* Physics is concerned with the measurements of the physical quantities which help to understand & relate the natural phenomena.

Transcription

1 Unit Chapter Phyical eaureent - Phyic: I the cience concerned with the tudy of the univeral phenoena by etting up atheatical law & relation to explain the logically. * Phyic i concerned with the eaureent of the phyical quantitie which help to undertand & relate the natural phenoena. * What i eant by eauring? - Coparing an unknown quantity to a known one of the ae kind called eauring unit to find out how any tie doe the firt include the lat. * Meauring eleent:. The phyical quantity to be eaured. (ex: Length). The eauring intruent needed to eaure. (ex: ruler ) 3. The eauring unit ued ( tandard unit). (ex: eter) * Meauring device ued to eaure phyical quantitie ay be:-. Analog device: - ue pointer oving on a cale.. Digital device:- ue nuber. 3. Siple intruent: - give direct reading. Ex: Length: Meter ribbon ernier Caliper Microeter- ruler. Ma: Roan balance- double pan balance ingle pan balance- digital balance. Tie : Sand watch Pendulu watch top watch digital watch- Ceaiu watch ued for cientific purpoe due to it high accuracy. Liquid denity : Hydroeter. Liquid volue : graduated cylinder.

2 Phyical quantitie Fundaental Derived - Ma (M), length (L), tie(t). N.B:- oe fundaental quantitie which aren't ued to derive other.. Light intenity Candela. Current intenity Apere 3. quantity of aterial Mole 4. Angular eaure Radian 5. Solid angle Steradian 6. Teperature o Kelvin Standard eauring unit:- - Thoe which can be expreed in ter of fundaental one. 3 Ex:-olue L L L L elocity LT acceleration LT Electric Reitance oh () Electric potential olt ( ) Electric capacity Farad (F) 3 - Each phyical quantity ha it own tandard eauring unit kept in pecial lab. called the calibration lab.. The tandard eter: - I the ditance between two ark engraved on an Ir/Pt rod kept at 0 o C near Pari. - Standard Kg:- - I calibrated by the a of a cylinder of 0 o C near Pari. 3- Second :- - I equal to Dienional forula : part of the average olar day. Ir alloy of fixed dienion kept at Pt I an algebraic expreion ued to expre the derived quantitie in ter of fundaental one. Ex: olue = S x S x S = L x L x L = L 3.

3 d.. L.. elocity :.. LT.. t.. T..... Accelerati on : a... t... Force : F a Work : W F S Denity : Geoetrical hape: Area: ol... olue: - Square L x w = ide - Cube L x w x h = ide 3 - Rectangle L x w - Cuboid L x w x h - Circle r - Cylinder r h - Sphere 4 r - Sphere 4 3 r 3 - Triangle B x h - Pri B x h x L Meauring yte of unit Gauial Metric Britih S.I. - Ma g kg Pound kg - Length c Foot - Tie Converion : Big unit x 0 + prefix Sall unit Sall unit x 0 - prefix Big unit Ex : Kg x 0 3 g g x 0-3 kg N.B: - Matheatical equation: - i a iple way to expre the relation between phyical quantitie and how their eaning. 3

4 - Soe contant relate oe variable in phyic by a definite anner. - Force & weight are eaured in Newton = (kg / ) ( correponding to Dyne (g c/ ) -Work & energy are eaured in Joule = (kg / ) ( correponding to Erg (g c / ) - Only iilar phyical quantitie can be added or ubtracted. Ex: 0 kg + 0 Kg = 30 kg. - Calculate the area of a rectangle whoe length i 3 and width 00 c. - Prefixe for ultiple of the S.I. of unit Multiple Prefix Sybol Multiple Prefix Sybol factor factor 0 tera T 0 - centi c 0 9 giga G 0-3 illi 0 6 ega M 0-6 icro 0 3 kilo K 0-9 nano n 0 hecto h 0 - pico p 0 deka da 0-5 feto f 0 - deci d 0-8 atto a N.B: - Angtro ( A o ) = = 000 Liter. - Ton = 000 kg. Exaple: Kg =.. g = g - 0 M Hz =..Hz = μ Hz - 0 c = k =.. 4

5 - 5 K = hr g 3 c = Kg = =.K KJ =.. J =.. Liter = c A =. μ.a. * Soe phyical quantitie and their unit:- Quantity Relation Unit Dienional Forula - elocity change in diplaceent d tie of change t LT - - Acceleration changeinvelocity tie of change t LT - - Moentu velocity Ma Kg MLT - - Force Ma acceleration Kg ( Newton) MLT - - Work Force diplaceent - Preure - Denity Kg ( Joule) ML T - Force Kg ML - T - Area a 3 Kg ML -3 olue - Kinetic energy Joule ML T - - potential energy g h Joule ML T - N.B:- It i alot ipoible to get 00% accuracy while eauring a phyical quantity uing a certain device, but we try to iniize the error if there i. 5

6 Caue of error:-. Chooing an iproper device ( uing bea balance intead of enitive... ). Uing a defected eauring tool (old or deagnetized, having a zero error, low power upply.) 3. Wrong procedure : ( reading at an oblique line, ignoring ultieter ). 4. Environental condition: ( t o, huidity, air current,denity ), reduced by keeping the device iolated in a gla box. Meaureent ay be : Quantity Direct eaureent Indirect eaureent Nuber of operation One More than one Calculation No calculation are needed Meaureent are ued to calculate the deired quantity Error Only one error More than one error leading to an accuulative error Exaple Meauring the volue uing a graduated cylinder Calculating the volue by ultiplying ( L x W x H ) after eauring each of the How to calculate the error: - Direct eaureent:- - Abolute error (Δx) : i the difference between the actual value (x o ) and the eaured value (x). where x xo x - Relative error (r) : I the ratio of the abolute error to the actual value. x r x o - N.B: -The value (Δx) i alway poitive a we are concerned only with the 6

7 agnitude of the error. -The relative error expree the accuracy of eaureent uch ore than the abolute error and eaureent i ore accurate a the relative error i aller. - Indirect eaureent:- * For a two tep operation: - Abolute error : x x x - Relative error: r r r - Solved exaple:. If the actual length of a pencil i 0 c while the length eaured i 9.9 c. Find both the abolute and the relative error for that eaureent. -Abolute error : x x x c - Relative error : o x 0. r 0.0 %. x 0 o. Calculate the relative error and the abolute error while eauring the area of a rectangle whoe length (6 0.) and width (5 0.). x. x Relative error in length : r Relative error in width : r 0.04 o x. x 5 o - Relative error in area : r r r Abolute error in area : A r, A o A r A 0 (0.057) (5 6).7. And the area A (30.7). Another olution: - A o = 6x5=30, A with abolute error = 6.x5. = ΔA= =.7. 7

