د.عبدالله محمد الزير

Transcription

1 03 PHYS-CH - Part.5 FINDING THE MOTION OF AN OBJECT Deriatin f equatins: All equatins that will be deried, are used t describe ONLY the mtins with cnstant acceleratin. t i 0 t f t x i x 0 i 0 x - x t ( ) x f x f + ( ) a t f f - - t i i - t ( 3 ) 03 Phys Frm (3), we will get a - t + at ( 4 ) Frm (),we will get x - x x x + t t Then, substitute the aerage elcity (abe) with that frm () x x x x t ( ) t ( 5 ) 03 Phys

2 03 PHYS-CH - Part Frm (5), substitute the with that frm (4) ( + at) + x x + x x t + at t Frm (5), substitute the t with that frm (4) ( 6 ) x x x x + a ( + ) a ( + )( ) a ( x x ) + a ( x x ) (7 ) 03 Phys 3 Summary; Equatins f mtin with cnstant acceleratin + at ( x,,a,t ) (,a,t ) withut the" x" x x t + at x x ( + )t + a ( x x ) ( x,a,t ) ( x,,t ) ( x,,a ) withut the" " withut the" a" withut the" t" Sign cnentin fr quantity x, and a is VERY IMPORTANT! 03 Phys 4

3 03 PHYS-CH - Part 03 Phys 5 Sign cnentin : ( ) t + a + at a a Bth and a hae ppsite sign! Bth and a hae same sign! READ EXAMPLES.6 t.8 in the Textbk 03 Phys 6 3

4 03 PHYS-CH - Part EXAMPLES A mtrist traeling at 90 km/h applied the brakes fr 5 s. If the deceleratin was 3 m/s, then his final speed will be: (a) 35 m/s (b) 5 m/s (c) 5 m/s + at m 3600 (d) 0 m/s A jet plane accelerates n a runway frm rest at 4 m/s, the distance and the elcity f the jet after 5 sec is: (a) 30 m, 0 m/s x t + at 50 m (b) 40 m, 0 m/s (c) 50 m, 0 m/s + at 0 m / s (d) 00 m, 0 m/s A car traels nrth at 40 m/s fr h. It stps fr 50 minutes and return suth traeling 0 km fr 0 minutes. Its aerage elcity and speed respectiely are: Displacement m (a) 0.5, 0 m/s Distant m (b).,.5 m/s Ttal time sec (c) 7., 9.7 m/s A. Velcity34000/ m/s (d) 4., 6 m/s A. Speed 54000/ m/s 03 Phys 7 A car is traeling 80 km/h in a schl zne. A plice car starts frm rest just as the speeder car passes it and accelerates at a cnstant rate f 8 km/h.s. (a) When des the plice car catch the speeder car? (b) Hw fast the plice car traeling when it catches the speeder? (a) Since the car is traeling with cnstant elcity, its psitin x c is gien by x x t + at ( 6 ), with x 0 and a 0: x c 0 t (80 km/h) t The psitin f x p f the plice car,is gien by x p at ( 8 km/h.s) t We find the time when the tw cars are at the same psitin by setting x c x p and sling fr t: ( 80 km/h) t ( 8 km/h.s) t OR t (4 t km/h.s -80 km/h) 0 03 Phys 8 4

