Motion in One Dimension

Transcription

1 Moton n One Dmenson Speed ds tan ce traeled Aerage Speed tme of trael Mr. Wolf dres hs car on a long trp to a physcs store. Gen the dstance and tme data for hs trp, plot a graph of hs dstance ersus tme.

2 Graphng Dstance Vs. Tme Slope = 64 mph Y X Knematcs Knematcs - usng mathematcs to descrbe how objects are mong One Dmensonal - Rectlnear moton, mong n a straght lne path, no rotaton examples: (Vertcal) Fallng brck, (Horzontal) Mong Truck on a flat road or a flat ramp

3 Reference Pont A zero locaton used to determne poston. Sometmes called the orgn Poston - x Dsplacement Defnton of Dsplacement: the shortest dstance between the two postons. Unt: meter (m) Represented as Δx

4 Poston and Dsplacement Intal Poston- The locaton where the physcs problem starts X Δx = x f - x Dsplacement s. Dstance Dsplacement s the shortest dstance between start and fnsh. Dstance s the total path length taken to arre at pont B from pont A.

5 Dsplacement s. Dstance cont. X X f Speed s. Velocty The Sears Tower n Chcago s 443 m tall. Joe wants to set the world s star clmbng record and runs all the way to the roof of the tower. If Joe s aerage upward speed s 0.60 m/s, how long wll t take Joe to clmb from street leel to the roof of the Sears Tower? Aerage speed Dstance Elapsed Tme

6 Speed s. Velocty The Sears Tower n Chcago s 443m tall. Joe wants to set the world s star clmbng record and run all the way to the roof of the tower. If Joe s aerage upward speed s 0.60 m/s, how long wll t take Joe to clmb form street leel to the roof of the Sears Tower? Dstance = 443 m Speed = 0.60 m/s Speed Dstance Tme Dstance Tme Speed 443 m

7 Speed s. Velocty cont. Dsplacement AerageVelocty Elapsed Tme x f x x t t t f Now Joe clmbs to the roof of the Sears and then back down n 1,476 sec. What s hs.. a) aerage speed? b) aerage elocty? x t f f x t 866 m 1,476 s x t (0 0) m (1,476 0)sec m s m s 443 m X f = 0

8 The Peregrne falcon s the fastest of flyng brds (and, as a matter of fact, s the fastest lng creature). A falcon can fly 1.73 km downward n 5 s. What s the aerage elocty of a peregrne falcon n m/s? The peregrne falcon s the fastest of flyng brds (and, as a matter of fact, s the fastest lng creature). A falcon can fly 1.73 km downward n 5 s. What s the aerage elocty of a peregrne falcon?

9 Instantaneous Velocty Instantaneous elocty s how fast the car s mong and the drecton t s mong at any nstant durng the moton. Frame of Reference The object or poston from whch moement s determned. The most common frame of reference s. the earth.

10 Meters, m Poston-Tme Graphs Let s plot the poston and tme for Joe Drer m, 0s 5m, 1s 50m, s 75m, 3s 100m, 4s Note that eery second, the poston ncreases by 5 m Tme, s What s the aerage elocty? Is the elocty constant? What s the slope of the lne? The slope of poston-tme graph = the elocty X t X t Acceleraton Acceleraton s when an object changes ts elocty oer a certan tme. Aerage acceleraton: Change n elocty Elapsed tme f a t t t Aerage acceleraton ponts n the same drecton as the change of elocty. f

11 Velocty m/s Velocty, m/s Velocty-Tme Graphs Let s plot the elocty and tme for Joe Drer. 0m, 0s 10m, 1s V=10 m/s 0m, s V=10 m/s 30m, 3s V=10 m/s 40m, 4 V=10 m/s The elocty s constant n ths case. Snce t s not changng (V = 0), the acceleraton = zero Tme,s Velocty-Tme Graphs What f Joe Drer ncreases hs elocty? 0m, 0s 5m, 1s V=10 m/s 0m, s V=0 m/s 45m, 3s V=30 m/s 80m, 4s V=40 m/s Tme, s The elocty s changng. The acceleraton can be determned from the slope of the elocty-tme graph. a = V t = Durng the 1 st second, the elocty ncreases from 0 to 10 m/s, durng the next second t ncreases another 10 m/s to 0 m/s, and so on. = 10 m/s s

12 Example: A drag racer crosses the fnsh lne, and the drer deploys a parachute and apples the brakes to slow down. The drer begns slowng down when t =9.0 s and the car s elocty s =+8 m/s. When t = 1 s the elocty of the car s = +13 m/s. What s the aerage acceleraton? What s the aerage acceleraton?

13 Equatons for Knematcs for Constant Acceleraton 5 Varables: x = dsplacement a = acceleraton = fnal elocty at tme t = ntal elocty at tme t t = tme elapsed snce t = 0 One Dmensonal Moton Wth Constant Acceleraton If acceleraton s constant (constant net force) and assumng the tme nteral starts at zero t 1 0 seconds. a f t

14 a t 1 sole for * f at Example: A golf ball rolls up a hll toward a putt-putt hole. a. If t starts wth a elocty of.0 m/s and accelerates at a constant rate of -0.5 m/s, what s ts elocty after.0 sec? b. If the acceleraton occurs for 6.0 s, what s ts fnal elocty?

