02. Force and Motion 2

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2.1 LINEAR MOTION

PhysicalQuantity

Definition, Quantity, Symbol and unit

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

Displacement,l

(a) The distance in a specified direction.(b) the distance between two locations measured along

the shortest path connecting them in a specificdirection.

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

Quantity: vector SI unit: meter (m)

Speed,vSpeed is the rate of change of distance

Speed = Distance traveled Time taken

Quantity: scalar SI 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 SI unit: m s-1

Averagespeed

v = Total distant traveled, sTotal time taken , t

Averagevelocity

v = Displacement, s Time taken, t

Example: A car moves atan average speed /velocity of 20 ms-1

On average, the car movesa distance / displacementof 20 m in 1 second for thewhole journey.

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Uniformspeed

Speed that remains the same in magnitude regardless ofits direction.

Uniform

velocity

Velocity that remains the same in magnitude and

direction.

An object hasa non-uniformvelocity if:

(a) the direction of motion changes or the motion isnot linear.

(b) The magnitude of its velocity changes.

Acceleration,a

t

uv

a

=

unit : ms-2

acceleration

is positive

When the velocity of an object changes, the object issaid to be accelerating.

Acceleration is defined as the rate of change of

velocity.

Acceleration = Change in velocityTime taken

= final velocity, v initial velocity, uTime taken, t

The velocity of an object increases from an initialvelocity, u, to a higher final velocity, v

Deceleration

accelerationis negative.

The rate of decrease in speed in a specified direction.

The velocity of an object decreases from an initialvelocity, u, to a lower final velocity, v.

Zeroacceleration

An object moving at a constants velocity, that is, themagnitude and direction of its velocity remainunchanged is not accelerating

Constantacceleration

Velocity increases at a uniform rate.When a car moves at a constant or uniform accelerationof 5 ms-2, its velocity increases by 5 ms-1for 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 / at rest5. negative velocity = object moves at opposite

direction6. zero acceleration = constant velocity7. negative acceleration = deceleration

Comparisons between distanceand displacement.

Distance Displacement

Total path lengthtraveled fromone location toanother

The distancebetween twolocationsmeasured alongthe shortest pathconnecting themin specificdirection

Scalar quantity Vector quantity

It has magnitude

but no direction

It has both

magnitude anddirection

SI unit meter SI unit : meter

Comparisons between speed andvelocity

Speed Velocity

The rate of changeof distance The rate of changeof displacement

Scalar quantity Vector quantity

It has magnitudebut no direction

It has bothmagnitude anddirection

SI unit : m s-1 SI unit : m s-1

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

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

..to the left.3. A steady acceleration of 4 ms-2= Speed goes up by 4 m/s every

.4. A steady deceleration of 4 ms-2= speed goes .. by 4 m/s

every .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.

(a) What is Rahims 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 distance

traveled by Rahim?

(ii) what is Rahims totaldisplacement from hishouse?

Example 2Every morning Amirul walks toAhmads house which is situated80 m to the east of Amiruls house.They then walk towards theirschool which is 60 m to the southof Ahmads house.

(a) What is the distance traveledby Amirul and hisdisplacement from hishouse?

(b) If the total time taken byAmirul to travel from his

house to Ahmads 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?

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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 / 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 the

plane?

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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Distance between the dotsdecrease uniformly

The velocity of the object isdecreasing uniformly

The object is experiencinguniform / constantdeceleration

Example 6The diagram above shows a ticker tapechart 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 change

from initial velocity to final velocity?(f) What is the acceleration of the

object.

THE EQUATIONS OF MOTION

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


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2.2 MOTION GRAPHS

DISPLACEMENT TIMEGRAPH

Velocity is obtained from the gradient ofthe graph.

A B : gradient of the graph is +ve and

constant 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.

Area below

graph

Distance / displacement

Positivegradient

Constant Acceleration(A B)

Negativegradient

Constant Deceleration(C D)

VELOCITY-TIME GRAPH

Zerogradient

Constant velocity / zeroacceleration(B C)

GRAPH s versus t v versus t a versus t

Zerovelocity

Negativevelocity

Constantvelocity

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2.3 INERTIA

Inertia The inertia of an object is the tendency of theobject to remain at rest or, if moving, to continueits motion.

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

Relation betweeninertia and mass

The larger the mass, the larger the inertia

SITUATIONS INVOLVING INERTIA

SITUATION EXPLAINATION

When the cardboard is pulled away quickly, the

coin 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, the

sauce 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, thepassengers moved forward.

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 its

downward 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 the

head 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.

