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# Physics f4 chapter2

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• 1. Discuss your physics question online at www.physics4spm.com2.1 LINEAR MOTION Physical Definition, Quantity, Symbol and unit Quantity Distance is the total path length traveled from oneDistance, l location to another. Quantity: scalar SI unit: meter (m) (a) The distance in a specified direction. (b)the distance between two locations measured alongDisplacement, the shortest path connecting them in a specificl direction. (c) The distance of its final position from its initial position in a specified direction. Quantity: vector SI unit: meter (m) Speed is the rate of change of distanceSpeed,v Speed = Distance traveled Time taken Quantity: scalar SI unit: m s-1 Velocity is the rate of change of displacement.Velocity, v Velocity = Displacement Time taken Direction of velocity is the direction of displacement Quantity : Vector SI unit: m s-1Average v = Total distant traveled, s Example: A car moves atspeed Total time taken , t an average speed / velocity of 20 ms-1 On average, the car movesAverage v = Displacement, s a distance / displacementvelocity Time taken, t of 20 m in 1 second for the whole journey.www.physics4spm.com 1
• 2. Discuss your physics question online at www.physics4spm.comUniform 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. t Acceleration = Change in velocityunit : ms-2 Time taken = final velocity, v – initial velocity, u Time taken, taccelerationis positive • The velocity of an object increases from an initial velocity, u, to a higher final velocity, vDeceleration The rate of decrease in speed in a specified direction.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 ms-2, its velocity increases by 5 ms-1 for every second that the car is in motion.www.physics4spm.com 2
• 3. Discuss your physics question online at www.physics4spm.com 1. Constant = uniform 2. increasing velocity = acceleration 3. decreasing velocity = deceleration 4. zero velocity = object at stationary / at rest 5. negative velocity = object moves at opposite direction 6. zero acceleration = constant velocity 7. negative acceleration = decelerationComparisons between distance Comparisons between speed andand displacement. velocity Distance Displacement Speed VelocityTotal path length The distance The rate of change The rate of changetraveled from between two of distance of displacementone location to locations Scalar quantity Vector quantityanother measured along the shortest path It has magnitude It has both connecting them but no direction magnitude and in specific direction direction SI unit : m s-1 SI unit : m s-1Scalar quantity Vector quantityIt has magnitude It has bothbut no direction magnitude and directionSI unit meter SI unit : meterFill 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 = …………………………………………… …………………………………………………………………………………www.physics4spm.com 3
• 4. Discuss your physics question online at www.physics4spm.comExample 1 Example 2Every day Rahim walks from his Every morning Amirul walks tohouse to the junction which is 1.5 Ahmad’s house which is situatedkm from his house. Then he turns 80 m to the east of Amirul’s house.back and stops at warung Pak Din They then walk towards theirwhich is 0.5 km from his house. school which is 60 m to the south of Ahmad’s house. (a) What is the distance traveled by Amirul and his displacement from his house? (b)If the total time taken by Amirul to travel from his house to Ahmad’s house and then to school is 15 minutes,(a) What is Rahim’s displacement what is his speed and from his house velocity? • when he reaches the junction. • When he is at warung Pak Din.(b)After breakfast, Rahim walks back to his house. When he reaches home, (i) what is the total distance traveled by Rahim? (ii) what is Rahim’s total displacement from his house?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
• 5. Discuss your physics question online at www.physics4spm.comExample 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 speed of the plane? (b)What is the average velocity of the plane? (c) What is the difference between average speed and average 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 swww.physics4spm.com 5
