Linear Motion Physics

8/6/2019 Linear Motion Physics

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Discuss your physics question online at www.physics4spm.com

2.1 LINEAR MOTIONPhysicalQuantity

Definition, Quantity, Symbol and unit

Distance, I Distance is the total path length traveled from onelocation to another.Quantity: scalar 51 unit: meter (m)

Displacement,I

(a)The distance in a specified direction.(b)the distance between two locations measured alongthe shortest path connecting them in a specificdirection.

(c)The distance of its final position from its initialposition in a specified direction.

Quantity: vector 51 unit: meter (m)

Speed,vSpeed is the rate of change of distance

Speed = Distance traveledTime taken

Quantity: scalar 51 unit: m S-1

Velocity, vVelocity is the rate of change of displacement.

Velocity = DisplacementTime taken

Direction of velocity is the direction of displacementQuantity: Vector 51 unit: m S-1

v = Total distant traveled, sTotal time taken, t Example: A car moves atan average speed Ivelocity of 20 rns"~----------+---------------------~ On average, the car movesa distance I displacementof 20 m in 1 second for thewhole journey.

Averagespeed

Averagevelocity

v = Displacement, sTime taken, t

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Uniform Speed that remains the same in magnitude regardless ofspeed its direction.Uniform Velocity that remains the same in magnitude andvelocity direction.An object has (a)the direction of motion changes or the motion isa non-uniform not linear.velocity if: (b)The magnitude of its velocity changes.Acceleration, When the velocity of an object changes, the object isa said to be accelerating.

v-u Acceleration is defined as the rate of change ofa= velocity.tunit: rns" Acceleration = Change in velocityTime taken

= final velocitYI v - initial velocitYI uTime taken, t

~._ ,,:d:"~ .. __,~ ._TF ...-:~51 tbLV --, .- --SiEgeacceleration (a)is positive irl..':...I" The velocity of an object increases from an initialvelocity, u, to a higher final velocity, vDeceleration The rate of decrease in speed in a specified direction.

_ . . . . . ~ . . . . . . . . , . . . 1 : . u . . _ . . . . . .JC.:a,..../:lQW,.l o i o e j. - QliI ' -_,,";.::~--:..,.~ " ~ - 0"(b). ,"", . . . .

acceleration The velocity of an object decreases from an initialis negative. velocity, u, to a lower final velocity, v.Zero An object moving at a constants velocity, that is, theacceleration magnitude and direction of its velocity remain

unchanged - is not acceleratingConstant Velocity increases at a uniform rate.acceleration When a car moves at a constant or uniform acceleration

of 5 rns", its velocity increases by 5 ms" for everysecond that the car is in motion.



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1. Constant = uniform2. increasing velocity = acceleration3. decreasing velocity = deceleration4. zero velocity = object at stationary I at rest5. negative velocity = object moves at oppositedirection6. zero acceleration = constant velocity7. negative acceleration = deceleration

Comparisons between distanceand displacement.

Distance DisplacementTotal path length The distancetraveled from between twoone location to locationsanother measured along

the shortest pathconnecting themin specificdirection

Scalar quantity Vector quantityIt has magnitude It has bothbut no direction magnitude anddirectionSI unit meter SI unit: meter

Comparisons between speed andvelocity

Speed VelocityThe rate of change The rate of changeof distance of displacementScalar quantity Vector quantityIt has magnitude It has bothbut no direction magnitude and

directionSI unit: m s" SI unit: m s"

Fill in the blanks:1. A steady speed of 10 m/s = A distance of is traveledevery ..

2. A steady velocity of -10 m/s = A Of 10m is traveled every........... to the left.

3. A steady acceleration of 4 ms" = Speed goes up by 4 m/s every4. A steady deceleration of 4 ms-2 = speed goes by 4 m/severy .5. A steady velocity of 10 m /s = .



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Example 1Every day Rahim walks from hishouse to the junction which is 1.5km from his house. Then he turnsback and stops at warung Pak Dinwhich is 0.5 km from his house.

O .S kIn 1.5 k n n(a)What is Rahim's displacementfrom his house when he reaches the junction.

When he is at warung PakDin.

(b)After breakfast, Rahim walksback to his house. When hereaches home,(i) what is the total distancetraveled by Rahim?

(ii) what is Rahim's totaldisplacement from hishouse?

Example 2Every morning Amirul walks toAhmad's house which is situated80 m to the east of Amirul's house.They then walk towards theirschool which is 60 m to the southof Ahmad's house.(a)What is the distance traveledby Amirul and hisdisplacement from hishouse?

(b)lf the total time taken byAmirul to travel from hishouse to Ahmad's house andthen to school is 15 minutes,what is his speed andvelocity?

Example 3Syafiq running in a race covers 60 m in 12 s.(a) What is his speed in m/s(b) If he takes 40 s to complete the race, what is his distance covered?www.physics4spm.com 4


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Example 4An aeroplane flys towards thenorth with a velocity 300 km/hr inone hour. Then, the planemoves to the east with thevelocity 400 km 1 hr in one hour.(a)What is the average speedof the plane?