Relationshipbetween 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 empty 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 an

attempt 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 MOMENTUM

Definition Momentum = Mass x velocity = mvSI unit: kg ms-1

Principle ofConservation ofMomentum

In the absence of an external force, the totalmomentum of a system remains unchanged.

Elastic Collision Inelastic collision

Both objects move

independently at theirrespective velocities after thecollision.

Momentum is conserved.

Kinetic energy is conserved. Total energy is conserved.

The two objects combine and

move together with acommon velocity after thecollision.

Momentum is conserved.

Kinetic energy is notconserved.

Total energy is conserved.

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Total Momentum Before = totalmomentum After

m1u1+ m2u2= m1v1+ m2v2

Total Momentum Before = TotalMomentum After

m1u1+ m2u2= (m1+ m2) v

Explosion

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

Total Momentumbefore collisionIs zero

Total Momentumafter collision :m1v1+ m2v2

From the law of conservation ofmomentum:Total Momentum = Total MomentumBefore collision after collision

0 = m1v1+ m2v2m1v1= - m2v2

-ve sign means opposite direction

EXAMPLES OF EXPLOSION (Principle Of Conservation Of Momentum)

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.


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The launching of rocket Mixture of hydrogen and oxygen fuels burn

explosively 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 rocketupwards.

In a swamp area, a fan boat is used.

The fan produces a high speed movement oair backward. This produces a large

momentum 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. after0 =Mom water + Mom squid0 = mwvw+ msvs

-mwvw= msvsThe magnitude of the momentum of water andsquid are equal but opposite direction.This causes the squid to jet forward.

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Example

Car A of mass 1000 kg moving at20 ms-1collides with a car B of mass1200 kg moving at 10 m s-1in samedirection. If the car B is shuntedforwards at 15 m s-1by the impact,what is the velocity, v, of the car Aimmediately after the crash?

Example

Before collision After collision

MA = 4 kg MB = 2 kgUA = 10 m/s to the leftUB = 8 m/s to the rightVB = 4 m/s to the left.

Calculate the value of VA.

Example

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 move

together. What is the velocity ofboth vehicles immediately aftercollision?

Example

A 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 FORCE

Example:Balanced ForceWhen 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 constant

velocity [ a = 0]

Weight, 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.

Unbalanced Force/Resultant Force

Effect : Can cause a body tochange it state at rest (an object will

accelerate- change it state of motion (a moving

object will decelerate or change itsdirection)

Force, Mass & Acceleration

The acceleration produced by a force on an object

is directly proportional to the magnitude of the netforce applied and is inversely proportional to themass of the object. The direction of theacceleration is the same as that of the net force.

Newtons Second

Law of Motion

When a net force, F, actson a mass, m it causesan acceleration, a.

Force = Mass x AccelerationF = ma

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Relationshipbetween a & F

a FThe acceleration, a, is directlyproportional to the applied force, F.

Relationshipbetween a andm

ma

1

The acceleration of an object isinversely proportional to the mass,

Experiment to Find The Relationship between Force, Mass & Acceleration

Relationship

between

a & F a & m

Situation

Both men are pushing thesame mass but man Aputs greater effort. So hemoves faster.

Both men exerted the samestrength. But man B movesfaster than man A.

Inference The acceleration

produced by an objectdepends on the net forceapplied to it.

The acceleration produced

by an object depends onthe mass

Hypothesis The acceleration of theobject increases whenthe force appliedincreases

The acceleration of theobject decreases when themass of the objectincreases

Variables:Manipulated :Responding :Constant :

ForceAccelerationMass

MassAccelerationForce

Apparatusand Material

Ticker tape and elastic cords, ticker timer, trolleys,power supply and friction compensated runway andmeter ruler.

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An elastic cord is hookedover the trolley. Theelastic cord is stretcheduntil the end of thetrolley. The trolley ispulled down the runwaywith the elastic cordbeing kept stretched bythe same amount of force

An elastic cord is hookedover a trolley. The elasticcord is stretched until theend of the trolley. Thetrolley is pulled down therunway with the elasticcord being kept stretchedby the same amount offorce

Determine theacceleration by analyzingthe ticker tape.

Accelerationt

uva

=

Determine the accelerationby analyzing the tickertape.

Accelerationt

uva

=

Procedure :-Controlling

manipulatedvariables.

-Controllingrespondingvariables.

-Repeatingexperiment.

Repeat the experiment byusing two , three, fourand five elastic cords

Repeat the experiment byusing two, three, four andfive trolleys.

Recordingdata

Analysingdata

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1. What force is required to move a2 kg object with an accelerationof 3 m s-2, 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 a

distance of 30 m. Find(a) the average deceleration,(b) the average braking force.

4. Which of the following systemswill produce maximum

acceleration?