• 6. Discuss your physics question online at www.physics4spm.comRelating displacement, velocity, acceleration and time using ticker tape. FORMULA VELOCITY Time, t = 10 dots x 0.02 s = 0.2 s displacement, s = x cm velocity = s = x cm t 0.2 s ACCELERATION Initial velocity, u = x1 0.2 final velocity, v = x2 0.2 elapse 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–u t TICKER TAPE AND TYPE OF MOTION CHARTS Constant velocity – slow moving Constant velocity – fast moving Distance between the dots increases uniformly the velocity is of the object is increasing uniformly The object is moving at a uniform / constant acceleration.www.physics4spm.com 6
• 7. Discuss your physics question online at www.physics4spm.com Distance between the dots decrease uniformly The velocity of the object is decreasing uniformly The object is experiencing uniform / constant decelerationExample 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 u = initial velocity v = final velocity t = time taken s = displacement a = constant acclerationwww.physics4spm.com 7
• 8. Discuss your physics question online at www.physics4spm.com2.2 MOTION GRAPHS DISPLACEMENT – TIME Velocity is obtained from the gradient of GRAPH the graph. A – B : gradient of the graph is +ve and constant ∴ velocity is constant. B – C : gradient of the graph = 0 ∴ the velocity = 0, object at rest. C – D : gradient of the graph –ve and constant. The velocity is negative and object moves in the opposite direction. VELOCITY-TIME GRAPH Area below Distance / displacement graph Positive Constant Acceleration gradient (A – B) Negative Constant Deceleration gradient (C – D) Zero Constant velocity / zero gradient acceleration (B – C) GRAPH s versus t v versus t a versus tZerovelocityNegativevelocityConstantvelocitywww.physics4spm.com 8
• 9. Discuss your physics question online at www.physics4spm.com GRAPH s versus t v versus t a versus tConstantaccelerationConstantdecelerationExample 6 Example 7 Contoh 11Based on the s – t graph above:(a) Calculate the velocity at (a) Calculate the acceleration at: (i) AB (ii) BC (iii) CD (i) JK (ii) KL (iii) LM(b) Describe the motion of the object at:(i) AB (ii) BC (iii) CD (b) Describe the motion of the object at: (i) JK (ii) KL (iii) LM(c)Find: (i) total distance (ii) total displacement Calculate the total displacement. (d) Calculate (i) the average speed (c) Calculate the average velocity. (ii) the average velocity of the moving particle.www.physics4spm.com 9
• 10. Discuss your physics question online at www.physics4spm.com2.3 INERTIAInertia The inertia of an object is the tendency of the object to remain at rest or, if moving, to continue its motion.Newton’s first law Every object continues in its state of rest or of uniform motion unless it is acted upon by an external force.Relation between The larger the mass, the larger the inertiainertia and mass 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 if the bottle is moved down fast with a sudden stop. The sauce inside the bottle moves together with the bottle. When the bottle stops suddenly, the sauce continue in its state of motion due to the effect of its inertia. Body moves forward when the car stops suddenly The passengers were in a state of motion when the car was moving. When the car stopped suddenly, the inertia in the passengers made them maintain their state of motion. Thus when the car stop, the passengers moved forward. A boy runs away from a cow in a zig zag motion. The cow has a large inertia making it difficult to change direction.www.physics4spm.com 10
• 11. Discuss your physics question online at www.physics4spm.com • The head of hammer is secured tightly to its handle by knocking one end of the handle, held vertically, on a hard surface. • This causes the hammer head to continue on its downward motion when the handle has been stopped, so that the top end of the handle is slotted deeper into the hammer head. • The drop of water on a wet umbrella will fall when the boy rotates the umbrella. • This is because the drop of water on the surface of the umbrella moves simultaneously as the umbrella is rotated. • When the umbrella stops rotating, the inertia of the drop of water will continue to maintain its motion.Ways to reduce 1. Safety in a car:the negative (a) Safety belt secure the driver to their seats.effects of inertia When the car stops suddenly, the seat belt provides the external force that prevents the driver from being thrown forward. (b)Headrest to prevent injuries to the neck during rear-end collisions. The inertia of the head tends to keep in its state of rest when the body is moved suddenly. (c) An air bag is fitted inside the steering wheel. It provides a cushion to prevent the driver from hitting the steering wheel or dashboard during a collision. 2. Furniture carried by a lorry normally are tied up together by string. When the lorry starts to move suddenly, the furniture are more difficult to fall off due to their inertia because their combined mass has increased.Relationship • Two empty buckets which are hung with ropebetween mass from a the ceiling.and inertia • One bucket is filled with sand while the other bucket is empty. • Then, both pails are pushed. • It is found that the empty bucket is easier towww.physics4spm.com 11
