion in OneDimensionChapter Goal: To describe and analyze linear motion. 2015 Pearson Education, Inc.Slide 2-2 2015 Pearson Education, Inc.Representing Position We will use an x-axis to analyze horizontal motion andmotion on a ramp, with the positive end to the right.Section 2.1 Describing Motion We will use a y-axis to analyze vertical motion, with thepositive end up.Ch. 2 Pre-Lecture Video #1on MP site. 2015 Pearson Education, Inc.Slide 2-4 2015 Pearson Education, Inc.Representing PositionThe motion diagram of a student walking to school and acoordinate axis for making measurements Every dot in the motion diagram of Figure 2.2 representsthe student’s position at a particular time. Figure 2.3 shows thestudent’s motion showsthe student’s position asa graph of x versus t.(not a picture of the motion) 2015 Pearson Education, Inc. 2015 Pearson Education, Inc.Slide 2-61

9/26/2015From Position to VelocityQuickCheck 2.1 On a position-versus-timegraph, a faster speedcorresponds to a steeperslope.Here is a motion diagram of a car moving along a straightroad:Which position-versus-time graph matches this motiondiagram? The slope of an object’sposition-versus-timegraph is the object’svelocity at that point inthe motion. 2015 Pearson Education, Inc.Slide 2-7 2015 Pearson Education, Inc.From Position to VelocityFrom Velocity to Position We can deduce the velocityversus-time graph from theposition-versus-time graph. We can deduce theposition-versus-time graphfrom the velocity-versustime graph. The velocity-versus-timegraph is yet another way torepresent an object’smotion. The sign of the velocitytells us whether the slopeof the position graph ispositive or negative. We can take the slope valuesof the position vs time graphand they become the yvalues of the velocity vstime graph. 2015 Pearson Education, Inc.Slide 2-8 The magnitude of thevelocity tells us how steepthe slope is.Slide 2-9Example 2.2 Analyzing a car’s position graph 2015 Pearson Education, Inc.Slide 2-10QuickCheck 2.3FIGURE 2.11 gives the position-versus-time graph of a car.Here is a motion diagram of a car moving along a straightroad:a. Draw the car’s velocityversus-time graph.b. Describe the car’s motionin words.Which velocity-versus-time graph matches this motiondiagram? 2015 Pearson Education, Inc.Slide 2-11 2015 Pearson Education, Inc.Slide 2-122

9/26/2015QuickCheck 2.4QuickCheck 2.7A graph of position versus time for a basketball playermoving down the court appears as follows:Which velocity-versus-time graphgoes with this position graph?Which of the following velocity graphs matches the positiongraph?A.B. 2015 Pearson Education, Inc.C.D.Slide 2-13 2015 Pearson Education, Inc.Slide 2-14Slide 2-15 2015 Pearson Education, Inc.Slide 2-16Uniform Motion Straight-line motion inwhich equal displacementsoccur during ANYsuccessive equal-timeintervals is called uniformmotion or constantvelocity motion. An object’s motion isuniform if and only if itsposition-versus-timegraph is a straight line. 2015 Pearson Education, Inc.Equations of Uniform Motion The velocity of an object in uniform motion tells us theamount by which its position changes during each second. The displacement x is proportional to the time interval t. 2015 Pearson Education, Inc.Slide 2-17 2015 Pearson Education, Inc.3

9/26/2015QuickCheck 2.8Example 2.3 If a train leaves Cleveland at2:00 Here is a position graphof an object:A train is moving due west at a constant speed. A passengernotes that it takes 10 minutes to travel 12 km. How long willit take the train to travel 60 km?At t 1.5 s, the object’svelocity isA.B.C.D.E.40 m/s20 m/s10 m/s–10 m/sNone of the above 2015 Pearson Education, Inc.Slide 2-19From Velocity to Position, One More Time 2015 Pearson Education, Inc.Slide 2-20QuickCheck 2.11 The displacement x is equal to the area under thevelocity graph during the time interval t.Here is the velocity graph of an object that is at the origin(x 0 m) at t 0 s.At t 4.0 s, the object’sposition isA.B.C.D.E. 2015 Pearson Education, Inc.Slide 2-21Instantaneous Velocity20 m16 m12 m8m4m 2015 Pearson Education, Inc.Slide 2-22Finding the Instantaneous Velocity For one-dimensional motion, an object changing itsvelocity is either speeding up or slowing down. An object’s velocity—a speed and a direction (vectorquantity)—at a specific instant of time t is called theobject’s instantaneous velocity. If the velocity changes, the position graph is a curved line.But we can compute a slope at a point by considering asmall segment of the graph. Let’s look at the motion in avery small time interval right around t 0.75 s. From now on, theword “velocity” willalways meaninstantaneous velocity. 2015 Pearson Education, Inc.Slide 2-23 2015 Pearson Education, Inc.Slide 2-244