(b)What is the averagevelocity of the plane?

(c)What is the differencebetween average speed andaverage velocity of theplane?

Example 5The speedometer reading for acar traveling north shows 80km/hr. Another car traveling at80 km/hr towards south. Is thespeed of both cars same? Is thevelocity of both cars same?

A ticker timer~ Use: 12 V a.c power supply~ 1 tick = time interval between two dots.~ The time taken to make 50 ticks on the ticker tape is 1 second.Hence, the time interval between 2 consecutive dots is 1/50 = 0.02 s.

~ 1 tick = 0.02 s



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Relating displacement, velocity. acceleration and time using ticker tape.FORMULA

VELOCITY Time, t = 10 dots x 0.02 s10 dots = 0.2 sdisplacement, s = x cmI f . . I . . , .. to " t I velocity = s =xcm

x em t 0.2 sACCELERATION Initial velocity,u= ~I l . . . . i i . i l i t ! 1 I 0.2: . . ,~ : final velocity,x , e rn x:!cm V = X2- - -.2elapse time, t = (5 - 1) x 0.2 s = 0.8 s acceleration,or t = (50 -10) ticks x 0.02 s = 0.8 s a=v-utTICKER TAPE AND TYPE OF MOTIONCHARTS~,~ ,,, '! ~ ' . " ,+ Constant velocity- slow moving~ . . . . . . . J - _ . Constant velocity[ . .. ..n g t h I m ) - fast moving. . . . . ', , " , " '. , ~ .. . . 1 - > ~ Distance between the dotsincreases uniformly( Length I em ) ~ the velocity is of the object is4.0 .............. ~ increasing uniformly.3 -.--.~-.- .. r+= The object is moving at a., 6 _ ........ ' " : " '" : . ' ~1.9 _. .. . r- : uniform I constant1.,2 . . ' - u acceleration. 0.5 1 2 J 4 5 6



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~. . ' . 1 -> ~ Distance between the dots~L,ength I em ) decrease uniformly

~ The velocity of the object isr -r decreasing uniformly -.--, ill I r - - - ~ The object is experiencing uniform I constant I n . deceleration" : ! I :,, . . ' I ! Ipanjamg (em)xample 6The diagram above shows a ticker tape

chart for a moving trolley. The frequencyof the ticker-timer used is 50 Hz. Eachsection has 10 dots-spacing.(a) What is the time between two dots.(b) What is the time for one strips.(c) What is the initial velocity(d) What is the final velocity.(e) What is the time interval to changefrom initial velocity to final velocity?(f) What is the acceleration of the

object. o . : . . . , '5 15 25 35 45 55 65 75 B E ! 95105 detilc

THE EQUATIONS OF MOTION

u = initial velocityv = final velocityt = time takens = displacementa = constant accleration



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2.2 MOTION GRAPHSDISPLACEMENT - TIMEGRAPH'!lIm B c

D~~--~~--~~~--~_'Ms

Velocity is obtained from the gradient ofthe graph.A - B : gradient of the graph is +ve andconstant ., velocity is constant.B - C : gradient of the graph = 0 .. thevelocity = 0, object at rest.C - D : gradient of the graph -ve andconstant. The velocity is negative andobject moves in the opposite direction.

VELOCITY-TIME GRAPHB c

Area below Distance I displacementraphPositiveradientNegativeradientZerogradient

GRAPH s versus t v versus t a versus tZero s vvelocity L,Negative s vvelocity

t

tConstant s v avelocity

t t twww.physics4spm.com 8


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GRAPH s versus t v versus t a versus tConstant s v a

Lt Ltcceleration

tConstant s v adeceleration L, Lt tExample 6IContoh 1 1

s ~ m1\50 - - - - - 7 [A/ l

c

Example 7

(a) Calculate the acceleration at:(i) JK (ii) KL (iii) LM

(b) Describe the motion of the object at:(i) JK (ii) KL (iii) LM

Calculate the total displacement.

(c) Calculate the average velocity.

o 10 3 0 3 5" t f sBased on the s - t graph above:(a) Calculate the velocity at(i) AB (ii) BC (iii) CD

(b) Describe the motion of the object at:(i) AB (ii) BC (iii) CD

(c)Find:(i) total distance(ii) total displacement(d) Calculate(i) the average speed

(ii) the average velocity of themoving particle.



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2.3 INERTIAInertia The inertia of an object is the tendency of the

object to remain at rest or, if moving, to continueits motion.

Newton's first law Every object continues in its state of rest or ofuniform motion unless it is acted upon by anexternal force.

inertia and massRelation between The larger the mass, the larger the inertia

SITUATIONS INVOLVING INERTIASITUATION EXPLAINATION\ "

~

When the cardboard is pulled away quickly, thecoin drops straight into the glass.The inertia of the coin maintains its state at rest.The coin falls into the glass due to gravity.