• 12. Discuss your physics question online at www.physics4spm.com push compared to the bucket with sand. • The bucket filled with sand offers more resistance to movement. • When both buckets are oscillating and an attempt is made to stop them, the bucket filled with sand offers more resistance to the hand (more difficult to bring to a standstill once it has started moving) • This shows that the heavier bucket offers a greater resistance to change from its state of rest or from its state of motion. • An object with a larger mass has a larger inertia.2.4 MOMENTUMDefinition Momentum = Mass x velocity = mv SI unit: kg ms-1Principle of In the absence of an external force, the totalConservation of momentum of a system remains unchanged.Momentum Elastic Collision Inelastic collision Both objects move The two objects combine and independently at their move together with a respective velocities after the common velocity after the collision. collision. Momentum is conserved. Momentum is conserved. Kinetic energy is conserved. Kinetic energy is not Total energy is conserved. conserved. Total energy is conserved.www.physics4spm.com 12
• 13. Discuss your physics question online at www.physics4spm.comTotal Momentum Before = total Total Momentum Before = Totalmomentum After Momentum After m1u1 + m2u2 = m1v1 + m2v2 m1u1 + m2u2 = (m1 + m2) v Explosion Before explosion both object stick together and at rest. After collision, both object move at opposite direction. Total Momentum Total Momentum before collision after collision : Is zero m1v1 + m2v2 From the law of conservation of momentum: Total Momentum = Total Momentum Before collision after collision 0 = m1v1 + m2v2 m1v1 = - 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 creates a momentum in the forward direction. From the principle of conservation of momentum, an equal but opposite momentum is produced to recoil the riffle backward. Application in the jet engine: A high-speed hot gases are ejected from the back with high momentum. This produces an equal and opposite momentum to propel the jet plane forward.www.physics4spm.com 13
• 14. Discuss your physics question online at www.physics4spm.com The launching of rocket Mixture of hydrogen and oxygen fuels burn explosively in the combustion chamber. Jets of hot gases are expelled at very high speed through the exhaust. These high speed hot gases produce a large amount of momentum downward. By conservation of momentum, an equal but opposite momentum is produced and acted on the rocket, propelling the rocket upwards. In a swamp area, a fan boat is used. The fan produces a high speed movement of air backward. This produces a large momentum backward. By conservation of momentum, an equal but opposite momentum is produced and acted on the boat. So the boat will move forward. A squid propels by expelling water at high velocity. Water enters through a large opening and exits through a small tube. The water is forced out at a high speed backward. Total Mom. before= Total Mom. after 0 =Mom water + Mom squid 0 = mwvw + msvs -mwvw = msvs The magnitude of the momentum of water and squid are equal but opposite direction. This causes the squid to jet forward.www.physics4spm.com 14
• 15. Discuss your physics question online at www.physics4spm.comExample ExampleCar A of mass 1000 kg moving at20 ms-1 collides with a car B of mass1200 kg moving at 10 m s-1 in samedirection. If the car B is shuntedforwards at 15 m s-1 by the impact, Before collision After collisionwhat is the velocity, v, of the car A MA = 4 kg MB = 2 kgimmediately after the crash? UA = 10 m/s to the left UB = 8 m/s to the right VB = 4 m/s to the left. Calculate the value of VA .Example Example A man fires a pistol which has aA truck of mass 1200 kg moving at mass of 1.5 kg. If the mass of the30 m/s collides with a car of mass bullet is 10 g and it reaches a1000 kg which is traveling in the velocity of 300 m/s after shooting,opposite direction at 20 m/s. After what is the recoil velocity of thethe collision, the two vehicles move pistol?together. What is the velocity ofboth vehicles immediately aftercollision?www.physics4spm.com 15