9/26/2015Instantaneous Velocity Even when the speed varies we can still use the velocityversus-time graph to determine displacement. The area under the curve in a velocity-versus-time graphequals the displacement even for non-uniform motion. 2015 Pearson Education, Inc.Slide 2-25 2015 Pearson Education, Inc.QuickCheck 2.5QuickCheck 2.9The slope at a point on a position-versus-time graph of anobject isWhen do objects 1 and 2 have the same velocity?A.B.C.D.E.A. At some instant beforetime t0B. At time t0C. At some instant aftertime t0D. Both A and BE. NeverThe object’s speed at that point.The object’s velocity at that point.The object’s acceleration at that point.The distance traveled by the object to that point.I am not sure. 2015 Pearson Education, Inc.Slide 2-26Slide 2-27 2015 Pearson Education, Inc.QuickCheck 2.10QuickCheck 2.13Masses P and Q move with the position graphs shown. DoP and Q ever have the same velocity? If so, at what time ortimes?A car moves along a straight stretch of road. The followinggraph shows the car’s position as a function of time:Slide 2-28At what point (or points) do the following conditions apply?A.B.C.D.P and Q have the same velocity at 2 s.P and Q have the same velocity at 1 s and 3 s.P and Q have the same velocity at 1 s, 2 s, and 3 s.P and Q never have the same velocity. 2015 Pearson Education, Inc. Slide 2-29The displacement is zero.The speed is zero.The speed is increasing.The speed is decreasing. 2015 Pearson Education, Inc.Slide 2-305

9/26/2015Chapter 2 Homework AssignmentsMasteringPhysics “2.1-2.3 HW”ORSection 2.4 AccelerationFrom Text: Q:(5 & 20) and P: (2, 3, 12 & 15)Ch. 2 Pre-Lecture Video #2 on MP Site 2015 Pearson Education, Inc.Slide 2-31 2015 Pearson Education, Inc.AccelerationRepresenting Acceleration We define a new motion concept to describe an objectwhose velocity is changing. We can find an acceleration graph from a velocity graph. The ratio of vx/ t is the rate of change of velocity. The ratio of vx/ t is the slope of a velocity-versus-timegraph. Units for acceleration are m/s2 Please see “Class Video” page 39 2015 Pearson Education, Inc.Slide 2-33 2015 Pearson Education, Inc.Slide 2-34The Sign of the AccelerationAn object can move right or left (or up or down) whileeither speeding up or slowing down. Whether or not anobject that is slowing down has a negative accelerationdepends on the direction of motion. (my chart) 2015 Pearson Education, Inc.Slide 2-356

9/26/2015QuickCheck 2.12QuickCheck 2.14A particle has velocityas it moves from point 1 to point2. The acceleration is shown. What is its velocity vectoras it moves away from point 2?The motion diagram shows a particle that is slowing down.The sign of the position x and the sign of the velocity vx are:A.B.C.D. 2015 Pearson Education, Inc.Slide 2-37Position is positive, velocity is positive.Position is positive, velocity is negative.Position is negative, velocity is positive.Position is negative, velocity is negative. 2015 Pearson Education, Inc.Slide 2-38QuickCheck 2.17QuickCheck 2.18These four motion diagrams show the motion of a particlealong the x-axis.Mike jumps out of a tree and lands on a trampoline. Thetrampoline sags 2 feet before launching Mike back into theair.1. Which motion diagrams correspond to a positiveacceleration?2. Which motion diagrams correspond to a negativeacceleration?At the very bottom, where the sag is the greatest, Mike’sacceleration isA. Upward.B. Downward.C. Zero. 2015 Pearson Education, Inc.Slide 2-39QuickCheck 2.19Slide 2-40QuickCheck 2.21A cart slows down while movingaway from the origin. What do theposition and velocity graphs look like? 2015 Pearson Education, Inc. 2015 Pearson Education, Inc.A cart speeds up while movingaway from the origin. What dothe velocity and accelerationgraphs look like?Slide 2-41 2015 Pearson Education, Inc.Slide 2-427