8 - A.7 r A 30 o *Uing the vernier caliper: - I ued to find all length or diaeter accurately. - An average error of 0.0 per diviion i added to get accurate reading. Procedure: -Place the object between the jaw of the caliper and pre gently. - Record the reading on the ain fixed cale jut before the zero ark of the vernier liding cale. - Find out the ark of the vernier cale that atche with a ark on the fixed cale. - The nuber of diviion on the vernier cale to that atching ark are then ultiplied by 0.0. (n o of vernier ark X 0.0 =. ). - The accurate reading i then calculated a : (Fixed cale reading + (n o of ark X 0.0 ) =... 8

9 x0.0= =3. Solved exaple: While eauring the diaeter of a cylinder, the reading of the fixed cale of a caliper i 3, while the vernier cale ark atching with one of the fixed cale ark wa the eighteenth. Find the accurate diaeter of thi cylinder. n o of vernier ark X 0.0 = 8 x 0.0 = 0.8. Diaeter = Fixed cale reading + (n o of ark X 0.0 ) = = 3.8. Finding The lateral area and the total area of a cylinder: πr Procedure:. Place the cylinder bae on a paper heet and trace it liit. h. Reove the cylinder and eaure the diaeter of it bae (Bae) ( r) uing a ruler. 3. Meaure the height of the cylinder (h). r 4. Find the lateral area of the cylinder a ( A= πrh ) 5. You can find the total area of the cylinder a: Total area = lateral area + top area + bae area (A t = πrh + ( x πr ) ) 9

10 Hoework - Define:- - Phyic - Derived quantitie 3- Analog device 4- Matheatical equation 5- Standard Kg 6- Standard econd 7- Digital device 8- Dienional forula - G.R.F:-. Ma cannot be added to velocity.. olue i a derived quantity.

11 3. Soe eauring device are kept in gla boxe. 4. It i ipoible to get 00 % accuracy during eauring phyical quantitie. 5. Relative error give ore accurate indication than abolute error. 6. Ceiu watch i preferably ued for cientific purpoe. 3- Write the dienional forulae for the following:-. elocity =... Acceleration = 3. Moentu =.. 4. Denity = 5. Preure =.. 6. Work = Coplete:- - Work i eaured in unit called or.. or - In the S.I. yte the force i eaured in. or.. 3- In the international yte the length i eaured in 4- Meauring phyical intruent are divided into..,. &. 5- Denity can be eaured in. 6- The.. i a device ued to eaure the liquid denitie. 7- Acceleration i a.. phyical quantity while current intenity &. intenity are The quantity of aterial i a... quantity eaured in 9- Candela i the unit ued to eaure while Radian i ued for.. 0- The unit of i Kg.. 5- Chooe the correct anwer:- - The unit of preure i... (.. Kg.. Kg.. kg.. Kg ) - The following can be ued all to eaure work except. Joule N ) ( N. Kg..

12 3- The teperature i eaured in.. in the S.I ( o Celiu - Kelvin - o Centigrade ) 4- The unit of the electric reitance i ( Apere - Oh - olt ) 5- The unit of electric potential i.. ( Apere - oh - olt ) 6- All the following are fundaental except. (Ma - Angular eaure - elocity - Tie) 7- All the following are derived except.. ( Teperature - acceleration - force - denity ) 8- The power i the quotient of work over tie, then it eauring unit i ( J/ - N./ - kg. / 3 all the previou) 9- The dienional forula of the a i.. ( M 0 LT 0 ML 0 T 0 - MLT MLT - ) 0- The value can be written a. (5x0-3 5x x0 3 5x0 4 ) - The value 0 3 i equal to ( ) - The. i ued to eaure the denity of a liquid directly. ( ruler icroeter hydroeter graduated cylinder. 3- Meauring the volue of a liquid uing the graduated cylinder i conidered a eaureent. ( coplex coplicated direct indirect ) 4- The dienional forula of a phyical quantity i M 0 L T -, then it eauring unit i. ( kg./ / -. - kg..) 5- The olid angle are eaured in ( Radian Degree Steradian Kelvin ) 6- Join:-

13 - elocity - olue - Preure -Moentu - Force - Work Kg 3 Kg Kg Kg 7- If the kinetic energy =, Potential energy = g h, where g i the acceleration due to gravity & h i the height fro the ground. Prove that they both have the ae eauring unit a that of work. * State the unit which can be ued to eaure the. 8- Uing the eauring dienional forula ( eauring unit), prove that:-. The relation S o t at i correct.. The relation o a S i incorrect. 9-Uing the dienional forula find whether the following relation are right or wrong: The volue of a cylinder i calculated a : ol = π r h The velocity : = ta The energy : E=c ( where c i the light velocity in pace). 0- If the radiu of the Saturn i 5.85x0 3 k, it a i 5.68x0 6 kg. Find the denity of Saturn. ( x0 5 kg/ 3 ) - If the actual length of a cla i 9.3 c while the length eaured i 9. c. Find both the abolute and the relative error for that eaureent. ( 0.0 c /93) -Find the relative error while eauring the volue of a cuboid knowing that: Quantity eaured ize (c) actual ize (c) Length

14 Width Height.8 3 ( 0.46 ) 3- The actual length of a field i 500 feet, a eauring intruent how the length to be 508 feet. Find the abolute error, the relative error and it percentage. ( 8 ft /5.6 %) 4- The real length of a door i 55 c while the eaured length i 50 c. Calculate the abolute and the relative error for that eaureent. ( 5 c /5 ) 5- Find the abolute error, the relative error and the error percentage for the approxiated value of π ( 3.4) whoe real value i (.59x0-3 5x %) 6- A dog weigh exactly 36.5 kg. When weighed on a defective balance it weigh wa 38 kg, Find the abolute and relative error a well a the percentage of the lat. (.5 kg 3/73 4.% ) Chapter Scalar and ector Phyical quantitie ector Scalar - Ha agnitude & direction - Ha agnitude only - If one change the vector change Ex: - diplaceent - velocity - Ditance - peed - Force weight - Ma 4