• 16. Discuss your physics question online at www.physics4spm.com2.5 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] Weight, W = Lift, U Thrust, F = drag, GUnbalanced Force/ When the forces acting on an object are notResultant Force balanced, there must be a net force acting on it. The net force is known as the unbalanced force or the resultant force. Effect : Can cause a body to - change it state at rest (an object will accelerate - change it state of motion (a moving object will decelerate or change its direction)Force, Mass & AccelerationNewton’s Second The acceleration produced by a force on an objectLaw of Motion is directly proportional to the magnitude of the net force applied and is inversely proportional to the mass of the object. The direction of the acceleration is the same as that of the net force. Force = Mass x AccelerationWhen a net force, F, acts F = maon a mass, m it causesan acceleration, a.www.physics4spm.com 16
• 17. Discuss your physics question online at www.physics4spm.comRelationship aαFbetween a & F The acceleration, a, is directly proportional to the applied force, F.Relationship a∝ 1between a and mm The acceleration of an object is inversely proportional to the mass,Experiment to Find The Relationship between Force, Mass & AccelerationRelationship a&F a&mbetweenSituation Both men are pushing the Both men exerted the same same mass but man A strength. But man B moves puts greater effort. So he faster than man A. moves faster.Inference The acceleration The acceleration produced produced by an object by an object depends on depends on the net force the mass applied to it.Hypothesis The acceleration of the The acceleration of the object increases when object decreases when the the force applied mass of the object increases increasesVariables: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
• 18. Discuss your physics question online at www.physics4spm.comProcedure : An elastic cord is hooked An elastic cord is hooked- Controlling over the trolley. The over a trolley. The elastic manipulated elastic cord is stretched cord is stretched until the variables. until the end of the end of the trolley. The trolley. The trolley is trolley is pulled down the pulled down the runway runway with the elastic with the elastic cord cord being kept stretched being kept stretched by by the same amount of the same amount of force force- Controlling Determine the Determine the acceleration responding acceleration by analyzing by analyzing the ticker variables. the ticker tape. tape. v−u v−u Acceleration a = Acceleration a = t t Repeat the experiment by Repeat the experiment by- Repeating using two , three, four using two, three, four and experiment. and five elastic cords five trolleys.RecordingdataAnalysingdatawww.physics4spm.com 18
• 19. Discuss your physics question online at www.physics4spm.com 1. What force is required to move a 2. Ali applies a force of 50 N to 2 kg object with an acceleration move a 10 kg table at a constant of 3 m s-2, if velocity. What is the frictional (a) the object is on a smooth force acting on the table? surface? (b) The object is on a surface where the average force of friction acting on the object is 2 N? 3. A car of mass 1200 kg traveling 4. Which of the following systems at 20 m/s is brought to rest over a will produce maximum distance of 30 m. Find acceleration? (a) the average deceleration, (b) the average braking force.2.6 IMPULSE AND IMPULSIVE FORCEImpulse The change of momentum m = mass mv - mu u = initial Unit : kgms-1 or Ns velocityImpulsive The rate of change of momentum in a v = finalForce collision or explosion velocity t = time Unit = NEffect of Impulsive force Longer period of time →Impulsivetime is inversely force decrease proportional to Shorter period of time →Impulsive time of contact force increasewww.physics4spm.com 19
• 20. Discuss your physics question online at www.physics4spm.com Situations for Reducing Impulsive Force in Sports Situations Explanation Thick mattress with soft surfaces are used in events such as high jump so that the time interval of impact on landing is extended, thus reducing the impulsive force. This can prevent injuries to the participants. Goal keepers will wear gloves to increase the collision time. This will reduce the impulsive force. A high jumper will bend his legs upon landing. This is to increase the time of impact in order to reduce the impulsive force acting on his legs. This will reduce the chance of getting serious injury. A baseball player must catch the ball in the direction of the motion of the ball. Moving his hand backwards when catching the ball prolongs 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 slab with his bare hand that moves at a very fast speed. The short impact time results in a large impulsive 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 short time interval produces a large impulsive force which drives the nail into the wood.www.physics4spm.com 20