5 03 PHYS-CH - Part The tw slutins are t 0 crrespnding t the initial cnditins and 80 km/h t 0 s 4 km/h.s The plice car thus catches the speeder at time t 0 s + (b) The elcity f the plice car is gien by, with 0 0: p at (8 km/h.s) t At t 0 s, the elcity f the plice car is; p (8 km/h.s)(0 s) 60 km/h At this time, the speed f the plice car is twice that f the speeder. This must be true because the aerage elcity f the plice car is half its final elcity, and since bth cars cer the same distance in the same time, they must hae equal aerage elcities. at 03 Phys 9 EXAMPLES 0 s ومدرج طوله 400 m حتى تقلع من السكون لذا تكون سرعتها عندما تترك عجلاتها تحتاج طاي رة ا لى الا رض هي (a) 0 m/s (b) 3 m/s (c) 40 m/s (d) 80 m/s.5 m/s حتى تصل تقطع حافلة مسافة 400 m بين نقطتي توقف 0 ا ذا بدا ت من السكون وتسارعت بمقدار 9 m/s وبعد ذلك استمرت بنفس السرعة لفترة من الزمن ومن ثم تباطا ت بمقدار m/s لكي سرعتها الى تقف 0 ا حسب الزمن الكلي الذي استغرقته الحافلة لقطع المسافة بين نقطتي التوقف 0 I II III 0 0 a+.5 m/s 9 m/s a0 9 m/s a- m/s x 03 Phys 0 5

6 03 PHYS-CH - Part خلال رحلة الحافلة نجد ا ن هناك ثلاث مراحل مبينة في الشكل السابق: المرحلة الا ولى:( I ) 0 0 ; a +.5 m/s ; f 9 m/s f 0+at t I ( f - 0 )/a 6 s خلال هذا الزمن تكون الحافلة قطعت مسافة x I ( f - 0 )/a 7 m المرحلة الثالثة:( II ) 0 9 m/s ; f 0 ; a - m/s t III ( f - 0 )/a 4.5 s خلال هذا الزمن تكون الحافلة قطعت مسافة x III ( f - 0 )/a 0.5 m وبناء علية تكون الحافلة قد قطعت مسافة في المرحلة الثانية (II) x II (x I +x III ) m و حيث ا ن 0a فى المرحلة الثانية (II) فا ن x II 0 t II t II x II / s الزمن الكلي للرحلة Tt I +t II +t III 50 s 03 Phys.6 Free Fall Free fall is a mtin under the influence f graitatinal pull (graity) nly; Which directin is a freely falling bject ming? Graitatinal acceleratin is inersely prprtinal t the distance between the bject and the center f the earth The graitatinal acceleratin is g9.80m/s n the surface f the earth, mst f the time. The directin f graitatinal acceleratin is ALWAYS tward the center f the earth, which we nrmally call (-y) ; where up and dwn directin are indicated as the ariable y Thus the crrect dentatin f graitatinal acceleratin n the surface f the earth is g-9.80m/s 03 Phys 6

7 03 PHYS-CH - Part 03 Phys 3 Free falling Objects In the absence f air resistance, all bjects fall twards the earth with the same cnstant acceleratin (a -g -9.8 m/s ), due t graity r a r g y y y y ; free falling acceleratin graitatinal acceleratin g 9.80 m/s Free fall mtins: Summary gt t gt ( )t + g ( y y ) y r a g 03 Phys 4 7

8 03 PHYS-CH - Part 03 Phys 5 Example B A man thrws a brick upward frm the tp f a building. TRUE OR FALSE. (Assume the crdinate system is defined with psitie being upward) A A C a) At A the acceleratin is psitie F b) At B the elcity is zer T c) At B the acceleratin is zer F d) At C the elcity is negatie T e) At C the acceleratin is negatie T f) The speed at C and at A are equal T g) The elcity at C and at A are equal F h) The speed is greatest at E T D D E 03 Phys 6 8

9 03 PHYS-CH - Part A ball is thrwn up frm the tp f a building 40 m high with initial elcity f 0.0 m/s, determine: (a) The time at which the ball reaches its maximum height. (b) The maximum height. (c) The time at which the ball returns t the psitin frm which it was thrwn. (d) The elcity f the ball at this instant. (e) The time at which the ball reach the grund. (f) The elcity f the ball when its reach the grund. (g) If the ball thrwn dwnward with the same elcity ( 0 m/s), what the elcity f the ball when its reach the grund? 03 Phys 7 h +y 0 (a) The time at which the ball reaches its maximum height. At max. height 0 y max gt t.0 s g 9.8 (b) The maximum height. y max g y 0 ( 0) 5. m g ( 9.8 ) g (c) & (d) left fr yu t try. (e) The time at which the ball reach the grund. y t gt y h 40 ( + 0 )t ( 9.8 )t 03 Phys 8 9