15 Moving Particle:- - I that which change it poition in pace with tie. Ditance & diplaceent:- -Ditance: i the total length of the path of a body fro the tart point to the end point. 0 A c 4 B d AC dac AC d C A d ( ) dac dc A ( ) A 3 5 d d ABC ABC B 4 C -Diplaceent (d) (S) (X) (y):- - I the poition of a body with repect to it initial poition. - Ditance covered by a body in a certain direction. N.B: Diplaceent ay be equal to ditance if the body ove in one direction. Graphical repreentation of vector: - Two vector are equal when the both have the ae agnitude and direction. - The agnitude of a vector i expreed by the nuerical value while the direction i expreed in ter of ign ( + & - ). - Reultant (net) vector: i one vector which can ubtitute a group of vector. - Adding vector: take place whether by copleting the triangle or by drawing a parallelogra whoe diagonal contitute the reultant. B A B A 5

16 A C = A + B B C = A + B - The reultant of two perpendicular vector (Force): F F θ - Reolution of vector (Force): F F F F 6 9 5N tan F y F x o F F 3 4 When a vector for an angle (θ) with the ( X ) axi ( horizontal ) We can reolve it into vector Y vector - ector (x) = vector co θ - ector (y) = vector in θ θ X - Multiplying vector:. Dot (calar)product: i a calar product reulting fro ultiplying the firt vector (A) by the econd vector (B) by (co θ) co. the angle between the. A. B AB co (increae a θ decreae) θ B B A A In other word you can get A.B by ultiplying the agnitude of the vector (A) by the agnitude of (B A )which i equal to Bcoθ, or by ultiplying the agnitude of vector (B) by the agnitude of (A B ) which i Acoθ.. The cro (vector) product: i a vector product reulting fro ultiplying the agnitude of the firt vector (A) by the agnitude of the econd vector (B) by (inθ) the in of the angle between the by ( n ). Where ( n) i a unit vector in the direction perpendicular the plane carrying both vector. C A B AB in n ( the ign ( ) i called (cro)). 6 θ A B

17 The direction of ( C ) i deterine by the right hand rule. By oving the finger of the right hand fro the firt vector toward the econd one through the aller angle eparating the, while keeping the thub directed toward the direction of their product ( perpendicular to the plane carrying the). Ex: If the agnitude of two vector A& B are 5 & 0 repectively and the angle between the i 60 o, find the value of their dot and cro product. A. B AB co 50co 60 5 C A B AB in n (50in 60) n 43.3 n C i the reultant vector having a agnitude 43.3 and a direction perpendicular to the plane of both A& B. Hoework: ) Write the cientific ter:. A phyical quantity expreed by it agnitude only. (...). A phyical quantity expreed by it agnitude and it direction.(.) 3. A force which can replace all the force affecting a body. (...) 4. The product of the agnitude of two vector A& B by the coine of the angle between the. (.) 5. The product of the agnitude of two vector A& B by the ine of the angle between the. 7 (.) 6. Rule ued to identify the direction of the vector reulting fro the cro product of two vector. ) Coplete: (.). If a force of 0 N for an angle of 60 o with horizontal, then it vertical vector i = N, while the horizontal one i =..N.. A body i affected by a vertical force of 0N and a horizontal one of 40N then the reultant force acting on that body =.. and it direction i at an angle with the horizontal.

18 3. If the agnitude of two vector A& B are 3 & 6 repectively and the angle between the i 30 o, then the value of their dot product = and that of their cro product =.. 3) What i eant by:. Ma i a calar quantity.. Force i a vector quantity. 3. The diplaceent of a body i The dot product of two vector A& B = The cro product of two vector A& B = 50.8 n 6. The total length of the path of a body fro the tart point to the end point i 50. 4) Chooe the correct anwer:. A car cover a ditance of 50 to Eat, then a ditance of 50 to Wet. The diplaceent of the car i. ( 50 zero 00 ). A an oved along a road whoe length i 00 then turned to right and oved for 5. The ditance covered by the an i.... ( ) 3. A an oved along a road whoe length i 00 then turned to right and oved for 5. The diplaceent covered by the an i.... ( ) 4. An object orbiting a circle whoe radiu i (r), coplete half a revolution, the ditance covered by that object i ( r r π r ) 5. An object orbiting a circle whoe radiu i (r), coplete half a revolution, the diplaceent covered by that object i ( r r π r ) 6. In the figure the vertical vector of the force i equal to 5 N, then the horizontal vector i equal N ( ) 5 N 7. Two equal vector are expreed a figure.. 30 o (.. 3. ) 8. The angle between the X axi and the reultant force of the 8N 8

19 force in the oppoite figure i. ( 45 o 5 50 o 53 o 7 ) 6N 9. The ditance covered by a body ay be equal to it diplaceent if the body travel in.. ( one direction an aphalted treet a circle ) 0. If the diplaceent covered by a body i equal to zero, then the body i at ( a point on the ae line a it tart point an end point iilar to the tart point the tart point ). The ditance covered by the body oving along the circuference A c fro A to B i. ( c 3c 4c c ) B 5) Copare between:. Scalar quantity and vector quantity.. Dot product and vector product in view of the relation ued to calculate each. 6) Proble:. A hip ailing North at a velocity of k/h. deviate to Wet, by the tide effect, at a velocity of 6 k/h. Find the agnitude and direction of the velocity of that hip. ( 0 k/h 36 o 5 North Wet). A otorcyclit drive to North at 80 k/h. while wind blow Wet at 60 k/h. Calculate the apparent velocity of the wind oberved by the otorcyclit. ( 00 k/h 53 o 7 North Wet ) 3. A force of 0N i applied along the (X axi) of a cube, while another force of 0 N i applied on it (Y axi). Find the agnitude and direction of the force oving the cube. (0 5 - At 63 o 6 fro the X axi ) Unit II Chapter () Motion in traight line Tranlatory Periodic - Ha a beginning and an end. - Ha no beginning or end 9

20 (Initial & final point) ucceively Ex: - Projectile. -elocity: (v):- - I the change in diplaceent per unit tie. - I the rate of change in diplaceent. - Motion repeated at equal tie interval Ex:-circular, ocillatory & Wave otion A B C D S S t t S t d LT t Graphical repreentation: - (S veru t) S t d - d t d - d cont t d d - cont. t d i unifor t t t t - The lope i a traight line = x y The lope indicate v a d t - Body cover equal S in equal tie interval. * If the lope i not a traight line: S d t d