• 21. Discuss your physics question online at www.physics4spm.com A football must have enough air pressure in it so the contact time is short. The impulsive force acted on the ball will be bigger and the ball will move faster and further. Pestle and mortar are made of stone. When a pestle is used to pound chilies the hard surfaces of both the pestle and mortar cause the pestle to be stopped in a very short time. A large impulsive force is resulted and thus causes 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 resident’s legs if he bends upon landing and takes 0.5 s to stop?(c) What is the impulsive force on the resident’s legs if he does not bend and stops in 0.05 s?(d) What is the advantage of bending his 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?www.physics4spm.com 21
• 22. Discuss your physics question online at www.physics4spm.com2.7 SAFETY VEHICLEComponent 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 the impulsive force can be reduceWindscreen 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.www.physics4spm.com 22
• 23. Discuss your physics question online at www.physics4spm.com2.8 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’s gravitational force. The earth’s gravitational force tends to pull everything towards its centre.Free fall An object is falling freely when it is falling under the force of gravity only. A piece of paper does not fall freely because its fall is affected by air resistance. An object falls freely only in vacuum. The absence of air means there is no air resistance to oppose the motion of the object. In vacuum, both light and heavy objects fall freely. They fall with the same acceleration ie. The acceleration due to gravity, g.Acceleration Objects dropped under the influence of the pull ofdue to gravity with constant acceleration.gravity, g 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 10 m s-2 for simplicity. The magnitude of the acceleration due to gravity depends on the strength of the gravitational field.Gravitational The gravitational field is the region around the earth infield which an object experiences a force towards the centre of the earth. This force is the gravitational attraction between the object and the earth. The gravitational field strength is defined as the gravitational force which acts on a mass of 1 kilogram. F g= Its unit is N kg-1. mwww.physics4spm.com 23
• 24. Discuss your physics question online at www.physics4spm.com 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 written either as 10 m s-2 or as 10 N kg-1.Weight The gravitational force acting on the object. Weight = mass x gravitational acceleration W = mg SI unit : Newton, N and it is a vector quantityComparison Mass Weightbetween The mass of an object is The weight of an object isweight & the amount of matter in the force of gravity actingmass the object on the object. Constant everywhere Varies with the magnitude of gravitational field strength, g of the location A scalar quantity A vector quantity A base quantity A derived quantity SI unit: kg SI unit : Newton, NThedifferencebetween afall in air anda free fall ina vacuum ofa coin and afeather.Both thecoin and the At vacuum state: At normal state:feather are There is no air resistance. Both coin and feather willreleased The coin and the feather fall because of gravitationalsimulta- will fall freely. force.neously from Only gravitational force Air resistance effected bythe same acted on the objects. the surface area of a fallenheight. Both will fall at the same object. time. The feather that has large area will have more air resistance. The coin will fall at first.www.physics4spm.com 24
• 25. Discuss your physics question online at www.physics4spm.com (a) The two sphere are (b)The two spheres are falling with an falling down with the acceleration. same acceleration The distance between The two spheres are at two successive images the same level at all of the sphere increases times. Thus, a heavyTwo steel showing that the two object and a light objectspheres are spheres are falling with fall with the samefalling under increasing velocity; gravitationalgravity. The falling with an acceleration.two spheres acceleration.are dropped Gravitationalat the same acceleration istime from independent of mass.the sameheight.Motion graph for free fall object Free fall object Object thrown upward Object thrown upward and fallExample 1A coconut takes 2.0 s to fall to theground. What is(a) its speed when it strikes the ground(b) the height of the coconut tree.www.physics4spm.com 25
