Einstein. Mechanics. In Grade 10 we investigated kinematics, or movement described in terms of velocity, acceleration, displacement, and so on.

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1 Cmbridge University Press Study nd Mster Physicl Sciences Grde 11 Lerner s Book Krin Kelder More informtion MODULE 1 Einstein Mechnics motion force Glileo Newton decelerte moment of force movement ccelerte momentum In Grde 10 we investigted kinemtics, or movement described in terms of velocity, ccelertion, displcement, nd so on. This module focuses on the resons for motion wht mkes n object t rest begin to move, wht cuses n object to ccelerte or decelerte. It invites you to explore the reltionship between motion nd the forces tht cuse motion. In this module you will work your wy through the following units: Newton s lws of motion Newton s Lw of Universl Grvittion momentum moment of force. rom everydy experience, we know tht n object cnnot move unless force is pplied to it. In the erly 1600s Glileo observed this phenomenon. We will strt our study with Glileo nd progress to Isc Newton, the fther of clssicl physics. Newton formulted the lws of motion nd the Universl Lw of Grvittion in We still use these lws tody, lthough Albert Einstein formulted new lws in To understnd the link between these two gret scientists, we will look briefly t their contributions to science. In sport, we tlk bout rugby or soccer plyer s momentum tht crries him forwrd. We will investigte how momentum cn be defined scientificlly, nd lso how we cn clculte its chnge. The reltionship between motion nd the forces tht cuse motion is clled dynmics. We will lso look t the reltionship between dynmics nd mchines. In science we consider mchine to be ny device tht mkes it esier for us to do work. 1 Cmbridge University Press

2 Cmbridge University Press Study nd Mster Physicl Sciences Grde 11 Lerner s Book Krin Kelder More informtion UNIT 1 inerti newton mss force motion NEWTON S LAWS O MOTION friction ccelertion time KEY CONCEPTS mss inerti forces force digrms ccelertion equilibrium net force ction-rection pir When you hve completed this unit, you should be ble to: define Newton s three lws of motion explin wht inerti is nd how it is relted to mss understnd nd define the mthemticl nd grphicl reltionship between force, ccelertion nd mss understnd how this reltionship between force, ccelertion nd mss led to Newton s Second Lw drw force digrm nd lbel the forces cting on n object distinguish between blnced nd unblnced forces clculte the net force nd use it in Newton s Second Lw identify ction-rection pirs ccording to Newton s Third Lw. Newton s irst Lw In the 17 th century, scientists invented the telescope. At this time, stronomers begn to study the movement of plnets in the hevens (or solr system). They noticed tht the plnets moved freely through spce, without ny force to push them. Glileo cme to the conclusion tht this ws the nturl motion of objects: An object t rest will sty t rest, unless force cuses it to strt moving. A moving object will continue to move t constnt speed in stright line, unless force cts on it. () Glileo devised severl experiments to test his ides. In one experiment, bll rolls down curved rmp, speeds up, nd then runs up the other side. If there is no friction, it reches the sme height s the strting height, s seen in (). If the second prt of the rmp is lowered to less steep slope, the bll reches the sme height s before, but now trvels (b) originl height (c) further horizontlly, s seen in (b). Wht hppens if the rmp is lowered to horizontl position? Glileo suggested tht the bll would roll on forever, s seen in (c). 2 MODULE 1: UNIT 1: NEWTON S LAW O MOTION Cmbridge University Press

3 Cmbridge University Press Study nd Mster Physicl Sciences Grde 11 Lerner s Book Krin Kelder More informtion To hve better understnding of Glileo s ide, let us look t nother exmple. When you push brick with rough surfce long tble top t constnt speed, you hve to exert certin mount of force. To push smooth wooden block with the sme mss cross the tble t the sme speed requires less force. If lyer of oil is poured onto the tble, the force required to move the block will be very smll. Imgine if the block ws not touching the tble t ll. Once strted, the block should move cross the tble with no further force pplied. v v v rough surfce smooth surfce no contct Newton used Glileo s results nd formulted his theory of motion in three lws. His irst Lw summrises Glileo s originl ides: Newton s irst Lw An object will remin t rest or continue to move t constnt velocity in stright line, unless n externl net force cts on it. Inerti nd mss The tendency of body to mintin its stte of rest or constnt motion in stright line is clled its inerti. Let s look t the following exmples: It is esier to ctch tennis bll thn cricket bll. It is esier to move sttionry bicycle thn sttionry cr. It is esier to turn n empty supermrket trolley thn fully lden one. rom these exmples, we cn deduce tht the greter the object s mss, the more difficult it is to chnge its motion. Newton used the term mss for the quntity of mtter of n object. Another wy to define mss is to sy tht it is mesure of body s inerti. The more mss body hs, the hrder it is to chnge its stte of motion. DID YOU KNOW? In Grde 10 we lernt tht mss is property of body itself. Mss is mesured in grms nd kilogrms. Weight is the force of grvity cting on body nd is mesured in newtons. 3 Cmbridge University Press