Chili sauce in the bottle can be easily poured out ifthe bottle is moved down fast with a sudden stop.The sauce inside the bottle moves together withthe bottle. When the bottle stops suddenly, thesauce continue in its state of motion due to theeffect of its inertia.Body moves forward when the car stops suddenlyThe passengers were in a state of motion when thecar was moving. When the car stopped suddenly,the inertia in the passengers made them maintaintheir state of motion. Thus when the car stop, the...______,.=----....."..=---I passengers moved forward.q-~.

:,ABOY_~

A boy runs away from a cow in a zig zag motion.The cow has a large inertia making it difficult tochange direction.



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The head of hammer is secured tightly to itshandle by knocking one end of the handle, heldvertically, on a hard surface.

This causes the hammer head to continue on itsdownward motion when the handle has beenstopped, so that the top end of the handle isslotted deeper into the hammer head.

The drop of water on a wet umbrella will fallwhen the boy rotates the umbrella.

This is because the drop of water on the surfaceof the umbrella moves simultaneously as theumbrella is rotated.

When the umbrella stops rotating, the inertia ofthe drop of water will continue to maintain itsmotion.

Ways to reducethe negativeeffects of inertia

1. Safety in a car:(a)Safety belt secure the driver to their seats.When the car stops suddenly, the seat beltprovides the external force that prevents thedriver from being thrown forward.

(b)Headrest to prevent injuries to the neckduring rear-end collisions. The inertia of thehead tends to keep in its state of rest whenthe body is moved suddenly.

(c)An air bag is fitted inside the steering wheel.It provides a cushion to prevent the driverfrom hitting the steering wheel or dashboardduring a collision.

2. Furniture carried by a lorry normally are tied uptogether by string. When the lorry starts tomove suddenly, the furniture are more difficultto fall off due to their inertia because theircombined mass has increased.

Relationsh iPbetween massand inertia

Two empty buckets which are hung with ropefrom a the ceiling.

One bucket is filled with sand while the otherbucket is empty.

Then, both pails are pushed. It is found that the em bucket is easier to



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push compared to the bucket with sand. The bucket filled with sand offers moreresistance to movement.

When both buckets are oscillating and anattempt is made to stop them, the bucket filledwith sand offers more resistance to the hand(more difficult to bring to a standstill once it hasstarted moving)

This shows that the heavier bucket offers agreater resistance to change from its state ofrest or from its state of motion.

An object with a larger mass has a larger inertia.

2.4 MOMENTUMDefinition Momentum = Mass x velocity = mv

81unit: kg rns"Principle of In the absence of an external force, the totalConservation of momentum of a system remains unchanged.Momentum

Elastic Collision Inelastic collisionLI~-+ V i-

The two objects combine andmove together with acommon velocity after thecollision.

Momentum is conserved. Kinetic energy is notconserved.

Total energy is conserved.

m,+m l

Both objects moveindependently at theirrespective velocities after thecollision.

Momentum is conserved. Kinetic energy is conserved. Total energy is conserved.



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VI 1'2----+- .. .,.

Total Momentum Before = totalmomentum Afterm1U1+ m2U2= m1V1+ m2V2

m .u

EXAMPLES OF EXPLOSION (Principle Of Conservation Of Momentum)

Total Momentum Before = TotalMomentum After

m1U1+ m2U2= (m, + m2)v

M=ffil+ ml~ ' -; o ;; I ;. ~ . ~ . . ~ . .SiiiiiiliIiii~.-~I!ti~rlary

( a) B e fo re e x p lo si on

ExplosionBefore explosion both object sticktogether and at rest. After collision,both object move at opposite direction.

Total Momentumbefore collision Total Momentumafter collision :

~ When a rifle is fired, the bullet of mass m,moves with a high velocity, v. This createsa momentum in the forward direction.

~ From the principle of conservation ofmomentum, an equal but oppositemomentum is produced to recoil the rifflebackward.

Application in the jet engine:A high-speed hot gases are ejected from theback with high momentum.This produces an equal and oppositemomentum to propel the jet plane forward.

From the law of conservation ofmomentum:Total Momentum = Total MomentumBefore collision after collisiono = m1V1+ m2V2

m1V1= - m2V2-ve si n means opposite direction



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The launching of rocket~ Mixture of hydrogen and oxygen fuels burnexplosively in the combustion chamber.Jets of hot gases are expelled at very highspeed through the exhaust.

~ These high speed hot gases produce a largeamount of momentum downward.

~ By conservation of momentum, an equal buopposite momentum is produced and actedon the rocket, propelling the rocketu rds.

In a swamp area, a fan boat is used.~ The fan produces a high speed movement oair backward. This produces a largemomentum backward.By conservation of momentum, an equal buopposite momentum is produced and actedon the boat. So the boat will move forward.