• 26. Discuss your physics question online at www.physics4spm.com2.9 FORCES IN EQUILIBRIUMForces in When an object is in equilibrium, the resultant force actingEquilibrium on it is zero. The object will either be 1. at rest 2. move with constant velocity.Newton’s3rd Law Examples( Label the forces acted on the objects)Resultant A single force that represents the combined effect of two ofForce more forces in magnitude and direction.Addition of Forces Resultant force, F = ____ + ____ Resultant force, F = ____ + ____www.physics4spm.com 26
• 27. Discuss your physics question online at www.physics4spm.comTwo forces acting at a point at an angle [Parallelogram method]STEP 1 : Using ruler and protractor, STEP 3draw the two forces F1 and F2 from a Draw the diagonal of thepoint. parallelogram. The diagonal represent the resultant force, F in magnitude and direction.STEP 2Complete the parallelogram scale: 1 cm = ……Resolution of A force F can be resolved into componentsForces which are perpendicular to each other: (a) horizontal component , FX (b) vertical component, FY Inclined PlaneFx = F cos θ Component of weight parallel to the plane = mg sin θFy = F sin θ Component of weight normal to the plane = mg cos θwww.physics4spm.com 27
• 28. Discuss your physics question online at www.physics4spm.comfind the resultant force(d) (e)Lift Stationary Lift Lift accelerate upward Lift accelerate downwardResultant Force = Resultant Force = Resultant Force =The reading of The reading of The reading ofweighing scale = weighing scale = weighing scale =www.physics4spm.com 28
• 29. Discuss your physics question online at www.physics4spm.comPulley1. Find theresultant force, F2. Find themoving mass,m3. Find theacceleration,a4. Find stringtension, Twww.physics4spm.com 29
• 30. Discuss your physics question online at www.physics4spm.com2.10 WORK, ENERGY, POWER & EFFICIENCYWork Work done is the product of an applied force and the displacement of an object in the direction of the applied force W = Fs W = work, F = force s = displacementThe 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 the forceCalculation of Work The displacement , s of the The displacement, s of the object is in the object is not in the direction of the force, F direction of the force, FW = Fs s F W = (F cos θ) s W=FsExample 1 Example 2 Example 3A boy pushing his bicycle A girl is lifting up a 3 kg A man is pulling a crate of fishwith a force of 25 N flower pot steadily to a along the floor with a force ofthrough a distance of 3 m. height of 0.4 m. 40 N through a distance of 6 m.Calculate the work done What is the work done inby the boy. What is the work done by pulling the crate? the girl?www.physics4spm.com 30
• 31. Discuss your physics question online at www.physics4spm.comNo work is done when:The object is stationary The direction of motion of No force is applied on the the object is perpendicular object in the direction of to that of the applied force. displacement (the object moves because of its own inertia) A satellite orbiting in space. There is no friction in space. No force is acting in theA student carrying his bag A waiter is carrying a tray direction of movement ofwhile waiting at the bus of food and walking the satellite.stop Concept Definition Formula & UnitPower The rate at which work is W done, or the amount of work P= t done per second. p = power, W = work / energy t = timeEnergy 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 transfer of energy from one object to another object. Therefore, when work is done, energy is transferred from one object to another. The work done is equal to the amount of energy transferred.Potential m = massEnergy Gravitational potential energy h = height is the energy of an object due g = gravitational to its higher position in the acceleration gravitational field. E = mghKinetic Kinetic energy is the energy of m = massEnergy an object due to its motion. v = velocity E = ½ mv2www.physics4spm.com 31