4 Cmbridge University Press Study nd Mster Physicl Sciences Grde 11 Lerner s Book Krin Kelder More informtion Exmples: Demonstrting Newton s irst Lw nd inerti The mss of n object is mesure of its inerti. The following demonstrtions explin this property of mtter. Exmple 1 Exmple 2 bll pull When the crdbord is flicked wy from the top of the glss, the coin drops in the glss. The force pplied to the crdbord is not relyed fst enough to the coin to ccelerte it with the crdbord. Exmple 3 A quick jerk breks the string t the bottom. There is not enough time to overcome the inerti of the bll, nd the pulling force breks the string t the bottom. A stedy, slow pull breks the string t the top. There is enough time to overcome the inerti of the bll, nd the weight of the bll together with the pulling force breks the top string. jerk When the pper is jerked wy, the glss of wter lnds on the tble. The friction between the tble nd the pper cnnot overcome the inerti of the glss. Before we cn continue our investigtion into the effect of force on the motion of n object, we need to refer bck to the concepts we used in Grde 10 to describe motion. The quntities of displcement (s), initil velocity (u), finl velocity (v), ccelertion () nd time (t) ll contribute to the type of motion of n object. This motion cn be described nd clculted by using words, grphs nd equtions. Displcement-time grphs plot the rte t which the displcement of n object chnges, nd velocity-time grphs plot the rte t which its velocity chnges. Any of the bove quntities cn be clculted by using set of equtions clled the equtions of motion. They re: v u t v 2 u 2 2s s ut 1 / 2 t 2 (u v)t s 2 4 MODULE 1: UNIT 1: NEWTON S LAW O MOTION Cmbridge University Press

5 Cmbridge University Press Study nd Mster Physicl Sciences Grde 11 Lerner s Book Krin Kelder More informtion Accelertion, force nd mss Newton s irst Lw describes n object t rest or with constnt motion. But wht hppens if n unblnced externl force is exerted on the object? Newton relised tht the velocity of the object will chnge. If the object experiences n increse or decrese in velocity, it will hve ccelertion. To understnd the reltionship between ccelertion, force nd mss, we will investigte the motion of minibus txi. Reltionship between ccelertion nd force A minibus txi driver is witing for the trffic lights to chnge. When the lights turn green, the driver pulls wy nd moves forwrd. The force provided by the engine cuses the minibus to ccelerte. The rrow in the sketch shows the force pushing the minibus forwrd. If the driver wnts to move wy from the lights more quickly, he cn push down hrder on the ccelertor. The forwrd force is then stronger, nd the minibus s ccelertion will be greter thn before. v v The grphic representtion of the motion of the minibus is: v (m) v (m) (m s 2 ) (m s 2 ) 5 Cmbridge University Press

6 Cmbridge University Press Study nd Mster Physicl Sciences Grde 11 Lerner s Book Krin Kelder More informtion At the next trffic light, the driver must stop. He pplies the brkes, which provides nother force to slow down the minibus. Although the minibus is moving forwrd, the brking force is directed bckwrd to decelerte the minibus. If the driver wnts to stop in hurry, he must pply stronger force by pushing down hrder on the brke pedl. The minibus s decelertion will therefore be greter thn before. v v The grphic representtion of the motion of the minibus is: v (m) v (m) (m s 2 ) (m s 2 ) Now we cn deduce from our observtions on the minibus tht: A force cn mke n object ccelerte. The object ccelertes in the direction tht the force is being exerted. The stronger the force cting on n object, the greter the ccelertion of the object. We sy tht the ccelertion produced by force is directly proportionl to the force. The mthemticl reltionship is written in symbols: We cn lso represent the reltionship grphiclly, s shown on the right. Accelertion is plotted ginst force 6 MODULE 1: UNIT 1: NEWTON S LAW O MOTION Cmbridge University Press

7 Cmbridge University Press Study nd Mster Physicl Sciences Grde 11 Lerner s Book Krin Kelder More informtion DID YOU KNOW? Becuse ccelertion is directly proportionl to the force which produces it, doubling the force will produce twice the ccelertion, three times the force will produce three times the ccelertion, nd so on. You cn find out more bout the mthemticl nd grphicl representtions of the reltionship between quntities in the introduction. Reltionship between ccelertion nd mss Another fctor tht influences n object s ccelertion is its mss. The txi driver knows tht when his txi is full of people, he will not be ble to ccelerte fst when he pulls wy from trffic light. Similrly, when he pplies the brkes, the txi will decelerte more slowly thn when it is empty. A good driver tkes these differences of mss into ccount when driving nd stopping the txi sfely. v v We cn deduce from our observtions on the minibus tht: If constnt force is pplied, the greter the mss of n object, the smller its ccelertion. We sy tht the ccelertion of n object produced by force is inversely proportionl to the mss m of the object. The mthemticl reltionship is written in symbols: 1/m The grphicl representtion is: Accelertion is inversely proportionl to mss m 1 m Accelertion is directly proportionl to 1/m 7 Cmbridge University Press