21 t * Body cover unequal d in equal tie interval * To calculate velocity - Intantaneou. can only be calculated a v i non-unifor. - A tangent to the lope at that intant i drawn & d the copleting it. d t at that intant only - v i non-unifor (un unifor) t & t are taken a the ide of * An average velocity or an average peed can be calculated for the trip:- T d total diplaceent T t total tie or T d total di tan ce T t total tie Average velocity: - I a velocity which can be ued uniforly by the body to cover the actual (d) or ( d ) in that actual tie. (I not actually ued by the body). 99 k ret 0 k Ex: - Cairo h h h Alex. Td K Tt 4 h 0 in ec. Td Tt 3 A c 4 in ec B 3- Acceleration:- - I the change in velocity per unit tie. - I the rate of change in velocity. a t LT - Graphical repreentation of the t curve:- - Unifor a - Non-unifor a

22 v v t t t - t - Intantaneou acceleration can be calculated. - cont t - a t - body increae it velocity - body increae it velocity equally in equal tie interval t unequally in equal tie interval N.B:- A body reducing it velocity i decelerated (retarded). * Explain the following graph: - (coent) d d d d t t t t v v v v t t t t d v v d y t t x t t d v z T t

23 - Which body i fater? why? d a b t Chapter () Motion with a unifor acceleration -Law of otion with unifor acceleration:- - ued to deterine unknown by knowing 3 other. - Knowing (a) i eential. a d 3

24 i t f t nd rd Law : 3 Law : Law : a t f i a t a t f i f a t...() f i i d t f i f i d ( ) t Subtitute v fro i at i d ( ) t i at d ( ) t i t at d d it at...() a t f i By quaring both ide at a t f i i f i a( it at ) ad f i ad...(3) f i * Or by ubtituting the value of t fro () in (). General forula a t f i f d t at Motion tart fro ret ( i =0) a t i Stopping at the end of otion( f =0) i d at d it at Motion at a unifor velocity(a=0) a t f i d it ad ad f i f a d i f i 0 - Equation can be derived fro the t curve: - v - Total area below the lope = Area + Area f i t ( f i ) t ( f i ) t t i t ( f i ) t i t 4 t i

25 ( ) t f i i t t t t t i a t Fro equation. * Free fall acceleration: (g) d i t a t total area below the lope Motion under gravity - A body falling freely in pace increae it velocity until reaching it axiu value jut before hitting the ground. - Thi i due to acceleration due to gravity (g). v - If the body ove up it i decelerated by (g).. - Graphical repreentation:- t - The lope of the traight line drawn experientally 9.8 Proof:- a d f i i 0 f a d f a d By knowing velocity & diplaceent, acceleration can be calculated. Projectile:-. ertical projectile: f 0 i d d h y g=-9.8 g=9.8 t t 5

26 i = f Exaple: The table below how the relation between the change in the velocity and diplaceent with tie for a body projected vertically upward at 0 /. Tie () Diplaceent () elocity (/) The otion can be repreented a: Q d () Q (/) 0 P N 0 A M 5 P N 0 P Q 5-0 A M The velocitie at point (Q, P & N) fro the lope tangent of the (d-t) graph are: , 0 Q P, N Acceleration i the lope of the (v-t) graph: 0 0 a 0 t 0 N.B: At (P) the body i decelerated uniforly, while at (Q) it i accelerated. t () t (). Projectile projected at an angle (otion in dienion) 6

27 - If a projectile i projected foring an angle (θ) with the horizontal (X-axi) at an initial velocity ( i ), we can reolve the ( ) into two vector ( & ). ix iy The horizontal velocity ( ix ) of the projectile conidered to be unifor ( neglecting any friction ) can be calculated a: co The vertical velocity ( iy ) of the projectile i variable a it i ubjected to an acceleration due to gravity (g), thu only the initial velocity can be calculated a : in iy i The final velocity ( f ) of the projectile at any intant i given by Pythagora a: ix i f fx fy The tie taken to reach the axiu height can be obtained by conidering ( ay g 9.8 ) & ( 0) fy and ubtituting in the firt law of otion a: t g iy The total tie taken fro the projection tie till reaching the ground back T t g iy The axiu height can be given fro the third law by ubtituting ( fy 0) a: h g iy The Range of the horizontal ditance ( R ) reached can be given by ubtituting 7

28 ( a 0 & d R) x in the econd law where (T = tie of the horizontal flight = flight tie = t ) a : R T ix t ix N.B: The axiu range for a projectile i attained when projected at 45 o. Exaple:- - A car tart fro ret to ove with a unifor acceleration after 0 ec. it velocity becae 0. Find the ditance covered. - f i a t d i t at a f i t d 0 (0) 0 a d At a certain intant the velocity of a car i Find acceleration & diplaceent. f i 30 0 a t 0 3- A plane land at a velocity of d it at (0 0) ( 0 ) 400 & tie taken to top. 0 and after 0 ec. it becoe & topped 500 apart. Find it acceleration ad f i a t f i a f i d t f a i a t A body projected upward at 49. Find the axiu height it can reach & the tie needed to reach it. 8

29 ad f i a t f i f i 40 d.5 a 9.6 f i 49 t 5ec a A otorcycle i launched at 5 / at an angle of 30 o to the horizontal. Find: A) The axiu height reached. B) The tie of flight. C) The horizontal range reached by the otorcycle. (g =0 /). co 5co 30 3 ix i in 5in iy i iy (7.5) iy 7.5 h.8, T t.5, R ix T g ( 0) g ( 0) 6- ABCD i a quare whoe ide i 0 long. If a an walk fro A to B to C then D in in. calculate, the ditance covered, the diplaceent covered and the average peed of the an. ( /) 7- A car oving at 0 ha been decelerated to top 80 away. Calculate it deceleration & the tie pent to top. (-.5 / 8 ec ) 8- A body with initial velocity 8 ove along a traight line with a unifor acceleration for 640 during 40 ec. Find it final velocity & it average peed. ( 4/ 6/ ) 9- A truck tart fro ret to be accelerated by 5. Find it velocity & diplaceent 4 ec later. (0/ 40 ) 0- A car i accelerated uniforly a it pae through two check point that are 30 apart. If the tie pent between the point i 4 ec & the car peed at the firt wa 5. Find the car' velocity at the econd checkpoint. 9