15 In 1934, the wnd speed on Mt. Washngton n New Hampshre reached a record hgh. Suppose a ery sturdy glder s launched n ths wnd, so that n 45.0 s the glder reaches the speed of the wnd. If the glder undergoes a constant acceleraton of.9 m/s, what s the wnd s speed? Assume that the glder s ntally at rest. f at

16 If acceleraton s constant and... ( 1 ) and set them equal and sole for * x x ( 1 ) t x t When s not known... substtute the frst equaton nto the second. 1 ( x 1 ) t nto a t * x t at 1 1

17 When s not known... t a t t a 1 1 sub. the tme expresson nto the second Equaton t a 1 nto * ax f t x f Equatons for Knematcs for Constant Acceleraton t x ax at t x at f f f 1 1

18 Applcatons of the Equatons of Knematcs Startng pont for all problems: 1. Make a drawng. Decde (+) drecton 3. Wrte down gens 4. Wrte down unknown 5. Wrte down equaton(s) that wll be used 6. Sole Example Problem 1 A VW Beetle goes from 0 to 60 mph wth an acceleraton of +.35 m/s. (A) How much tme does t take for the Beetle to reach ths speed? (B) A top-fuel dragster can go from 0 to 60 mph n seconds. Fnd the acceleraton of the dragster (m/s )

19 Example Problem A jetlner, traelng northward, s landng wth a speed of 69 m/s. Once the jet touches down, t has 750 m of runway n whch to reduce ts speed to 6.1 m/s. (A) Compute the aerage acceleraton of the plane durng landng. (B) How long dd t take the plane to accomplsh ths? Example Problem 3 A car s traelng at a constant speed of 33 m/s on a hghway. At the nstant ths car passes an entrance ramp, a second car enters the hghway from the ramp. The second car starts from rest and has a constant acceleraton. What acceleraton must t mantan so that the two cars meet for the frst tme at the next ext, whch s.5 km away?

20 Freely Fallng Bodes In the absence of ar resstance, all bodes fall at the same rate. Galleo Gallee dscoered ths property oer 400 years ago. Idealzed Moton s called free-fall. Acceleraton due to graty s: g = 9.80 m/s or 3. ft/s Equatons for Knematcs for Constant Acceleraton (a = -g) 1 x t at ax x Before 1 at t 1 y t gt gy y After 1 gt t

21 How far does t fall? Galleo predcted that all objects regardless of mass, fall at the same rate. In hs experments he also dscoered a relatonshp between the dstance coered durng the frst second of trael and each consecute tme nteral of one second. V 0 = 0

22 Example Problem 4 A stone s dropped from rest from the top of a tall buldng. After 3 seconds of free fall, what s the dsplacement of the stone? What s the elocty of the stone after 3 seconds? Example Problem 5 The John Hancock Center n Chcago s the tallest buldng n the Unted States n whch there are resdental apartments. The Hancock Center s 343 m tall. Suppose a resdent accdentally causes a chunk of ce to fall from the roof. What would be the elocty of the ce as t hts the ground? Neglect ar resstance.

23 1 y t gt gy y 1 t Up and Down Problems When solng for a problem n whch the object traels up and then down, t s helpful to break the problem nto two parts. The up moton and the down moton.

24 Up and Down Problems The Up moton. The objects ntal elocty s not zero. The objects fnal elocty s zero. a = -g Up and Down Problems The Down Moton The ntal elocty s zero. The fnal elocty s not zero. (In the case where t returns to the startng poston, the fnal elocty s equal n magntude to the startng elocty.) a = -g t down = t up (f returnng to startng poston)

25 Example Problem 6 A rock s tossed up nto the ar wth an ntal elocty of 15 m/s. How hgh does the rock trael? How long s t n the ar? How fast s t traelng when t reaches ts startng poston? Example Problem 7 A young grl s standng on a char whch s 1 meter aboe the ground when she tres to toss an apple to her frend n a tree house. She tosses up the apple wth a elocty of 5 m/s. The apple doesn t make t all the way to the tree house. As the apple falls back down, the grl msses the apple and t contnues to ht the ground. How fast was the apple traelng rght before mpact? How long was the apple n the ar?

26 Graphcal Analyss of Knematcs Readng graphs s another mportant part of Physcs. Informaton regardng the moton of an object can be obtaned by ether fndng the slope of the graph or by fndng the area under the cure of a graph. Graphng In a graph of Poston s. Tme, the elocty of the object can be obtaned from fndng the slope of the graph. Snce the dsplacement coered s 8 m and t took seconds, then the aerage elocty s 4 m/s.

27 In the aboe graph, we can fnd the aerage elocty of the object by fndng the slopes at dfferent ponts n the moton. 1. = m/s. = 0 m/s 3. = -1 m/s Changng Velocty When the elocty of the object s changng, the poston s. tme graph s a cure. To fnd the nstantaneous elocty, draw a tangent lne to the pont n queston and fnd the slope.

28 Poston cm Velocty s. Tme When you hae a graph of elocty s. tme, then the slope ges the acceleraton of the object. Fndng the area under the cure for a certan tme nteral ges the dsplacement of the object.

29 The aerage acceleraton of the graph s gen by the slope, 6 m/s. All Rghts Resered 010 Conerted by: Arzelo D. Ras