8 Cmbridge University Press Study nd Mster Physicl Sciences Grde 11 Lerner s Book Krin Kelder More informtion DID YOU KNOW? Since ccelertion is inversely proportionl to the mss of n object, doubling the mss of the object will hlve ccelertion if the force remins constnt. Newton s Second Lw We cn now combine the reltionship between ccelertion nd force with the reltionship between ccelertion nd mss: or m m Newton s Second Lw When net force is exerted on n object, it cuses the object to ccelerte in the direction of the force. This ccelertion is directly proportionl to the force nd inversely proportionl to the mss of the object. This proportionlity is not n exct reltionship yet. To insert n equl sign ( ), the totl numericl vlue of the SI units on the left of the proportionlity must equl the totl numericl vlue of the SI units on the right. To chieve this, we hve to include proportionlity constnt k: km DID YOU KNOW? The unit of force, the newton, ws nmed fter Sir Isc Newton, who plyed gret prt in developing the scientific concept of force. The newton is one of seven bsic SI units. Red more bout these units in the introduction on pge vi. By setting k equl to 1, our formul becomes: m We hve now defined the mgnitude (size) of the unit of force (newton) in terms of existing units, the kilogrm, metre nd second. One newton is the force tht will give mss of one kilogrm ccelertion of one metre per second squred: 1 N 1 kg m s 2 The quntities re relted by the formul m Quntity Symbol Unit orce N (newtons) Mss m kg (kilogrms) Accelertion m s 2 (metres per second squred) Note: Different scientific sources use different nmes for the force tht results in ccelertion of n object net force; unblnced force; resultnt force. They ll refer to exctly the sme force. 8 MODULE 1: UNIT 1: NEWTON S LAW O MOTION Cmbridge University Press

9 Cmbridge University Press Study nd Mster Physicl Sciences Grde 11 Lerner s Book Krin Kelder More informtion WORK IN GROUPS Activity 1: Investigting Newton s Second Lw LO1: AS1, AS2, AS3, AS4; LO2: AS1, AS2 Note: To compre two vlues experimentlly, ll other fctors must remin constnt during the course of the experiment. The trolley experiments re used to investigte the reltionship between the pplied force, ccelertion nd mss of n object. Ask your techer for detils on the experimentl procedure. The concepts of the experiments re explined here briefly so tht you cn nswer the questions in the ctivity. In this ctivity, two reltionships re investigted: the effect of force on ccelertion, nd the effect of mss on ccelertion. ruler ticker-timer mrk tpe elstic bnd trolley trck In the experiments, force is pplied to trolley which is on slightly rised trolley rmp. The trolley rmp is rised to compenste for friction. When the trolley is given light push, the ticker-tpe tht shows the trolley s displcement t constnt time intervls, resembles the tpe in the sketch. 1. Wht does the spcing of the dots on the ticker-tpe tell you bout the motion of the trolley? 2. Wht is the vlue of the net force on the trolley tht produced the ticker-tpe? 3. Drw n exmple of ticker-tpe in which the trolley ccelertes. Stretched elstic bnds provide the force tht ccelertes the trolley. Cre is tken to stretch the elstic bnds to the sme length ll the time so tht constnt force is pplied. All the elstic bnds re tested beforehnd to ensure tht they ll give the sme force. Ticker-tpes from ech run re collected nd processed. The results re recorded in tbles nd grphs to show the vrious reltionships. 9 Cmbridge University Press

10 Cmbridge University Press Study nd Mster Physicl Sciences Grde 11 Lerner s Book Krin Kelder More informtion Investigtion 1: Determining the reltionship between force nd ccelertion on n object with constnt mss v (m s 1 ) Velocity is plotted ginst time The trolley is ccelerted with one, two nd three elstic bnds in succession. The results re used to drw velocity-time grphs. 4. Wht conclusions cn you mke from these grphs? 3 elstic bnds 5. Wht is the mthemticl reltionship 2 elstic bnds between v nd t? 6. Drw sketch grph to show the reltionship between the net force on the 1 elstic bnd trolley nd the ccelertion it produces. 7. The following ticker-tpe gives you the experimentl vlues for one force (one elstic bnd). A B C D E 0,125 m 0,178 m 0,238 m 0,292 m 0,353 m Use the displcements bove to complete the following tble nd to clculte the ccelertion of the trolley. Displcement Time Averge Instntneous Chnge in Accelertion s (m) between velocity velocity velocity = v 10 dots v s (m s 1 v (m s ) ) v (m s 1 ) t (m s 2 ) t A to (reding 1 2) 0,2 (reding C 1 2 0,4 vlue 6) B (vlue 6) B to (reding 2 3) 0,2 (reding (vlue 7 (vlue 10 0,2) D 2 3 0,4 vlue 6 vlue 7) vlue 10) C (vlue 7) C to (reding 3 4) 0,2 (reding (vlue 8 (vlue 11 0,2) E 3 4 0,4 vlue 7 vlue 8) vlue 11) D (vlue 8) D to (reding 4 5) 0,2 (reding (vlue 9 (vlue 12 0,2) 4 5 0,4 vlue 8 vlue 9) vlue 12) E (vlue 9) 10 MODULE 1: UNIT 1: NEWTON S LAW O MOTION Cmbridge University Press