30 - A car' velocity increae uniforly fro 6 to ( 0 / ) 0 while covering 70. find the acceleration & the tie taken. (.6 / 5.38 ) - A plane tart fro ret to be accelerated along 600 for ec. before takeoff. Find it velocity while taking off. ( 00 /) 3- A train running at 30 i lowed uniforly to top 44 ec later. Find the acceleration and ditance covered. ( / ) 4- An object oving at 3 accelerate uniforly at the rate of for 6 econd. Find it final velocity, the ditance it cover. 5- A plane land at ( 5/ 4 ) each econd 500 & top 00 away fro the landing point. Find the tie taken by the plane to top. ( 0.4 ) 6- A car pae a point at a velocity of cover 0 each econd & ove for 0 ec. 0. Find it final velocity given that it (0 /) 7- The relation 36 0d expree the otion of a car. Find it acceleration, f initial velocity & final velocity after 0 ec. ( 5/ 6/ 56 / ) 8- A car tart fro ret to be accelerated along 500 by0, the driver then kept hi velocity for 00 after which he tarted to ue the brake to be retarded uniforly to top 5 ec. later. Find the average velocity of the car along trip. 3 ( 53.5 / ) 9- A body fall freely. Find the ditance covered in 3 ec, it peed after 80, the tie required to reach a velocity of 5 & the tie needed to cover 500.

31 ( g = 0 / ) ( 45 40/.5 0 ) 0- A body i projected upward at 30. Find the axiu height it can reach and the tie taken to reach it ( g 0 ). ( 45 3 ) - A tone dropped fro a bridge trike water 5 ec later. Calculate the height of the bridge and the velocity at which the tone collide againt water. (.5-49 / ) - The relation 0d expree the otion of a body oving vertically. f Find:- - Whether it ove up or down - It initial velocity 3- It velocity after ec. ( down zero 0 / ) 3- A tone fell fro the top of a building & reached the ground at 40. If the height of each floor i 4. Find the nuber of floor in the building. ( g 0 ). ( 0 floor ) 4- A tone falling fro the roof of a building, pae by a peron tanding in a balcony 5 higher than the ground, 4 econd later. (g=0/ ). Find the height of the building and the velocity of the tone while paing that peron. ( 85 40/ ) 5- A fruit falling fro a tree took ec. to reach the ground. Find it velocity jut before hitting the ground, it average velocity while falling and the height fro which it fell.(g=0 / ) ( 0/ 5 / 5 ) 6- A body i thrown vertically upward fro the top of a hill at 5 & reached the ground at the bae of the hill 5 ec later. Find the height of that hill. ( g 0 ). ( 00 ) 7- A tone fell fro a bridge 45 higher than water level at the ae tie a boat 6 long & of negligible height wa 48 apart fro the bridge & wa oving 3

32 toward it at 4. Uing the calculation needed, find out, if the tone will hit the boat or not. ( g 0 ). ( No 3.5 ) 8- Calculate the average velocity of the car whoe otion i expreed by the graph. - The axiu diplaceent =.. S - The total diplaceent = 40 - The total ditance = t (40 Zero 80 ) 9- Calculate:- - The acceleration at ab. v - The total ditance covered. 0 b c - The average peed of the car. 0 a d t 30. A projectile i thrown up at 40 / foring an angle of 35 o with the horizontal. Find :. The tie taken to reach the top of it trajectory.. The axiu height the projectile can reach. 3. How far doe the projectile land fro the tarting point. 4. The tie taken till it get back to the ground. ( ) 3. A football i kicked with an initial velocity of 5 / at an angle of 45 o with the horizontal, Find the tie of flight, the horizontal range and the peak height of the football. ( ) 3. A tone thrown up at an angle of 5 o with the horizontal pend 3 ec in air. Find it initial velocity and it horizontal range.(g=0/ ). (35.5/ 96.5 ) - G.R.F:- - The (d-t) curve i a traight line when v i unifor. - The body oving with a unifor acceleration ha a non-unifor velocity. - elocity i a vector quantity.

33 - A body thrown up vertically reduce it velocity uniforly. - A body projected upward get back to the ground with a velocity equal to it initial one. - What i eant by:- - A body ove with a unifor velocity of 0 - A body ove with a unifor acceleration of 0 - A body i accelerated by 9.8 due to gravity - A body i decelerated by 9.8 due to gravity - A body ove with a non-unifor velocity - A body ove with a non-unifor acceleration - Write the cientific ter:- - The rate of change in diplaceent. - Poition of a body with repect to the tart point. 3- Ditance covered in a certain direction. 4- Rate of change in velocity. 5- Unifor increae in velocity per unit tie. 6- A vector quantity eaured in eter. 7- The total ditance covered per total tie. 8- Rate of unifor decreae in velocity. - Chooe the correct anwer:. When the value of the velocity i negative, the body i.. ( lowing down decreaing it diplaceent projected upward ). A free falling body change it. ( a acceleration velocity weight ) 3. Two object falling freely to the ground, the a of the firt i twice that of the Second, then the ratio of their acceleration a : a i.. 33

34 ( : :3 : : ) 4. When an object fall freely, the ditance covered i. tie. ( directly proportional to directly proportional to the quare of the inverely proportional to inverely proportional to the quare of the ) 5. At the axiu height reached by a body projected up, the. i nil (zero). ( gravity acceleration velocity energy ) 6. The tie taken by an object projected up to get back to it tart point i.. the tie taken by the object to reach it axiu height. ( equal to half twice no correct anwer ) 7. If the flight tie of a projectile i 8. then the tie of it rie i ( ) 8. A projectile reache the greatet horizontal range when it i projected at an angle. With the horizontal. ( 0 o 75 o 45 o 90 o ) 9. When the angle of projection of a body increae the.. decreae. ( axiu height horizontal range tie of flight ) 0. Two bodie with different ae fall freely ( the heavier reache the ground firt both reach the ground together the heavier i ore accelerated) -Find the actual value for each of the following lope when i i equal zero: d t d t - The graph repreent the relation between the vertical coponent of the velocity of a projectile projected under gravity at an angle of 30 o fro the ground and tie. - Find the tie taken to reach the axiu height. y - Find the tie of flight Find the axiu height reached. 34

