Slide. King Saud University College of Science Physics & Astronomy Dept. PHYS 103 (GENERAL PHYSICS) CHAPTER 5: MOTION IN 1-D (PART 2) LECTURE NO.

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1 Slde Kng Saud Unersty College of Scence Physcs & Astronomy Dept. PHYS 103 (GENERAL PHYSICS) CHAPTER 5: MOTION IN 1-D (PART ) LECTURE NO. 6 THIS PRESENTATION HAS BEEN PREPARED BY: DR. NASSR S. ALZAYED

2 Lecture Outlne Here s a quck lst of the subjects that we wll coer n ths presentaton. It s based on Serway, Ed Projectle Moton 4.4 Unform Crcular Moton 4.5 Tangental and Radal Acceleraton Examples Lecture Summary Acttes (Interacte Flashes) Quzzes Kng Saud Unersty, College of Scence, Physcs & Astronomy Dept. PHYS 103 (General Physcs) 013

3 4.3 Projectle Moton Anyone who has obsered a baseball n moton has obsered projectle moton. The ball moes n a cured path, and ts moton s smple to analyze f we make two assumptons: (1) the free-fall acceleraton g s constant oer the range of moton and s drected downward, and () the effect of ar resstance s neglgble. We fnd that the path of a projectle, whch we call ts trajectory, s always a parabola The parabolc path of a projectle that leaes the orgn wth a elocty. The x component of remans constant n tme. The y component of elocty s zero at the peak of the path. Kng Saud Unersty, College of Scence, Physcs & Astronomy Dept. PHYS 103 (General Physcs) 013

4 4.3 Projectle Moton (x & y equatons) We wll be hang sets of equatons: 1 for x and 1 for y drectons: Fro x drecton: = x cos θ (4.10a) ( θ ) x = t = cos t (4.11a) f x Fro y drecton: = sn θ y 1 1 y f = yt + ayt = ( sn θ ) t gt (4.1) Please note that you can sole for x or y ndependently. (4.10b) Kng Saud Unersty, College of Scence, Physcs & Astronomy Dept. PHYS 103 (General Physcs) 013

5 4.3 Projectle Moton (trajectory equaton) We wll be hang sets of equatons: 1 for x and 1 for y drectons: (4.11a) t = x f cosθ f f y f =( sn θ) g cosθ cosθ y =(tan θ ) x f f f cosθ OR : y = ax bx x g Ths s the equaton of a parabola that passes through the orgn. 1 x x Kng Saud Unersty, College of Scence, Physcs & Astronomy Dept. PHYS 103 (General Physcs) 013

6 4.3 Projectle Moton (moton dagram) Kng Saud Unersty, College of Scence, Physcs & Astronomy Dept. PHYS 103 (General Physcs) 013

7 Tme of Flght of a Projectle We wll consder the maxmum heght reached by a projectle: 1st: tme of fleght: at max. heght = 0 = + at= yf y y 0 = snθ gt snθ t max = g snθ t fleght = g 0 max Tme of flght s twce the tme requred to reach to the max. pont. We call ths Tme-Of-flght and s true only f the projectle fnal destnaton s on the same leel as ts startng pont. yf Kng Saud Unersty, College of Scence, Physcs & Astronomy Dept. PHYS 103 (General Physcs) 013

8 Maxmum Heght of a Projectle Maxmum heght of a projectle can be calculated usng last equaton: at max. pont, t s t max 1 y =( sn θ ) t g t [ ] max max max y =( sn θ ) snθ g max 1 snθ g snθ 1 snθ or : h = ( sn θ) g g g h = snθ g g (4.13) Kng Saud Unersty, College of Scence, Physcs & Astronomy Dept. PHYS 103 (General Physcs) 013

9 Horzontal Range of a Projectle Horzontal Range of a projectle can be calculated usng last equaton: t fleght R= t snθ = g x sn( θ) = snθcosθ fleght sn θ g Not that R s Max. when θ = 45 o. sn sn cos θ θ θ R = ( cosθ ) = g g R = R max = g (4.14) Kng Saud Unersty, College of Scence, Physcs & Astronomy Dept. PHYS 103 (General Physcs) 013

10 Effect of startng angle on a Projectle A projectle launched from the orgn wth an ntal speed of 50 m/s at arous angles of projecton. Kng Saud Unersty, College of Scence, Physcs & Astronomy Dept. PHYS 103 (General Physcs) 013

11 Example 4.3 The Long Jump # A long-jumper leaes the ground at an angle of 0.0 aboe the horzontal and at a speed of 11.0 m/s. (A) How far does he jump n the horzontal drecton? We can fnd the dstance from Range (R): sn θ 11 sn 40 R = = = 7.94 m g 9.8 (B) What s the maxmum heght reached? We can use the max. heght equaton drectly: h snθ 11 sn 0 = = = 0.7 m g 9.8 Kng Saud Unersty, College of Scence, Physcs & Astronomy Dept. PHYS 103 (General Physcs) 013