• 32. Discuss your physics question online at www.physics4spm.comPrinciple of Energy can be changed from one form to another, butConservation it cannot be created or destroyed.of Energy The energy can be transformed from one form to another, total energy in a system is constant. Total energy before = total energy afterExample 4 Example 5A worker is pulling a wooden block of A student of mass m is climbing up aweight,W,with a force of P along a flight of stairs which has the height of h.fritionless plank at height of h. The He takes t seconds..distance traveled by the block is x.Calculate the work done by the worker topull the block. What is the power of the student?Example 6 Example 7A stone is thrown upward with initial -1velocity of 20 ms . What is the maximumheight which can be reached by thestone? A boll is released from point A of height 0.8 m so that it can roll along a curve frictionless track. What is the velocity of the ball when it reaches point B?Example 8 Example 9www.physics4spm.com 32
• 33. Discuss your physics question online at www.physics4spm.comA trolley is released from rest at point Xalong a frictionless track. What is the A ball moves upwards along a frictionlessvelocity of the trolley at point Y? track of height 1.5 m with a velocity of -1 6 ms . 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?www.physics4spm.com 33
• 34. Discuss your physics question online at www.physics4spm.com2.12 ELASTICITYElasticity A property of matter that enables an object to return to its original size and shape when the force 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 be displaced closer to each other. Repulsive intermolecular force acts to push the molecules back to their original positions. Stretching a solid causes its molecules to be displaced away from each other. Attractive intermolecular force acts to pull back the molecules to their original positions.Stretching a wire by an Its molecules are slightly displaced away fromexternal force: one another. Strong attractive forces act between the molecules to oppose the stretching When the external force is removed: The attractive intermolecular forces bring the molecules back to their equilibrium separation. The wire returns to its original positionwww.physics4spm.com 34
• 35. Discuss your physics question online at www.physics4spm.comHooke’s Law The extension of a spring is directly proportional to the applied force provided the elastic limit is not exceeded. F = kx F= force on the spring x = extension k = force constant of the springForce extension graph Based on the graph: Relationship between F & x : F is directly proportional to x The gradient of the graph represent = force constant of the spring, k Area under the graph equal to the work done to extent the spring: = elastic potential energy = ½ Fx = ½ kx2The elastic limit of a The maximum force that can be applied to aspring spring such that the spring will be able to be restored to its original length when the force is removed. If a force stretches a spring beyond its elastic limit, the spring cannot return to its original length even though the force no longer acts on it. The Hooke’s law is not obeyed anymore.Force constant of the The force required to produce one unit ofspring, k extension of the spring. F k= unit N m-1 or N cm-1 or N mm-1 x k is a measurement of the stiffness of the spring The spring with a larger force constant is harder to extend and is said to be more stiff. A spring with a smaller force constant is easier to extend and is said to be less stiff or softer.www.physics4spm.com 35
• 36. Discuss your physics question online at www.physics4spm.comFactors that effect elasticity Factor Change in factorHow does it affects the elasticity Length Shorter spring Less elastic Longer spring More elastic Diameter of spring Smaller diameter More elastic wire Larger diameter Less elastic Diameter spring Smaller diameter Less elastic Larger diameter More elastic Type of material Springs made of different materials Elasticity changes according to the type of material Arrangement of the spring In series In parallelThe same load is applied to each The load is shared equally among thespring. springs.Tension in each spring = W Tension in each spring = WExtension of each spring = x 2Total extension = 2x Extension of each spring = xIf n springs are used: 2The total extension = nx If n springs are used: x The total extension = nExample 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)?www.physics4spm.com 36
• 37. Discuss your physics question online at www.physics4spm.comwww.physics4spm.com 37