35 - Find the horizontal range t(ec) The following table how the relation between the diplaceent covered by a car (d) and the tie interval (t): d () t () Draw a graph relating (d) on (y) axi and (t) on (x) axi.. Decribe each part of the graph. - The following table how the relation between the velocity of a body () and tie (t): (/) t () Draw a graph relating () on (y) axi and (t) on (x) axi.. Fro the graph find: a. The acceleration during the lat two econd. b. The covered ditance. - The following table how the relation between the diplaceent (d) for an object fall freely and quare of tie (t ): d( ) t ( ) Draw a graph relating (d) on (y) axi and (t ) on (x) axi.. Fro the graph find the free fall acceleration. 35

36 - Deterination of the acceleration due to gravity (g):- - Let water in the container fall drop by drop on the etallic plate, in uch a way to keep only one drop in air - Meaure the tie taken by 5 drop to fall uing a top watch. ( t ) 3- Repeat tep () everal tie to find t ) & ( ) ( t3 4- Calculate the average tie for 5 drop to fall. t t t t3 3 etallic plate 5- Calculate the tie to allow one drop to fall. S g t t 5 6- Meaure the height (h) (y) (d) t nd 7- Apply the law of otion to find (g). & 0 d t d it g t i d g t & g 36

37 Chapter (3) Force and otion Newton' law Galileo' experient:- - The peed of the falling ball reache it axiu at the botto of the lope. - The diplaceent covered on the inclined urface are different & increae a the inclination increae. 3- The height reached by the ball i contant. 4- In cae of a horizontal frictionle urface the ball keep rolling with a unifor velocity. Inertia: - I the tendency of a body to retain it tate of ret or otion with a unifor velocity. Newton' t law:- "A body retain it tate of ret or otion on traight line with unifor velocity, unle it i affected by an external force." Ex: - A bicycle rider keep oving after he top peddling for a ditance depending on the oothne of the road (friction). If thi i reoved he keep oving with a unifor velocity. N.B:- Newton' t law i doinant when F 0 37

38 I the uation ign & F i a vector. N 5N N 3 N F 3 5 N F 5 3N F F F Inertia of a body Ma. Inertial a:- I the reitance of the body to change it velocity on colliion. Ex:- - Pull a cardboard placed on a cup & on which i placed a coin. - Pull a cardboard placed on a table & on which i placed a block. - Paenger fall forward when a car uddenly top. - Paenger fall backward when a car ove uddenly. - A bicycle keep oving after the rider top peddling. * The firt law of Newton i called law of inertia * A body affected by everal force where ( F 0) ove inertialy (keep it tate of ret or otion with unifor velocity). - Moentu: - I the product of the a of a body by it velocity. p Kg * A oving body alway ha a oentu depending on it a and velocity. Relation between a and velocity at a contant oentu: - Copre a pring between rider ae tied with a thread on an air track. (Frictionle urface) - Cut the thread to releae the pring, both bodie gain the ae oentu. 38

39 N.B:- S t S t P L ( linear oentu ) - The bullet ove fater than the gun hooting it, becaue both gain the ae oentu but the bullet i lighter and nd Newton' law:- 39 "The net force acting on a oving body equal the rate of change of it oentu & it direction i that of the change in oentu." The net force acting on a body i equal to the product of it a by it acceleration. F t i con tant F t F a N Kg - The acceleration of a oving body to the reultant force acting on it ( F a). Force: - Newton: - I the influence which caue the change in the velocity or tate of a body. I the force which when acting on a body of kg accelerate it by. Experient to how the relation between force and acceleration: - Prepare the device hown in the fig. - Meaure the length of the plane (d). - Put a a ( ) on the pan and let the car ove. - Calculate (W = F g = g).

40 - Calculate the tie taken by the car to cover (d). d - Calculate the acceleration of the car a: ( a ) t - Increae the a and repeat the previou tep everal tie and record the reult: Ma Weight Tie t d a F F - Plot the graph (F v a) and oberve that it i traight. lope ( of the car) a Relation between a & acceleration under equal force force:- If two equal force act on two bodie of ae & Weight: - F a & F a a a a a a I the force of gravity acting on a body. W t F g a N.B:- The weight of a body on the oon i it weight on earth a g oon g. 6 earth 6 N.B:- Motion on an inclined frictionle plane. F N (reaction) - The force oving the body i in F. g θ F g in F g co 4

41 Ma - I the quantity of aterial in a body. - Meaured in Kg. - Contant anywhere. - Meaured by the enitive balance. - Scalar quantity. Weight - I the force due to gravity acting on a body. - Meaured in N. - Change with poition (g) - Meaured by the pring balance. - ector quantity. rd Newton' 3 law:- - If a body exert a force on another, the reaction of the econd will be equal in agnitude but in oppoite direction. - For every action there i an equal & oppoite reaction. A F F F B F - Exaple : - Ball and a racket, ball and wall, rocket engine and ground, gun and hooter houlder. - N.B: The action and reaction can never caue equilibriu becaue they act * Exaple:- on two different bodie. - Find the gravitational force acting on a an of 70 Kg. g Fg g N. 4 ( 0 ). - A car pulled by a tractor which affect it by a force of N & the car i accelerated by. Find it a & weight. 3

42 F a W g Kg W W 9800 N 3- Find the acceleration of a plane of F a a F Kg a forced by N. Proble:- 4- A car whoe a i ton tart to ove fro ret on a horizontal road for 00 where it velocity becae 00. Find - The force of the engine. 5- Find the force accelerating a a of Kg fro ret to - The tie taken by the car to cover The gravitational force acting on the car. 4 ( 5000 N 4 zero ) 0 in 4 ec. ( 5 N ) 6- A body i puhed by a force of 5000 N. If it a i 00 Kg. Find the acceleration of the body. If the force i halved, find the new acceleration? ( 50 / 5 / ) 7- A car of a 000 Kg i oving in a traight line with a velocity of engine i topped to let the car coe to ret 5 ec later. Calculate:- - The ditance covered by the car to top. 0 then the - The frictional force acting on the car. ( 50 _ N ) 8- A body of a 50 Kg tarted fro ret for 0 ec after which it velocity becae 500 c Find - The acceleration.. - The force accelerating it. - The gravitational force acting on it.