12 Example 4.5 That s Qute an Arm! A stone s thrown from the top of a buldng upward at an angle of 30.0 to the horzontal wth an ntal speed of 0.0 m/s, as shown n the Fgure. If the heght of the buldng s 45.0 m. (A) how long does t take the stone to reach the ground? 1 y f =( sn θ) t gt o = 0 m / s, θ = 30, y f = - 45 m 1 45 = (0sn 30) t 9.8t 4.9t 10t 45 = 0 10 ± Solng : t = = 4.s 9.8 Kng Saud Unersty, College of Scence, Physcs & Astronomy Dept. PHYS 103 (General Physcs) 013

13 Example 4.5 (Contnued) (B) What s the speed of the stone just before t strkes the ground? To sole: we must fnd components of elocty ( xf and yf ) just at the ground leel. Then we calculate the magntude = speed = = 0 cos 30 = 17.3 m / s xf x = gt = sn t yf y = 0sn (4.) = m / s yf speed = = + = ( 31.36) = 35.9 m / s f xf yf (C) What s the dstance between the buldng and the strkng pont? x = t = 0 cos 30(4.) = 73.1m f x Kng Saud Unersty, College of Scence, Physcs & Astronomy Dept. PHYS 103 (General Physcs) 013

14 Example 4.6 a package dropped by arplane A plane drops a package of supples to a party of explorers. If the plane s traelng horzontally at 40.0 m/s and s 100 m aboe the ground, where does the package strke the ground relate to the pont at whch t s released? x = t = 40 t (we need t) f x 1 y f = yt gt = 0 9.8t 100 t = = 4.5s 9.8 x = = 181m f Kng Saud Unersty, College of Scence, Physcs & Astronomy Dept. PHYS 103 (General Physcs) 013

15 4.4 Unform Crcular Moton A unform crcular moton s of an object (e.g. a car) mong n a crcular path wth constant speed. Note: een though speed s constant: elocty s not. We consder elocty not constant n three cases: 1. Magntude of s changng. Drecton of s changng 3. Both of magntude and drecton are changng centrpetal acceleraton s gen as follows: a c = r (4.15) where: s the speed, r s the radus of crculaton. Perod of crculaton: T = π r (4.16) Kng Saud Unersty, College of Scence, Physcs & Astronomy Dept. PHYS 103 (General Physcs) 013

16 4.5 Tangental and Radal Acceleraton In crcular moton; there are dfferent acceleratons: Radal: a r and Tangental: a t. Total Acceleraton s the Vector sum of both of these components. a = a + a (4.17) r where: t d at = and ar = -ac = - dt r a = a + a r t Kng Saud Unersty, College of Scence, Physcs & Astronomy Dept. PHYS 103 (General Physcs) 013

17 Lecture Summary Projectle moton s one type of two-dmensonal moton under constant acceleraton, where a x = 0 and a y = -g. It s useful to thnk of projectle moton as the superposton of two motons: (1) constant-elocty moton n the x drecton () free-fall moton n the ertcal drecton subject to a constant downward acceleraton of magntude g = 9.80 m/s. A partcle mong n a crcle of radus r wth constant speed s n unform crcular moton. If a partcle moes along a cured path n such a way that both the magntude and the drecton of change n tme, then the partcle has an acceleraton ector that can be descrbed by two component ectors: (1) a radal component ector a r that causes the change n drecton of and () a tangental component ector a t that causes the change n magntude of. Kng Saud Unersty, College of Scence, Physcs & Astronomy Dept. PHYS 103 (General Physcs) 013

18 Actty Flash In the next slde you wll be allowed to run an nteracte flash. There wll be a quz about the flash. In ths flash: please do the followng: 1. Set Intal speed to: 40 m/s. Set Intal Launch angle to: 50o 3. Press RUN and wat for the projectle to land. 4. Record the followng results: Tme Of Flght Horzontal Range Magntude of elocty n the moment of landng Please answer the quz that wll be gen upon fnshng the flash usng the results you recorded. Kng Saud Unersty, College of Scence, Physcs & Astronomy Dept. PHYS 103 (General Physcs) 013

19 Actty Flash

20 Quz about Actty Flash Quz on Projectle Interactty Flash Clck the Quz button on Sprng Pro toolbar to edt your quz

21 Reew Quzzes: Please allow about 30 mnutes to answer all Quzzes n the next slde. You can easly moe to the end of presentaton by clckng outsde the quz area. Kng Saud Unersty, College of Scence, Physcs & Astronomy Dept. PHYS 103 (General Physcs) 013

22 Quzzes Clck the Quz button on Sprng Pro toolbar to edt your quz

23 End Kng Saud Unersty, College of Scence, Physcs & Astronomy Dept. PHYS 103 (General Physcs) 013