• 38. Discuss your physics question online at www.physics4spm.comSECTION 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 kmh-1 from A to B for two minutes. Figure 1.2(a) Describe the acceleration of the car as it travels from A to E. 2 ………………………………………………… m …………………………….(b) Compare the resultant force as it travels along AB and CD. 1 ………………………………………………… m ……………………………(c) Give a reason to your answer in (b) ………………………………………………… 1 ………………………… m(d) Calculate the distance AB 2 m(e) The velocity of a car increases if the force exerted on the accelerator of a car increases. Explain why the velocity of the car increases from D to E although the force on the accelerator of the car is the same as a long C to D. 2 ………………………………………………… mwww.physics4spm.com 38
• 39. Discuss your physics question online at www.physics4spm.com …………………………… ………………………………………………… …………………………...QUESTION 2 (SPM 1999)www.physics4spm.com 39
• 40. Discuss your physics question online at www.physics4spm.com (e) Why is it necessary to ha capacity limit for the safe A bus bus? the traveled from KotaQUESTION 3 ( SPM 2000) Lumpur at 9:00 pm. The cap passenger in the bus is 40 ……………………………… Figure 2 mass of the bus with the ca …………………………… and the average frictional foFigure 2 shows a car of mass 1 000kg moving a bus tire and the road for the jo ………………………………straight but hilly road. QRST and TU is the part The bus moves at average sp ……………………………of the hill that have constant slope where the Kota Bharu before stopover aslope of QRST is higher that the slope of TU. The at 12:00 mid night on the sfrictional force that acts along QRSTU is 2 000N. hour later the bus continueThe velocity if the car at P is Kuala Lumpur with average80kmh-1 and takes 3 minutes to move from point The bus arrived at 6:00 am onP to Q. The motion of the car along (a) Put in a table all the physPQRSTU represent by a velocity-time graph in involved in the informatioFigure 3. two groups. (b) Calculate the total distanc the bus. (c) Sketch a distance-time gr the motion of the bus. (d) (i) What is the value of the tr the bus when it moves at speed? (ii) ……………………………… …………………………… Give a reason for the ans ………………………………www.physics4spm.com …………………………… 40
• 41. Discuss your physics question online at www.physics4spm.com(a) Classify the physical quantity into two groups. 2m(b) From the graph in Figure 3, explain the acceleration of the car from point P to S. ………………………………………………………………………………………… ………………………………………………………………………………………… 2m(c) (i) Compare the resultant force of the car when the move along PQ and ST. 1m …………………………………………………………………………………….. (ii) State a reason for your answer in c(i) 1m ……………………………………………………………………………………...(d) Calculate the distance form point P to Q 2mQUESTION 4 (SPM 2002) 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? …………………………………………………………………………………… 1m (ii) Give a reason for your answer in (a)(i) …………………………………………………………………………………… 1m(b) Calculate the acceleration of the diver at ST.www.physics4spm.com 41
• 42. Discuss your physics question online at www.physics4spm.com 2m(c) Sketch an acceleration-time graph for the motion of the skydiver at point S, T, U, V and W at the space below. 3m(d) Suggest one way that can the skydiver apply to reduce injuries on his leg during landing. Explain your answer. ………………………………………………………………………………………... ……………………………………………………………………………………….. 2mQUESTION 5 (SPM 1988) Figure 4(i)www.physics4spm.com 42
• 43. Discuss your physics question online at www.physics4spm.comFigure 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 0.495kg. (i) If the bullet speed is 400ms-1, what is the momentum of the bullet? 2m (ii) What is speed of the object after the bullet obscured into the object after the gunshot? 2m(c) The object and the bullet that obscured in the object aloft at a maximum height of H, as shown in Figure 4(ii). Figure 4(ii) (i) What is the value of kinetic energy of the object together with the bullet inside the object? 2mwww.physics4spm.com 43
• 44. Discuss your physics question online at www.physics4spm.com (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 boat as the man jumps onto the jetty. ………………………………………………………………………………………… 1m(b) Explain why the boat moves away from the jetty when the man jumps. ………………………………………………………………………………………… 1m(c) The mass of the man is 50 kg and he jumps at a velocity 2ms-1. The mass of the boat is 20kg. Calculate the velocity of the boat as the man jumps. 2m(d) Name one application of the physics principle stated in (a) in an exploration of outer space. ………………………………………………………………………………………… mwww.physics4spm.com 44
• 45. Discuss your physics question online at www.physics4spm.comwww.physics4spm.com 45