A squid propels by expelling water at highvelocity. Water enters through a large openingand exits through a small tube. The water isforced out at a high speed backward.

Total Mom. before= Total Mom. aftero =Mom water + Mom squido =mwvw+ msvs-mwvw= rn,v,

The magnitude of the momentum of water andsquid are equal but opposite direction.This causes the squid to jet forward.



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Example

B.serVm,= 1 (lQO kg m z '" 1 200 lr;gCar A of mass 1000 kg moving at20 ms" collides with a car B of mass1200 kg moving at 10 m S1 in samedirection. If the car B is shuntedforwards at 15 m S1 by the impactwhat is the velocity, v, of the car Aimmediately after the crash?

Example

'8 'I+'- ~

Examplev- -

(a) Before :col lision (b ) Af te r collis io n

A truck of mass 1200 kg moving at30 m/s collides with a car of mass1000 kg which is traveling in theopposite direction at 20 m/s. Afterthe collision, the two vehicles movetogether. What is the velocity ofboth vehicles immediately aftercollision?

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M NBefore collision After collisionM A = 4 kg M B = 2 kgUA = 10 m/s to the leftUB = 8 m/s to the rightV B = 4 m/s to the left.Calculate the value of V A .

Example30 0 m Sl-+D

10 9

(a) Be fore shootin g (b ) A fte r shootin gA man fires a pistol which has amass of 1.5 kg. If the mass of thebullet is 10 g and it reaches avelocity of 300 m/s after shooting,what is the recoil velocity of thepistol?

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2.5 FORCEBalanced Force Example:When the forces acting onan object are balanced, theycancel each other out.The net force is zero.Effect:the object at is at rest [velocity = 0]or moves at constantvelocity [ a = 0]

Unbalanced ForcelResultant Force

Force Mass & Acceleration

FQr.;:~eXe!lted by'table 0 1 1 1 Ilhe e:up

Iift,U J drag , G

Newton's Second The acceleration produced by a force on an objectLaw of Motion is directly proportional to the magnitude of the netforce applied and is inversely proportional to the

mass of the object. The direction of theacceleration is the same as that of the net force.

. . .Weight, WWeight, W = Lift, U Thrust, F = drag, G

When the forces acting on an object are notbalanced, there must be a net force actingon it.The net force is known as the unbalancedforce or the resultant force.Effect: Can cause a body tochange it state at rest (an object willaccelerate

- change it state of motion (a movingobject will decelerate or change itsdirection

Force = Mass x AccelerationF=mahen a net force, F, actson a mass, m it causesan acceleration, a.



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Relationship auF abetween a & F The acceleration, a, is directly

L Froportional to the applied force, F.Relationship 1 aaoc- L J _etween a and mm The acceleration of an object isinversely proportional to the mass, mExperiment to Find The Relationship between Force, Mass & AccelerationRelationsh iP a&F a&mbetweenSituation I~ ; I ~ ~~. . 1 f f i l- f - ; ; ] I --! II.". !!. r i Lr=l-l " ~ . . , - -... t -v ~ ":::...Both men are pushing the Both men exerted the same

same mass but man A strength. But man B movesputs greater effort. So he faster than man A.moves faster.

Inference The acceleration The acceleration producedproduced by an object by an object depends ondepends on the net force the massapplied to it.

Hypothesis The acceleration of the The acceleration of theobject increases when object decreases when thethe force applied mass of the objectincreases increases

Variables:Manipulated: Force MassResponding Acceleration AccelerationConstant Mass ForceApparatus Ticker tape and elastic cords, ticker timer, trolleys,and Material power supply and friction compensated runway and

meter ruler.www.physics4spm.com 17


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T i k " ~R e IQ ItS !andleeT llmer .Tidker '!ape J E l' r d ! s

l~ , - _0>-1' ~ 1 > 1 _ J _ oo-< om ", .. < oIn rn w " r.-~r o l l e y. . . . . . 'Procedure: An elastic cord is hooked An elastic cord is hooked- Controlling over the trolley. The over a trolley. The elasticmanipulated elastic cord is stretched cord is stretched until thevariables. until the end of the end of the trolley. The

trolley. The trolley is trolley is pulled down thepulled down the runway runway with the elasticwith the elastic cord cord being kept stretchedbeing kept stretched by by the same amount ofthe same amount of force force

- Controlling Determine the Determine the accelerationresponding acceleration by analyzing by analyzing the tickervariables. the ticker tape. tape.

Acceleration a = v - u Acceleration a = v - ut t

Repeat the experiment by Repeat the experiment by- Repeating using two, three, four using two, three, four andexperiment. and five elastic cords five trolleys.Recording F o r c e , F I N o o f e la s t ic ~ ~ I ~ J ~ w i i $ i i i l i m , ~~Midata c o r d I m s J f l Q ~ t r o l l ~ l i m I~

Analysing a aLFCJ L,CJata mwww.physics4spm.com 18


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Discuss your physics question online at www.physics4spm.com1. What force is required to move a2 kg object with an accelerationof 3 m S2, if

(a) the object is on a smoothsurface?