2.6 IMPULSE AND IMPULSIVE FORCE

Impulse The change of momentummv - muUnit : kgms-1 or Ns

ImpulsiveForce

The rate of change of momentum in acollision or explosion

Unit = N

m = massu = initialvelocityv = finalvelocityt = time

Longer period of time Impulsiveforce decrease

Effect oftime

Impulsive forceis inverselyproportional totime of contact

Shorter period of time Impulsiveforce increase

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Situations for Reducing Impulsive Force in Sports

Situations Explanation

Thick mattress with soft surfaces are used inevents such as high jump so that the time

interval 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 seriousinjury.

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 change

so as to reduce the impulsive force.

Situation of Increasing Impulsive Force

Situations 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.

A massive hammer head moving at a fast

speed 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 6 ms-1.(a) Calculate the impulse when his

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

the residents legs if he bendsupon landing and takes 0.5 s to

stop?(c) What is the impulsive force on

the residents 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 of

1500 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 drivers head.

Air bag Absorbing impact by increasing the amount of time thedrivers head to come to the steering. So that theimpulsive force can be reduce

Windscreen The protect the driver

Crumplezone

Can be compressed during accident. So it can increasethe amount of time the car takes to come to a completestop. So it can reduce the impulsive force.

Frontbumper Absorb the shock from the accident. Made from steel,aluminium, plastic or rubber.

ABS Enables drivers to quickly stop the car without causingthe brakes to lock.

Side impactbar

Can be compressed during accident. So it can increasethe amount of time the car takes to come to a completestop. So it can reduce the impulsive force.

Seat belt To reduce the inertia effect by avoiding the driver fromthrown forward.

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2.8 GRAVITY

GravitationalForce

Objects fall because they are pulled towards the Earthby the force of gravity.

This force is known as the pull of gravity or the earthsgravitational force.

The earths gravitational force tends to pull everythingtowards its centre.

Free fall

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 gravity, g.

Acceleration

due togravity, g

Objects dropped under the influence of the pull of

gravity with constant acceleration. This acceleration is known as the gravitational

acceleration, g.

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

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

Gravitational

field

The gravitational field is the region around the earth in

which 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.

m

Fg = Its unit is N kg-1.

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Gravitational field strength, g = 10 N kg-1

Acceleration due to gravity, g = 10 m s-2

The approximate value of g can therefore be writteneither as 10 m s-2 or as 10 N kg-1.

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

Comparisonbetweenweight &mass

Mass Weight

The 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 quantity

A base quantity A derived quantity

SI unit: kg SI unit : Newton, N

Thedifferencebetween a

fall in air anda free fall ina vacuum ofa coin and afeather.

Both thecoin and thefeather arereleasedsimulta-neously fromthe sameheight.

At vacuum state:There is no air resistance.The coin and the feather

will fall freely.Only gravitational forceacted on the objects.Both will fall at the sametime.

At normal state:Both coin and feather willfall because of gravitational

force.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 steelspheres arefalling undergravity. Thetwo spheresare droppedat the same

time fromthe sameheight.

(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 acceleration

The two spheres are atthe same level at alltimes. Thus, a heavyobject and a light objectfall with the samegravitationalacceleration.

Gravitationalacceleration is

independent of mass.

Motion graph for free fall object

Free fall object Object thrown upward Object thrown upwardand fall

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

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.

Newtons3rdLaw

Examples( Label the forces acted on the objects)

ResultantForce

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

Addition of Forces

Resultant force, F = ____ + ____

Resultant force, F = ____ + ____

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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.

STEP 2Complete the parallelogram

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

scale: 1 cm =

Resolution ofForces

A force F can be resolved into componentswhich are perpendicularto each other:(a) horizontal component , FX(b) vertical component, FY

Fx= F cos

Fy= F sin

Inclined Plane

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

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find the resultant force

(d) (e)

Lift

Stationary Lift Lift accelerate upward Lift acceleratedownward

Resultant Force = Resultant Force = Resultant Force =

The reading ofweighing scale =



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Pulley

1. Find theresultant force, F

2. Find themoving mass,m

3. Find theacceleration,a

4. Find stringtension, T

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2.10 WORK, ENERGY, POWER & EFFICIENCY

Work Work done is the product of an applied forceand the displacement of an object in thedirection of the applied force

W = Fs W = work, F = force s = displacement

The SI unit of work is thejoule, J 1 joule of work is done when a force of 1 N

moves an object 1 m in the direction of theforce

Calculation of Work

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The displacement, s of the object is in the

direction of the force, F

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

W = Fs

W = F s

W = (F cos ) s

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

Calculate the work doneby the boy.

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

What is the work done bythe girl?

Example 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?