9/26/2015QuickCheck 2.22QuickCheck 2.25Here is a motion diagram of a car speeding up on a straightroad:Which velocity-versus-time graphgoes with this acceleration graph?The sign of the acceleration ax isA. Positive.B. Negative.C. Zero.Slide 2-43 2015 Pearson Education, Inc. 2015 Pearson Education, Inc.Slide 2-44Constant Acceleration EquationsExample 2.8 Coming to a stopFor motion with constant acceleration:As you drive in your car at 15 m/s (just a bit under 35 mph), yousee a child’s ball roll into the street ahead of you. You hit thebrakes and stop as quickly as you can. In this case, you come torest in 1.5 s. How far does your car travel as you brake to a stop? Velocity changes steadily: The position changes as the square of the time interval: We can also express the change in velocity in terms ofdistance, not time:Text: p. 43Slide 2-45 2015 Pearson Education, Inc.Problem-Solving Strategy for Motion withConstant AccelerationText: p. 48 2015 Pearson Education, Inc. 2015 Pearson Education, Inc.Slide 2-46Example 2.11 Kinematics of a rocket launchA Saturn V rocket is launched straight up with a constantacceleration of 18 m/s2. After 150 s, how fast is the rocketmoving and how far has it traveled?Slide 2-47 2015 Pearson Education, Inc.Slide 2-488

9/26/2015Chapter 2 Homework AssignmentsMasteringPhysics “2.4 – 2.6 HW”Section 2.7 Free FallORCh. 2 Pre-Lecture Video #3 on MP SiteFrom Text: Q:(14) and P: (19, 26, 28, 30, 37)**** 39 is Extra Credit ****Slide 2-49 2015 Pearson Education, Inc.Free Fall 2015 Pearson Education, Inc.Free Fall If an object moves under theinfluence of gravity only, andno other forces, we call theresulting motion free fall. Any two objects in free fall,regardless of their mass,have the same acceleration. On the earth, air resistance isa factor. For now we willrestrict our attention tosituations in which airresistance can be ignored.Apollo 15 lunar astronaut David Scottperformed a classic experiment on the moon,simultaneously dropping a hammer and afeather from the same height. Both hit theground at the exact same time—somethingthat would not happen in the atmosphere ofthe earth!Slide 2-51 2015 Pearson Education, Inc. The figure shows the motion diagram for an object thatwas released from rest and falls freely. The diagram andthe graph would be the same for all falling objects. 2015 Pearson Education, Inc.Slide 2-52Free FallFree Fall The free-fall acceleration always points down, no matterwhat direction an object is moving. g, by definition, is always positive, but you will need toindicate the directions with either a or – when makingcalculations. Any object moving under the influence of gravity only,and no other force, is in free fall. A falling object speeds up because the velocity and freefall acceleration are both pointing down. Because free fall is motion with constant acceleration, wecan use the kinematic equations for constant acceleration. g is not called “gravity.” g is the free-fall acceleration. g 9.80 m/s2 only on earth. Other planets have differentvalues of g.Class Video “Free Fall” We will sometimes compute acceleration in units of g. 2015 Pearson Education, Inc.Slide 2-53 2015 Pearson Education, Inc.Slide 2-549

9/26/2015 2015 Pearson Education, Inc. 2015 Pearson Education, Inc.Slide 2-56QuickCheck 2.26QuickCheck 2.28A ball is tossed straight up in the air. At its very highestpoint, the ball’s instantaneous acceleration ay isAn arrow is launched vertically upward. It moves straight up to amaximum height, then falls to the ground. The trajectory of thearrow is noted. Which graph best represents the vertical velocityof the arrow as a function of time? Ignore air resistance; the onlyforce acting is gravity.A. Positive.B. Negative.C. Zero. 2015 Pearson Education, Inc.Slide 2-57 2015 Pearson Education, Inc.Example 2.14 Analyzing a rock’s fallExample Problem: Champion JumperA heavy rock is dropped from rest at the top of a cliff and falls 100 mbefore hitting the ground. How long does the rock take to fall to theground, and what is its velocity when it hits?The African antelope known as aspringbok will occasionally jump straightup into the air, a movement known as apronk. The speed when leaving the groundcan be as high as 7.0 m/s.Slide 2-58If a springbok leaves the ground at 7.0 m/s:A. How much time will it take to reach its highest point?B. How long will it stay in the air?C. When it returns to earth, how fast will it be moving? 2015 Pearson Education, Inc.Slide 2-59 2015 Pearson Education, Inc.Slide 2-6010

9/26/2015Chapter 2 Homework AssignmentsMasteringPhysics “2.7 HW”ORFrom Text: Q:(4) and P: (45, 48 & 57) 2015 Pearson Education, Inc. 2015 Pearson Education, Inc.Slide 2-6211

Nov 19, 2013 · 9/26/2015 4 Slide 2-19 QuickCheck 2.8 Here is a position graph of an object: At t 1.5 s, the obje

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