(b) The object is on a surface wherethe average force of frictionacting on the object is 2 N?

2. Ali applies a force of 50 N tomove a 10 kg table at a constantvelocity. What is the frictionalforce acting on the table?

3. A car of mass 1200 kg travelingat 20 m/s is brought to rest over adistance of 30 m. Find(a) the average deceleration,

(b) the average braking force.

4. Which of the following systemswill produce maximumacceleration?A m

I Q Q i N . 1 ' . " - ' " ' ~ _ ' . 1 . :e Q N. :- ~";"-~:'.~~ .

C mSN~' - . t " " " : \ _ '=.N~' ~?-~-~C

2.6 IMPULSE AND IMPULSIVE FORCEImpulse The change of momentum m = mass

mv-mu u = initialUnit: kgms1 or Ns velocity

Impulsive The rate of change of momentum in a v = finalForce collision or explosion velocitymv - mu t = timetUnit = N

Effect of Impulsive force Longer period of time -olmpulelvetime is inversely force decrease

proportional to Shorter period of time ~Impulsivetime of contact force increasewww.physics4spm.com 19


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Situations for Reducin Impulsive Force in SportsSituations Explanation

Thick mattress with soft surfaces are used inevents such as high jump so that the timeinterval of impact on landing is extended, thusreducing the impulsive force. This can preventinjuries to the participants.

Goal keepers will wear gloves to increase thecollision time. This will reduce the impulsiveforce.

A high jumper will bend his legs upon landing.This is to increase the time of impact in order toreduce the impulsive force acting on his legs.This will reduce the chance of getting seriousinu .A baseball player must catch the ball in thedirection of the motion of the ball. Moving hishand backwards when catching the ballprolongs the time for the momentum to changeso as to reduce the impulsive force.

Situation of Increasin Impulsive ForceSituations Explanation

'

A karate expert can break a thick wooden slabwith his bare hand that moves at a very fastspeed. The short impact time results in a largeimpulsive force on the wooden slab.

www.physics4spm.com

A massive hammer head moving at a fastspeed is brought to rest upon hitting the nail.The large change in momentum within a shorttime interval produces a large impulsive forcewhich drives the nail into the wood.

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A football must have enough air pressure in itso the contact time is short. The impulsiveforce acted on the ball will be bigger and theball will move faster and further.

Pestle and mortar are made of stone. When apestle is used to pound chilies the hardsurfaces of both the pestle and mortar causethe pestle to be stopped in a very short time. Alarge impulsive force is resulted and thuscauses these spices to be crushed easily.

Example 1A 60 kg resident jumps from the firstfloor of a burning house. Hisvelocity just before landing on theground is 6ms",(a) Calculate the impulse when his

legs hit the ground.(b) What is the impulsive force on

the resident's legs if he bendsupon landing and takes 0.5 s tostop?

(c) What is the impulsive force onthe resident's legs if he does notbend and stops in 0.05 s?

(d) What is the advantage of bendinghis legs upon landing?

Example 2Rooney kicks a ball with a force of1500 N. The time of contact of hisboot with the ball is 0.01 s. What isthe impulse delivered to the ball? Ifthe mass of the ball is 0.5 kg, what isthe velocity of the ball?



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2.7 SAFETY VEHICLE

Component FunctionHeadrest To reduce the inertia effect of the driver's head.Air bag Absorbing impact by increasing the amount of time the

driver's head to come to the steering. So that theimpulsive force can be reduce

Windscreen The protect the driverCrumple Can be compressed during accident. So it can increasezone the amount of time the car takes to come to a complete

stop. So it can reduce the impulsive force.Front Absorb the shock from the accident. Made from steel,bumper aluminium, plastic or rubber.ABS Enables drivers to quickly stop the car without causing

the brakes to lock.Side impact Can be compressed during accident. So it can increasebar the amount of time the car takes to come to a complete

stop. So it can reduce the impulsive force.Seat belt To reduce the inertia effect by avoiding the driver from

thrown forward.



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2.8 GRAVITYGravitational Objects fall because they are pulled towards the EarthForce by the force of gravity.

This force is known as the pull of gravity or the earth'sgravitational force.

Free fall

The earth's gravitational force tends to pull everythingtowards its centre.

~ An object is falling freely when it is falling under theforce of gravity only.

~ A piece of paper does not fall freely because its fall isaffected by air resistance.~ An object falls freely only in vacuum. The absence ofair means there is no air resistance to oppose themotion of the object.

~ In vacuum, both light and heavy objects fall freely.They fall with the same acceleration ie. Theacceleration due to

Accelerationdue togravity, g

~ Objects dropped under the influence of the pull ofgravity with constant acceleration.~ This acceleration is known as the gravitationalacceleration. g.

~ The standard value of the gravitational acceleration,g is 9.81 m S2. The value of g is often taken to be 10m S-2 for simplicity.