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No work is done when:

The object is stationary

A student carrying his bagwhile waiting at the busstop

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

A waiter is carrying a trayof food and walking

No force is applied on theobject in the direction ofdisplacement (the objectmoves because of its

own inertia)A satellite orbiting inspace. There is nofriction in space. Noforce is acting in thedirection of movement ofthe satellite.

Concept Definition Formula & Unit

Power The rate at which work isdone, or the amount of workdone per second.

t

WP =

p = power, W = work /energy t = time

Energy

Energy is the capacity to do work. An object that can do work has energy Work is done because a force is applied and the

objects 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.

PotentialEnergy Gravitational potential energy

is the energy of an object dueto its higher position in thegravitational field.

m = massh = heightg = gravitational

acceleration

E = mgh

KineticEnergy

Kinetic energy is the energy ofan object due to its motion.

m = massv = velocity

E = mv2

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Principle ofConservationof Energy

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

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.

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

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What is the power of the student?

Example 6A stone is thrown upward with initial

velocity of 20 ms-1

. What is the maximumheight which can be reached by thestone?

Example 7

A boll is released from point A of height

0.8 m so that it can roll along a curvefrictionless track. What is the velocity ofthe ball when it reaches point B?

Example 8 Example 9


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A trolley is released from rest at point Xalong a frictionless track. What is thevelocity of the trolley at point Y?

A ball moves upwards along a frictionlesstrack of height 1.5 m with a velocity of

6 ms-1

. What is its velocity at point B?

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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2.12 ELASTICITY

Elasticity 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.

Stretching a wire by anexternal force:

Its molecules are slightly displaced away fromone another.

Strong attractive forces act between the

molecules to oppose the stretchingWhen the external force is removed: The attractive intermolecular forces bring the

molecules back to their equilibrium separation The wire returns to its original position

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Hookes Law The extension of a spring is directly proportionalto the applied force provided the elastic limit isnot exceeded.

F = kx

F= force on the springx = extensionk = force constant of the spring

Force extension graph Based on the graph:Relationship between F & x :F is directly proportional to x

The gradient of the graph represent = forceconstant of the spring, k

Area under the graph equal to the work done toextent the spring:

= elastic potential energy = Fx = kx2

The elastic limit of a

spring

The maximum force that can be applied to a

spring 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 leven though the force no longer acts on it.

engt

The Hookes law is not obeyed anymore.

Force constant of thespring, k

The force required to produce one unit ofextension of the spring.

x

Fk = unit N m-1or N cm-1or N mm-1

k 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 elasticity

Factor Change in factor How does it affects theelasticity

Shorter spring Less elasticLength

Longer spring More elasticSmaller diameter More elasticDiameter of springwire Larger diameter Less elastic

Smaller diameter Less elasticDiameter spring

Larger diameter More elastic

Type of material Springs made of different materialsElasticity changes according to the type ofmaterial

Arrangement of the spring

In series

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

In parallel

The load is shared equally among thesprings.

Tension in each spring =2

W

Extension of each spring =2

x

If n springs are used:

The total extension =n

x

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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SECTION A

QUESTION 1

Figure 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 kmh-1from 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.

1m

(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.

2m


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...

QUESTION 2 (SPM 1999)


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A bus traveled from Lumpur at 9:00 pm. Thpassenger in the bus

mass of the bus with tand the average frictiobus tire and the road forThe bus moves at averaKota Bharu before stopat 12:00 mid night on hour later the bus coKuala Lumpur with aveThe bus arrived at 6:00 a

(a) Put in a table all theinvolved in the infotwo groups.

(b) Calculate the total dthe bus.

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

(d)

(i)

(ii)

What is the value ofthe bus when it movspeed?

Give a reason for th

(e) Why is it necessarycapacity limit for ththe bus?

QUESTION 3 ( SPM 2000)

Figure 2

Figure 2 shows a car of mass 1 000kg moving 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 000N.The velocity if the car at P is80kmh-1and takes 3 minutes to move from point

P to Q. The motion of the car alongPQRSTU represent by a velocity-time graph inFigure 3.


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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


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.

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

....


Figure 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?

..(ii) Explain your answer in (a)(i)

...

1m

1m

(b) The bullet shot the object of mass 0.495kg.

(i) If the bullet speed is 400ms-1, what is the momentum of the

bullet?

(ii) What is speed of the object after the bullet obscured into theobject after

the gunshot?

2m

2m

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

Figure 4(ii)

(i) What is the value of kinetic energy of the object together withthe bullet

inside the object? 2m

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

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

2m

1m


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 2ms-1. Th

mass of the boat is 20kg. Calculate the velocity of the boat as the ma

jumps.

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


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02. Force and Motion 2