10 03 PHYS-CH - Part 4.9 t 0 t 40 0 t 4.05 s + 0 a x gt slutin x + b x + c 0 - b ± - (9.8)(4.05 ) b 4ac a (f) The elcity f the ball when its reach the grund. Try using m/s g y (g) left fr yu t try. 03 Phys 9 Example. A stne thrwn frm the tp f a building is gien an initial elcity f 0.0 m/s straight upward. The building is 50 m high. Using t A 0 as the time the stne leaes the thrwers hand at psitin A, determine: (a) The time at which the stne reaches its maximum height. (b) The maximum height. (c) The time at which the stne returns t the psitin frm which it was thrwn. (d) The elcity f the stne at this instant (e) The elcity and and psitin f the stne at t 5.00 s. 03 Phys 0 0

11 03 PHYS-CH - Part A bx falls frm an eleatr that is ascending with a elcity f m/s. It strikes the grund in 3 sec. (a) Hw lng will it take the bx t reach its maximum height? (b) Hw far frm the grund was the bx when it fell ff the eleatr? (c) What is the height f the eleatr when the bx is at its highest pint? When the bx falls frm the eleatr, its initial elcity will be 0 m/s and a -g. (a) At maximum height, the bx elcity is 0 0 -gt 0 0 gt t 0 / g 0.04 s m/s 0 m/s +y (b) t 3 sec ; 0 m/s y 0t gt y ( )( 3 ) ( 9.8 )( 3 ) 38. m g 03 Phys (c) The bx will reach the maximum height in t 0.04 sec. During this time, the eleatr will me up with cnstant elcity ( m/s ) and acceleratin a 0. y 0t + at y ( )( 0.04 ) m Therefre the height f the eleatr, frm the grund, when the bx at its highest pint m 03 Phys

12 03 PHYS-CH - Part ا ( ا ( ب( ب( 0 m/s قذف حجر ا لى ا على بسرعة ابتداي ية مقدارها شخص يقف على ارتفاع 5 m من نقطة القذف. احسب سرعة الحجر عند م سكه. ( احسب الزمن الذي استغرقه الحجر في الهواء. ( احسب ا قصي ارتفاع يصل ا ليه الحجر. (ج) ثم م س ك خلال عودته ا لى اسفل بواسطة g 5 m +y 0 m/s (a) gy ± m / s 0 (b) 0 t s - (-7.4)-(0) gt 3.8 -g -9.8 (c) at max. height 0 gy gy 0 0 -(0) y 0.4 m ( frm grund) -g -(9.8) 03 Phys 3 The pilt f a hering helicpter drps a lead brick frm a height f 000 m. Hw lng des it take t reach the grund and hw fast is it ming when it gets there? (neglect air resistance) 4.3 s -40 m/s 000 m 03 Phys See example -9, Cliff Dier 4

13 03 PHYS-CH - Part Preius Exam Questins A sandbag that is drpped frm a balln strikes the grund after 0 s. If the balln is ming ertically upward with a elcity f 0 m/s then the height f the balln when the sandbag is drpped is: (a) 360 m (b) 960 m (c) 400 m (d) 560 m 03 Phys 5 A man ascending at 7 m/s in a balln 0 m abe the grund accidentally drps a bx. The elcity f the bx just befre tuching the grund is: (a) 4 m/s 0 gy (b) 8 m/s (c) m/s ( 7 ) ( 9.8 )( 0 ) 44 (d) 58 m/s m/s A ball is thrwn ertically upward frm the grund with a speed f 9.4 m/s. The time it takes the ball t arrie at a height f 9.6 m n its way back is: (a) 5.35 s (b).345 s (c) 0.65 s (d) 0.05 s READ EXAMPLES.9 &. in the Textbk T get A+ : Study and Sle Prblems As MUCH As yu CAN 03 Phys 6 3