~ The magnitude of the acceleration due to gravitydepends on the strength of the gravitational field.

Gravitationalfield

The gravitational field is the region around the earth inwhich an object experiences a force towards the centreof the earth. This force is the gravitational attractionbetween the object and the earth.The gravitational field strength is defined as thegravitational force which acts on a mass of 1 kilogram.g = F Its unit is N kg-1m



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Gravitational field strength, g = 10 N kg"Acceleration due to gravity, g = 10m S-2The approximate value of g can therefore be writteneither as 10m S-2 or as 10 N kg-1

Weight The gravitational force acting on the object.Weight = mass x gravitational accelerationW = mg 81 unit: Newton, N and it is a vector quantity

Comparisonbetweenweight &mass

Thedifferencebetween afall in air anda free fall ina vacuum ofa coin and afeather.Both thecoin and thefeather arereleasedsimulta-neously fromthe sameheight.

Mass WeightThe mass of an object isthe amount of matter inthe object

The weight of an object isthe force of gravity actingon the object.

Constant everywhere Varies with the magnitudeof gravitational fieldstrength, g of the location

A scalar quantity A vector quantityA base quantity A derived quantity81 unit: kg 81 unit: Newton, N

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At vacuum state:There is no air resistance.The coin and the featherwill fall freely.Only gravitational forceacted on the objects.Both will fall at the sametime.

I I_ ,?"o

At normal state:Both coin and feather willfall because of gravitationalforce.Air resistance effected bythe surface area of a fallenobject.The feather that has largearea will have more airresistance.The coin will fall at first.

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Two steel

spheres arefalling undergravity. Thetwo spheresare droppedat the sametime fromthe sameheight.

M ti hf f

(a)The two sphere arefalling with anacceleration.The distance betweentwo successive imagesof the sphere increasesshowing that the twospheres are falling withincreasing velocity;falling with anacceleration.

(b)The two spheres arefalling down with thesame accelerationThe two spheres are atthe same level at alltimes. Thus, a heavyobject and a light objectfall with the samegravitationalacceleration.Gravitationalacceleration isindependent of mass.

o Ion grapl or ree a o 'JecFree fall object Object thrown upward Object thrown upwardand fall

v v

L, L, va a tLt Ltf II bl t

Example 1A coconut takes 2.0 s to fall to theground. What is(a) its speed when it strikes theground(b) the height of the coconut tree.



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2.9 FORCES IN EQUILIBRIUM

Newton's3rd Law

Forces inEquilibrium

When an object is in equilibrium, the resultant force actingon it is zero.The object will either be

1. at rest2. move with constant velocity.

Examples

--0+W'=

Resultant A single force that represents the combined effect of two ofForce more forces in magnitude and direction.

Addition of Forces

O = = + FResultant force, F = +"'Fl

r ' .. 2Q .. Fl Resultant force, F = +F24www.physics4spm.com 26


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Two forces acting at a point at an angle [Parallelogram method]

STEP 1 : Using ruler and protractor,draw the two forces F1and F2from apoint.

F~

STEP 2Complete the parallelogram

Resolution ofForces

A force F can be resolved into componentswhich are perpendicular to each other:(a) horizontal component, Fxb vertical component, Fy

F ,

Inclined Plane~

STEP 3Draw the diagonal of theparallelogram. The diagonalrepresent the resultant force, F inmagnitude and direction.

scale: 1 cm = .

Component of weight parallel to the plane= mg sin 9Component of weight normal to the plane= m cos 9

F,Fx= F cos 9Fy= F sin 9www.physics4spm.com 27


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find the resultant force

(d) (e)

LiftStationary Lift

DLift accelerate upward

taLift acceleratedownward

Resultant Force = Resultant Force = Resultant Force =The reading ofweighing scale = The reading ofweighing scale = The reading ofweighing scale =www.physics4spm.com 28


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P IIey'.h J [ ,Frictio~31 ]C force,Z,N ~(~ C .

~\j ~~ 3 kg

~1. Find theresultant force, F2. Find themoving mass,m3. Find theacceleration ,a

4. Find stringtension, T



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2.10WORK, ENERGY, POWER& EFFICIENCYWork

The 81 unit of work is thejoule, J

---1m- ....1 N , - - - - - - . '__?_,J I,

Work done is the product of an applied forceand the displacement of an object in thedirection of the applied forceW = Fs W =work, F = force s = displacement

1 joule of work is done when a force of 1 Nmoves an object 1 m in the direction of theforce

Calculation of WorkThe displacement, s of the object is in the

direction of the force, F

W=Fs

Example 1A boy pushing his bicyclewith a force of 25 Nthrough a distance of 3 m.

Calculate the work doneby the boy.

s

The displacement, s of thobject is not in thedirection of the force, F

D W = (F cos 9) sExample 3A man is pulling a crate of fishalong the floor with a force of40 N through a distance of 6 m

What is the work done inpulling the crate?

