Presentation on theme: "Motion in One Dimension"— Presentation transcript:
1 Motion in One Dimension Chapter 2Motion in One Dimension
2 Group QuestionIf I am traveling in a moving car and suddenly slam on my brakes, will I speed up or slow down? What quantity expresses this idea of change in speed? If I slam the car in reverse and floor it how do I differentiate moving backwards verses a forward speed?
3 HistoryThe first noted study of mechanics can be traced back to ancient Sumeria and Egypt whose people were primarily interested in the study of celestial bodies’ movements.
4 Geocentric ModelThe Greeks began in earnest their study of the skies around 300BCThe geocentric model was accepted in this time which said the Earth was the center of the Universe1609- Galileo brings physics into the modern era with his celestial observations, tracking the sun and our movement around it.
5 DynamicsThe branch of physics involving the motion of an object and the relationship between that motion and other physics conceptsKinematics is a part of dynamicsIn kinematics, you are interested in the description of motionNot concerned with the cause of the motion
6 Quantities in Motion Any motion involves three concepts DisplacementVelocityAccelerationThese concepts can be used to study objects in motion
7 Position Defined in terms of a frame of reference A choice of coordinate axesDefines a starting point for measuring the motionOr any other quantityOne dimensional, so generally the x- or y-axis
8 Displacement Defined as the change in position f stands for final and i stands for initialUnits are meters (m) in SI
9 Displacement Examples From A to Bxi = 30 mxf = 52 mx = 22 mThe displacement is positive, indicating the motion was in the positive x directionFrom C to Fxi = 38 mxf = -53 mx = -91 mThe displacement is negative, indicating the motion was in the negative x direction
11 ExerciseYou start of from your house and travel 20.0m to the mailbox. What's the distance traveled? What's the displacement?If you travel 15.0m to the tree first and then 15.0 to the mailbox what's your distance traveled? What's your displacement? At what angle did you leave the mailbox?
12 Vector and Scalar Quantities Vector quantities need both magnitude (size) and direction to completely describe themGenerally denoted by boldfaced type and an arrow over the letter+ or – sign is sufficient for this chapterScalar quantities are completely described by magnitude only
13 Displacement Isn’t Distance The displacement of an object is not the same as the distance it travelsExample: Throw a ball straight up and then catch it at the same point you released itThe distance is twice the heightThe displacement is zero
14 Classifications Scalars Vectors Distance Displacement Speed Velocity AccelerationMagnitude of a ForceForcesMagnitude of a MomentumMomentumTorque
15 SpeedThe average speed of an object is defined as the total distance traveled divided by the total time elapsedSpeed is a scalar quantity
16 Speed, contAverage speed totally ignores any variations in the object’s actual motion during the tripThe total distance and the total time are all that is importantBoth will be positive, so speed will be positiveSI units are m/s
17 ExampleI drive my car 0.50 km to the closest Chipotle. It takes me 2.5min to get there. I realize I forgot my wallet and have to drive back home to get it, then drive back which takes me 7.0min total (Ignoring the time it took to find the wallet). What is my average speed during the total trip?
18 Velocity It takes time for an object to undergo a displacement The average velocity is rate at which the displacement occursVelocity can be positive or negativet is always positive
19 Velocity continuedDirection will be the same as the direction of the displacement, + or - is sufficientUnits of velocity are m/s (SI)Other units may be given in a problem, but generally will need to be converted to theseIn other systems:US Customary: ft/s
20 Speed vs. VelocityLets look at two cars going from point P to Q. Car Red travels in a straight line and Car Blue travels a swerved line. Both cars reach point Q at the same time. Which has a higher Velocity? Speed?
21 Speed vs. VelocityCars on both paths have the same average velocity since they had the same displacement in the same time intervalThe car on the blue path will have a greater average speed since the distance it traveled is larger
22 Example 2.1A turtle and a rabbit engage in a footrace over a distance of 4.00km. The rabbit runs 0.500km and then takes a nap for 90.0min. Upon awakening, he remembers the race and runs twice as fast. Finishing the course in a total time of 1.75hours the rabbit wins the race.
23 Example 2.1 Calculate the average speed of the rabbit. What was his average speed before he stopped for a nap? Assume no detours or doubling back.
24 Graphical Interpretation of Velocity Velocity can be determined from a position-time graphAverage velocity equals the slope of the line joining the initial and final positionsAn object moving with a constant velocity will have a graph that is a straight line
25 Average Velocity, Constant The straight line indicates constant velocityThe slope of the line is the value of the average velocity
26 Notes on Slopes The general equation for the slope of any line is The meaning of a specific slope will depend on the physical data being graphedSlope carries units
27 Average Velocity, Non Constant The motion is non-constant velocityThe average velocity is the slope of the straight line joining the initial and final points
28 Instantaneous Velocity The limit of the average velocity as the time interval becomes infinitesimally short, or as the time interval approaches zeroThe instantaneous velocity indicates what is happening at every point of time
29 Instantaneous Velocity on a Graph The slope of the line tangent to the position-vs.-time graph is defined to be the instantaneous velocity at that timeThe instantaneous speed is defined as the magnitude of the instantaneous velocity
30 Example 2.2A train moves slowly along a straight portion of track according to the graph of position versus time. Find the average velocity for the trip, the average velocity during the first 4.00 seconds of motion, the average velocity during the second 4.00 seconds of motion and lastly the instantanious velocity at both t=2.00s and t=9.00s.