43 43 ( 0.5 / 5 N Zero ) 9- Two ae 5 Kg & are affected by the ae force, the firt i accelerated by 0 while the velocity of the econd change fro ret to 00 in 0 ec. Find the value of (). ( 0 kg ) 0- A car of ton i accelerated fro ret to 30 in 0 ec. If the car i expoed to an air reitance of 40 N & frictional force of 60 N. Find the force of it engine. ( 300 N ) - A an of 70 Kg i riding a otor cycle of 30 Kg if the engine produce a force of 000 N to accelerate the bicycle by. Find the force of reitance to which 3 the bicycle i expoed. ( 00 N ) - In the figure the rider ae & are repectively 0 Kg & 5 Kg. when S the thread wa cut covered 0. S 0 Find the ditance covered by at that intant. ( 5 ) 3- Two ae were expoed to the ae force. If the firt a i twice the econd, Find the rate of change in the velocity of the firt relative to that of the econd. 4- A bullet of a 5 g i projected to collide againt target at & topped ec later. Calculate: The oentu of the bullet jut before colliion. - The change in oentu after ec fro colliion The rate of change in oentu. - The frictional force of the target acting on the bullet. - The deceleration of the bullet. - The ditance covered inide the target. ( ½ ) 0 & penetrated in ( 0.kg/ kg/ -0N - -0N / 0.05 )

44 5- Chooe the correct anwer:. The relation expreing Newton third law i. ( F = F - F +F = ΣF - F + F = 0). A the a of the body increae it. increae. ( velocity inertia acceleration) 3. If the a of a body i doubled under the effect of the ae force, it.. i doubled. ( velocity oentu acceleration ) 4. The dienional forula of the weight i.. ( ML T - - MLT - - M L T - ) 5. The force which act on a a of 5kg to change it velocity fro 3/ to 9/ in ec. i equal to ( 0 N 5 N/ 5 kg/ ) 6. If the a of a body i halved and the force acting on it i reduced to the quarter, it acceleration i ( contant - doubled - halved ) 7. If the force acting on a body i doubled while it a i halved, then it acceleration i ( halved - increae to four tie - quartered ) 8. If the net force acting on a body equal zero, then the body ove with ( unifor acceleration unifor oentu non-unifor velocity ) 9. When a car increae it oentu, then it ut be increaing it.. ( a - tie of otion velocity ) 0. The thrut of a rocket i an application of Newton.. law. ( Firt - econd - third ) 6- Coplete:- - The force i a.. quantity eaured in &.. 44

45 - The a i a..quantity eaured in. while weight i.. quantity eaured in.. 3- The force acting on a a of 0 Kg to accelerate it by 0 equal the force acting on a a of 00 Kg to accelerate it by.. 4- The oentu equal & it dienional forula i. 5- The oentu of a oving body i doubled when. i doubled while the force acting on it i doubled when.. i doubled. 6- The inertia i. 7- Copare between:- - Force & oentu. - Ma & weight. 8- What i eant by:- - The oentu of a body i 0. - A body ove inertialy. 3- The force acting on a body i 0 N. 4- Newton. 5- The oentu of a body i 0kg/. 9- G.R.F:- - A body ay reain oving with unifor velocity inpite of being affected by everal force. - A bu oving at the ae velocity a a car ha a higher detructive power. 3- Paenger fall forward when a car uddenly top. 4- Paenger fall backward when a car ove uddenly. 5- A gun ove backward when a bullet fired. 6- The weight of a body i variable according to it poition. 7- The weight of a body on the oon i it weight on earth. 6 45

46 8- A car driver hould wear the uit belt. 9- It i eaier to puh a light body than a heavy one. 0- A body ay keep it equilibriu inpite of being affected by any force. - A body ay be affected by equal & oppoite force but doen't keep it equilibriu. - The action and reaction ay be equal and oppoite but caue no equilibriu. 3- The oentu of a body increae a it velocity increae. 4- While hooting, the rebounding peed of the gun i uch le than the peed of the bullet. 0- Prove that: (Derive). - Newton' econd law. - Nae the value of the lope in each of the following cae & tate the atheatical relation relating the variable. - In graph () & () which one expree the effect of force on one body only? F F a a a F - Define:- 46

47 - Inertia - Law of inertia - Force - a - Newton' firt law - Moentu - Newton' econd law - Newton - Newton' third law - Weight 3-The following table how the relation between the acting force (F) on a body and the acquired acceleration (a): F (N) 0 00 A a (/ ) B 0. Draw the graph relating (F) on (Y) axi and (a) on (X) axi.. Fro the graph find: a. The value of (A) and (B). b. The a of the body. Unit III Chapter () Circular Motion - A body oving in a circle with a unifor peed i aid to be accelerated. - Thi body change it direction and o it velocity. - The acceleration change the direction of the velocity without changing it agnitude i called centripetal acceleration. - The preence of an acceleration require the preence of a force alo called centripetal force. Centripetal acceleration:- - Act on a body oving in a circle to change the direction of it velocity without changing it agnitude. v 47

48 - A body oving along the circuference v with radiu (r) ha intantaneou velocity B A v at A & B. r o r - v change it direction but keep it agnitude contant. - repreent the change in velocity (direction only) Ao B A B r & are iilar ( ) If AB egent = A B arc & AB i the diplaceent fro A to B & A B at......(3) Fro t.....(), t at r t a r t & 3. a c r Centripetal acceleration. Centripetal force:- - I the force acting on a body oving in a circle to accelerate it by changing the direction of it velocity without changing it agnitude. F F C C a C r N.B: - The factor affecting the centripetal force are: F a of thebody F the quqre of the gential velocity tan ( ) F radiu of theorbit of rotation - The centrifugal force: i a force equal and oppoite to the centripetal force puhing the body away fro the centre of rotation, reulting fro the rotation 48

49 of the body at a high velocity. - N.B: The tenion force, the gravitational force, the friction force, the reaction force and the lifting force ay all act a Centripetal force. -Experiental verification of the centripetal force: - Attach a cork topper of a () to a platic tube through a tring. - Rotate the cork and notice that the centripetal force (F c ) reulting fro the tenional force of the tring (F t ) i equal to the weight of the hanged a (g). - Uing the previou tool and a top watch to calculate the tangential velocity, you can find that: Fc Ft or g r A body oving in a circle perfor a periodic otion. Periodic tie (T):- - I the tie needed to cover one cycle. S t If the body cover one cycle 49