W=FsExample 2A girl is lifting up a 3 kgflower pot steadily to aheight of 0.4 m.

What is the work done bythe girl?



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Discuss your physics question online at www.physics4spm.comNo work is done when:The object is stationary~'\J;I

. .A student carrying his bag A waiter is carrying a traywhile waiting at the bus of food and walkingstop

The direction of motion ofthe object is perpendicularto that of the applied force.

No force is applied on theobject in the direction ofdisplacement (the objectmoves because of itsown inertia)A satellite orbiting inspace. There is nofriction in space. Noforce is acting in thedirection of movement ofthe satellite.

Con Definition Formula & UnitPower The rate at which work is

done, or the amount of workdone per second.

p=Wt

p = power, W = work Ien t = time

Energy

KineticEnergy

~ Energy is the capacity to do work.~ An object that can do work has energy~ Work is done because a force is applied and theobjects move. This is accompanied by the transferof energy from one object to another object.

~ Therefore, when work is done, energy is transferredfrom one object to another.~ The work done is equal to the amount of energytransferred.

Kinetic energy is the energy of m =massan object due to its motion. v =velocity

Gravitational potential energyis the energy of an object dueto its higher position in thegravitational field.

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m =massh = heightg = gravitationalacceleration

E= mgh

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Energy can be changed from one form to another, butit cannot be created or destroyed.The energy can be transformed from one form toanother, total energy in a system is constant.Total energy before = total energy after

Principle ofConservationof Energy

Example 4A worker is pulling a wooden block ofweight,W,with a force of P along afritionless plank at height of h. Thedistance traveled by the block is x.Calculate the work done by the worker topull the block.

w

Example 6A stone is thrown upward with initialvelocity of 20 ms", What is the maximumheight which can be reached by thestone?

Example 5A student of mass m is climbing up aflight of stairs which has the height of h.He takes t seconds ..

Example 8www.physics4spm.com

What is the power of the student?

Example 7

A boll is released from point A of height0.8 m so that it can roll along a curvefrictionless track. What is the velocity ofthe ball when it reaches point B?

Example 932


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1.5m6ms-1 _ _ _ _ 1 _

x

2.5m1 V1.0m____ AzA trolley is released from rest at point Xalong a frictionless track. What is thevelocity of the trolley at point Y?

Example 10A boy of mass 20 kg sits at the top of aconcrete slide of height 2.5 m. When heslides down the slope, he does work toovercome friction of 140 J. What is hisvelocity at the end of the slope?

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A ball moves upwards along a frictionlesstrack of height 1.5 m with a velocity of6 ms",What is its velocity at point B?

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2.12 ELASTICITYElasticity

Stretching a wire by anexternal force:

A property of matter that enables an object toreturn to its original size and shape when theforce that was acting on it is removed.

No external force is applied.Molecules are at their equilibrium separation.Intermolecular force is equal zero.

Compressing a solid causes its molecules to bedisplaced closer to each other.Repulsive intermolecular force acts to push themolecules back to their original positions.

Stretching a solid causes its molecules to bedisplaced away from each other.Attractive intermolecular force acts to pull backthe molecules to their original positions.

~ Its molecules are slightly displaced away fromone another.

~ Strong attractive forces act between themolecules to oppose the stretchingWhen the external force is removed:

~ The attractive intermolecular forces bring themolecules back to their equilibrium separation.

~ The wire returns to its original position



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Hooke's Law The extension of a spring is directly proportionalto the applied force provided the elastic limit isnot exceeded.F = kxF= force on the springx = extensionk = force constant of the spring

Force extension graphFIN

"-----------+ x( em)

The elastic limit of aspringfJHI~,: elasticlimit

Force constant of thespring, k

F ( N ),75

12.5

Based on the graph:Relationship between F & x :F is directly proportional to xThe gradient of the graph represent = forceconstant of the spring, kArea under the graph equal to the work done toextent the spring:= elastic potential energy =% Fx =% kx2

The maximum force that can be applied to aspring such that the spring will be able to berestored to its original length when the force isremoved.If a force stretches a spring beyond its elasticlimit, the spring cannot return to its original lengtheven though the force no longer acts on it.The Hooke's law is not obeyed anymore.The force required to produce one unit ofextension of the spring.k = F unit N m" or Nern" or N rnm"xk is a measurement of the stiffness of the spring~ The spring with a larger force constant isharder to extend and is said to be more stiff.

~ A spring with a smaller force constant is easierto extend and is said to be less stiff or softer.



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Factors that effect elasticitFactor Change in factor How does it affects the

elasticitLength Less elastic

More elasticDiameter of spring More elasticwire Lar er diameter Less elasticDiameter spring Smaller diameter Less elastic

Lar er diameter More elastic

The same load is applied to eachspring.Tension in each spring = WExtension of each spring = xTotal extension = 2xIf n springs are used:The total extension = nx

Type of material

Example 1The original length ofeach spring is 10 cm.With a load of 10 g, theextension of eachspring is 2 cm.What is the length of thespring system for (a),(b) and (c)?