31 ExampleA motorist drives north for 35.0 minutes at 85.0 km/h and then stops for 15.0 minutes. He then continues north traveling 130km in 2 hours. What is his total displacement? What is his average velocity?
32 Acceleration Changing velocity means an acceleration is present Acceleration is the rate of change of the velocityUnits are m/s² (SI), cm/s² (cgs), and ft/s² (US Cust)
33 ExampleA car is sitting on a hill. The E-Brake fails and the car starts rolling downhill. If after 10 seconds the car is moving 5m/s what is the acceleration?
34 Average Acceleration Vector quantity When the sign of the velocity and the acceleration are the same (either positive or negative), then the speed is increasingWhen the sign of the velocity and the acceleration are in the opposite directions, the speed is decreasing
35 Negative Acceleration A negative acceleration does not necessarily mean the object is slowing downIf the acceleration and velocity are both negative, the object is speeding up
36 Instantaneous and Uniform Acceleration The limit of the average acceleration as the time interval goes to zeroWhen the instantaneous accelerations are always the same, the acceleration will be uniformThe instantaneous accelerations will all be equal to the average acceleration
37 Graphical Interpretation of Acceleration Average acceleration is the slope of the line connecting the initial and final velocities on a velocity-time graphInstantaneous acceleration is the slope of the tangent to the curve of the velocity-time graph
39 Relationship Between Acceleration and Velocity Uniform velocity (shown by red arrows maintaining the same size)Acceleration equals zero
40 Relationship Between Velocity and Acceleration Velocity and acceleration are in the same directionAcceleration is uniform (blue arrows maintain the same length)Velocity is increasing (red arrows are getting longer)Positive velocity and positive acceleration
41 Relationship Between Velocity and Acceleration Acceleration and velocity are in opposite directionsAcceleration is uniform (blue arrows maintain the same length)Velocity is decreasing (red arrows are getting shorter)Velocity is positive and acceleration is negative
42 Motion Diagram Summary Please insert active figure 2.12
43 Kinematic EquationsUsed in situations with uniform acceleration
44 Notes on the equationsGives displacement as a function of velocity and timeUse when you don’t know and aren’t asked for the acceleration
45 Notes on the equationsShows velocity as a function of acceleration and timeUse when you don’t know and aren’t asked to find the displacement
46 Notes on the equationsGives displacement as a function of time, velocity and accelerationUse when you don’t know and aren’t asked to find the final velocity
47 Notes on the equationsGives velocity as a function of acceleration and displacementUse when you don’t know and aren’t asked for the time
48 ExampleA race car starting from rest accelerates at a constant rate of 5.00m/s^2. What is the velocity of the car after it has travelled 30.5m? How much time has elapsed?
49 Example 2.5A car traveling at a constant speed of 24.0m/s passes a sneaky trooper hidden behind a billboard. One second after the speeding car passes the billboard the trooper sets off in chase with a constant acceleration of 3.00m/s^2. How long does it take the trooper to overtake the speeding car? How fast is the trooper going?
50 ExampleA jet plane lands with a speed of 100m/s and can accelerate at a maximum rate of -5.00m/s^2 as it comes to rest.What is the minimum time needed to come to a complete stop?Is a 800m long runway going to be long enough to stop the plane?
51 ExampleA car is traveling due east at 25.0m/s at some instant. If its constant acceleration is 0.750m/s^2 due west, find its velocity after 8.50s have elapsed.
52 Free FallAll objects moving under the influence of gravity only are said to be in free fallFree fall does not depend on the object’s original motionAll objects falling near the earth’s surface fall with a constant accelerationThe acceleration is called the acceleration due to gravity, and indicated by g
53 Acceleration due to Gravity Symbolized by gg = 9.80 m/s²When estimating, use g » 10 m/s2g is always directed downwardToward the center of the earthIgnoring air resistance and assuming g doesn’t vary with altitude over short vertical distances, free fall is constantly accelerated motion
54 Free Fall – an object dropped Initial velocity is zeroLet up be positiveUse the kinematic equationsGenerally use y instead of x since verticalAcceleration is g = m/s2vo= 0a = g
55 Free Fall – an object thrown downward a = g = m/s2Initial velocity 0With upward being positive, initial velocity will be negative
56 Free Fall -- object thrown upward Initial velocity is upward, so positiveThe instantaneous velocity at the maximum height is zeroa = g = m/s2 everywhere in the motionv = 0
57 Thrown upward, cont. The motion may be symmetrical Then tup = tdownThen v = -voThe motion may not be symmetricalBreak the motion into various partsGenerally up and down
58 Non-symmetrical Free Fall Need to divide the motion into segmentsPossibilities includeUpward and downward portionsThe symmetrical portion back to the release point and then the non-symmetrical portion
59 Example 2.8A stone is thrown with a speed of 20.0m/s straight upward at a height of 50m above ground. Find:Time it takes to reach max heightMax heightTime needed to hit the groundVelocity and position at t=5.00s
60 Example It is possible to shoot an arrow at a speed as high as 100m/s. If friction is neglected, how high would the arrow travel if shot straight up into the air?How long would the arrow be in the air?