50 t T S circuference r. r T Where: - (r) i the radiu of the circular path. (v) i the velocity called orbital velocity. (tangential velocity). Motion of atellite:- - Satellite are ent with a very high peed to allow the to overcoe (g) & reach a pecific poition in pace where they rotate at contant orbit under the effect of the centripetal force. - The equation of circular otion are applied on atellite. r F C r h r a C r e r T N.B:- (r) radiu of the orbit= radiu of the earth + height fro the earth urface. Exaple:- - Find the centripetal force acting on a car of 000 Kg oving in a circle of 50 radiu with 5. F C r 000 (5) N. - A body of a 0.5 Kg ove in a circle whoe radiu i at 0. Find it centripetal acceleration & force. 5

51 a C r (0) 50 F C a C N 3- Find the orbital velocity & the tie to cover one cycle, for a atellite oving at a height of 300 K around the earth whoe radiu i 6400 K. ( g 9.8 ). r g r g r g r K r T 670 T T Proble: 4- Find the force acting on a atellite of 5 ton revolving at a height of 300 K fro 3 the center of the earth at 8 0. ( N ) 5- A car ove in a circular path of radiu 50 at 00. If it a i 500 Kg. Find the centrifugal force acting on the car. ( N ) 5

52 6- A Satellite of a ton i orbiting the earth at a height of 600 K. if the radiu. of the Earth i 6400 K & the acceleration due to gravity0 Find: - The orbital velocity. - The centripetal acceleration. - The force acting on the atellite. - The periodic tie. ( / 0/ 0000 N ) 7- Coplete: - The centripetal force i directly proportional to. &..& inverely proportional to - A body oving in a circle ove with a unifor..& a non- unifor Give reaon for: - A body oving with unifor peed in a circle i aid to be accelerated. - The orbit of the earth around the un i contant. 9- Prove that: (Derive). - g r. - a r 0- Nae the value of the lope in each of the following cae & tate the atheatical relation relating the variable. F c a c a c 5 r

53 v a c r r - Define:- - Centripetal force - Periodic tie - Chooe the correct anwer:. If the velocity of a body oving in a circular path i doubled while the radiu of it orbit i kept contant, then the centripetal acceleration.. ( i doubled becoe four tie i quartered i halved ). The orbital velocity of a body i independent of ( it acceleration the radiu of it path it a no correct anwer ) 3- An object ove in a circular path, the following table relate it centripetal acceleration (a) and the reciprocal of radiu of curvature(/r). a c (/ ) /r ( - ) Draw a graph relating (a) on (y) axi and (/r) on (x) axi.. Fro the graph find the tangential velocity with which the object ove. Chapter () Univeral Gravitation and circular otion - The force of attraction between bodie with F ae & i directly proportional to the product of their ae. r 53

54 F - Thi force i alo inverely proportional to the quare of the ditance between the center of both bodie & denoted by r. F r F r & F cont. r Thi contant called gravitational contant & i denoted by (G). F G r Gravitational contant:- - I the utual force of attraction between ae of Kg for each, whoe center are apart. G F r N Kg Kg 3 S G N Kg Application on the gravitational law:- - Calculate the orbital velocity:- - A atellite orbiting the earth i affected by a centripetal force. r F C S M r 54

55 - The atellite of a ( S utual gravitational force. G M F r ) & the earth of a ( e M ) affect each other by a r G M r GM r GM r - To find the gravitational field intenity. - Conider a a ( =kg) at a height (h) fro it h Surface. The ditance between the center of both (r) will be equal ( r e h). M r & M F G & F g g r M g G r g GM expree the acceleration due to gravity of Earth. r - If (g) i calculated at the Earth urface ( r = r earth ). - To copare (g) for two planet: g M r g M r - Gravitational field intenity: i the force acting norally per unit a placed in the gravitational field of the Earth. ( nuerically = the acceleration due to gravity = 9.8 N/kg where g F ). 3. Motion of atellite: - Newton noticed that a projectile projected at a higher velocity reache the Earth at a further ditance. - He dicovered that if the curvature of the projection path becoe parallel to the curvature of the Earth, 55

56 the projectile will rotate at a particular path and becoe an Earth follower uch a the oon. NB: - If the velocity of the projectile becoe zero, it fall traight to the earth. -If the Earth gravitational force vanihe it ove traight along the tangent of it circular path. 4. Iportance and ue of atellite:. Counication atellite: tranit phone, T and radio ignal.. Atronoical atellite: are huge telecope to iage orb. 3. Reote ening atellite: help to find underground earth reource, protecting yield againt weather condition, tudy bird eigration 4. Explanatory and pying atellite: ued for ilitary and political inforation and onitor cobat. - Coplete:- - Between any two ae there i a. Force - The utual gravitational force between bodie i to their ae & inverely proportional to the.. 3- The gravitational contant i denoted by. & i equal to. eaured in.. 4- The orbital velocity of a atellite depend on,. & 5- The acceleration due to gravity can be deterined depending on the radiu of the planet & it a fro the relation. 6- Counication atellite are ued to.. 7- Atronoical atellite carry.. ued to - Prove (Derive):- - G r G - g r 56

57 4- Proble:- - If the a of a planet i 6 tie that of earthy & it radiu i twice that of earth. Find the acceleration due to gravity on it urface relative to that of earth. (3/) - The radiu of earth i 6400 K, the acceleration due to gravity i 9.8, then the acceleration due to gravity affecting a body raied to a height of 600 K fro it urface will be equal to.. 3- If the diaeter of the oon i 4 that of earth & it a i 96 ( 8.9 / ) that of earth. Find the acceleration due to gravity on the oon' urface relative to that of earth. ( /6) 4- A body i placed at a ditance (d) fro the earth center i diplaced to a ditance ( 3d ) fro the center, copare the acceleration due to gravity acting on it repectively, then copare it weight at both poition. ( 9/ 9/ ) 5- A atellite of a 500 Kg i revolving around the earth in a circular orbit at a height of 600 K fro it urface. Auing that the a of the earth i 6 N 4 0 Kg, G & it radiu i 6400 K. Kg Calculate: - The orbital velocity of the atellite. - The centripetal force acting on the atellite. ( 756.7/ 4.9x0 5 N) Work:- Unit (I) Chapter () Work and Energy 57