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Arran ement of the sprin

Springs made of different materialsElasticity changes according to the type ofmaterial

The load is shared equally among thesprings.Tension in each spring = w2Extension of each spring = x2If n springs are used:The total extension = xn

C d ]

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SECTION AQUESTION 1Figure 1.1 shows a car moving along a straight line but hilly road.

Figure 1.1Figure 1.2 shows how the velocity of the carvaries with time as it travels from A to E. The cartravels at 60 krnh" from A to B for two minutes.

Figure 1.2(a) Describe the acceleration of the car as it

travels from A to E. 2m

(b) Compare the resultant force as it travelsalong AB and CD. 1

m(c) Give a reason to your answer in (b)

1m

(d) Calculate the distance AB

2m

(e) The velocity of a car increases if theforce exerted on the accelerator of a carincreases. Explain why the velocity of thecar increases from D to E although theforce on the accelerator of the car is thesame as a long C to D. 2

mwww.physics4spm.com 38


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QUESTION 2 (SPM 1999)



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QUESTION 3 ( SPM 2000)Figure 2

Figure 2 shows a car of mass 1 OOOkgmoving astraight but hilly road. QRST and TU is the partof the hill that have constant slope where theslope of QRST is higher that the slope of TU. Thefrictional force that acts along QRSTU is 2 OOON.The velocity if the car at P is80kmh-1 and takes 3 minutes to move from pointP to Q. The motion of the car alongPQRSTU represent by a velocity-time graph inFigure 3.

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(e) Why is it necessarycapacity limit for thA ~ tI~led from

Lumpur at 9:00 pm. Thpass~!1g~.~.!!1.\~.~..~':I.~.mass of the bus with tand iliea;;era~iefriciiobus \ i .~~.~n~..~~~ ~ . c : t .~rThe ~':I~.IT I .9 .Y~~.~~.~Y~r~Kota Bharu before stopoat 12:00 mid night onhour later the bus conKuala Lumpur with aveThe bus arrived at 6:00 a(a) Put in a table all theinvolved in the infor

two groups.

(b) Calculate the total dthe bus.

(c) Sketch a distance-timthe motion of the bu

(d)(i) What is the value ofthe bus when it mov

speed?( u ) .............................

Give a reason for th

40.............................


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(a) Classify the physical quantity into two groups.

(b) From the graph in Figure 3, explain the acceleration of the car frompoint P to S.

(c) (i) Compare the resultant force of the car when the move along PQ andST.

(ii) State a reason for your answer in c(i)

(d) Calculate the distance form point P to Q

QUESTION4 (SPM2002)Figure 3(i)Figure 3(ii)

Figure 3(i) shows a sky diver start to make a jump from an aircraft at acertain height. Figure 3(ii) shows a velocity-time graph for the skydiver atposition S, T, U, V and W from the earth surface.(a) (i) At which point the parachute start to open?

(ii) Give a reason for your answer in (a)(i)

(b) Calculate the acceleration of the diver at ST.



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(c) Sketch an acceleration-time graph for the motion of the skydiver apoint S, T, U, V and W at the space below.s T u v w

(d) Suggest one way that can the skydiver apply to reduce injuries on hisleg during landing. Explain your answer.

QUESTION5 (SPM 1988)

~/-

1 iz f bFigure 4(i)



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Figure 4(i) show a gun fires a bullet of mass 5g to an object.(a) (i) What happen to the gun during the shot?

1m(ii) Explain your answer in (a)(i)

1m

(b) The bullet shot the object of mass O.495kg.(i) If the bullet speed is 400ms1, what is the momentum of thebullet?

2m(ii) What is speed of the object after the bullet obscured into theobject afterthe gunshot? 2m

(c) The object and the bullet that obscured in the object aloft at amaximum height of H, as shown in Figure 4(ii).

2m I1 : - - - - - - - - - - - - - ~ - -G-------------------------t. _Figure 4(ii)

(i) What is the value of kinetic energy of the object together withthe bulletinside the object? 2m



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(ii) Calculate maximum height, H achieved by the object?2m

1m(iii) In real situation it is possible to achieved maximum height, H.Why?

QUESTION 6 (SPM 1994)Figure 5 shows a man standing on a stationary boat. He then jumps out ofthe boat onto the jetty. The boat moves a way from the jetty as he jumps.

Figure 5

(a) State the physics principle that is involved in the movement of the boaas the man jumps onto the jetty.

(b) Explain why the boat moves away from the jetty when the man jumps.

(c) The mass of the man is 50 kg and he jumps at a velocity 2ms1 Thmass of the boat is 20kg. Calculate the velocity of the boat as the majumps.

(d) Name one application of the physics principle stated in (a) in aexploration of outer space.....................................................................................................



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Linear Motion Physics

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