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`Hoo Sze YenPhysics SPM 2008CHAPTER 2: FORCES AND MOTION2.1 Linear MotionKinematics ­ the study of movement without reference to the forces that cause the movement Linear Motion ­ movement with constant acceleration Classification Physical quantity with... Example Scalar Magnitude only Distance Speed Vector Magnitude and direction Displacement Velocity Acceleration2.1.1 Equations of Linear MotionIf s = displacement (succession) [m] u = initial velocity [m s-1] v = final velocity [m s-1] t = time [s] s = ½ (u + v) t -- --a=From : Insert intov-u t:v = u + at s = ½ (u + u + at) t s = ut + ½ at2--From: :t=v-u aInsert intos = ½(u + v)=(v - u ) tv2 - u2 2a 2 2 v = u + 2as--Chapter 2: Forces and MotionPage 1 of 11Hoo Sze YenPhysics SPM 20082.2Linear Motion Graphs2.2.1 Ticker timerTicker timer used to study movement in a short period of time 50 Hz used to determine: o time o displacement o average velocity o acceleration o type of movementExplanation Consistent distance = uniform velocityMovementShort distance = low velocity Long distance = high velocity Increasing distance = increasing velocity / acceleration Decreasing distance = decreasing velocity / deceleration2.2.2 StroboscopeNumber of images in one second = number of slits × number of spins per second T= where T = period (time taken per image) [s] n = number of slits on the stroboscope f = number of spins per second [Hz] 1 nfChapter 2: Forces and MotionPage 2 of 11Hoo Sze YenPhysics SPM 20082.2.3 Linear Motion GraphsDisplacement-time graphsVelocity = slope of the graph v=0 (a = 0)Velocity-time graphsAcceleration = slope of the graph Displacement = area under the graphv/m s-1Acceleration-time graphsVelocity = area under the graphs/ma/m s-2t/st/s v/m s-1 a/m s-2t/sv= constant (a = 0)s/mt/st/s v/m s-1t/s a/m s-2v a= constants/mt/st/s v/m s-1 a/m s-2t/sv a= constants/mt/st/st/s v/m s-1 a/m s-2v at/st/s a/m s-2v av/m s-1t/st/s a/m s-2a increasing ratet/sa decreasing ratea/m s-2t/sChapter 2: Forces and MotionPage 3 of 11Hoo Sze YenPhysics SPM 20082.3InertiaDynamics ­ the study of movement caused by force Inertia ­ natural characteristics of an object to oppose any attempted change on its original state, whether at rest or in motion ­ tendency of an object to remain at rest, or to keep moving at constant speed in a straight line Newton's First Law of Motion (Law of Inertia) Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.2.4MomentumMomentum = mass × velocity p = mvwhere p = momentum [kg m s-1] m = mass [kg] v = velocity [m s-1]Principle of conservation of momentum In any collision or interaction between two or more objects in an isolated system, the total momentum before collision is equal to the total momentum after collision.m1u1 + m2u2 = m1v1 + m2v2 Three situations: 1) Elastic collision: When both objects move separately after collision.Note: In an elastic collision, the kinetic energy is conserved.m1u1 + m2u2 = m1v1 + m2v2 2) Inelastic collision: When both objects move together after collision. m1u1 + m2u2 = (m1 + m2)v 3) Explosion: When both objects are stationary before the explosion. 0 = m1v1 + m2v2Chapter 2: Forces and MotionPage 4 of 11Hoo Sze YenPhysics SPM 20082.5ForceForce changes the size, shape, state of rest, velocity and/or direction of an object. Force is a vector quantity. Newton's Second Law of Motion The acceleration of a body, a, is directly proportional to the net force acting upon it, F, and inversely proportional to its mass, m.F = ma where F = force [N] m = mass [kg] a = acceleration caused by F [m s-2]2.5.1 Balanced ForcesBalanced forces = net force is zeroAn object that is stationary, or moving with uniform velocity in a straight line, is said to be in a state of balanced forces.2.5.2 Unbalanced ForcesUnbalanced forces may cause an object to start moving, to speed it up, to slow it down, or to bring it to a stop. The greater the unbalanced force, the greater the acceleration or deceleration produced.2.5.3 Net Force / Resultant ForceNet force on an object is the overall force resulting from the combination of the individual forces acting upon the object. When the forces are balanced, the net force is zero; as if there is no force acting upon the object. When the forces are unbalanced, the net force is the difference between the forces acting in opposite directions.Chapter 2: Forces and MotionPage 5 of 11Hoo Sze YenPhysics SPM 20082.6Impulse and Impulsive ForceImpulse = change of momentum Ft = mv ­ muImpulsive force is the change of momentum in a very short period of time. Impulsive force = rate of change of momentum mv - mu F= t where Ft = impulsive [kg m s-1] F = impulsive force [N] m = mass [kg] u = initial velocity [m s-1] v = final velocity [m s-1]2.7Safety Features in Vehicles1. Padded dashboards 2. Shatterproof windscreen glass 3. Inflatable airbags 4. Collapsible steering wheels 5. Headrest 6. Padded seats 7. Seatbelt 8. Antilock brake systems (ABS) 9. Variable-ratio response steering systems 10. Intelligent speed adaptation systems 11. Reverse collision warning systems 12. Bumper bars2.8GravityAll objects are pulled towards the centre of the earth by a force known as the earth's gravitational force. Any object dropped towards earth which falls under the influence of the earth's gravitational force (without any influence of other external forces, such as air friction) is said to be going through a free fall. In reality, free falls only happen within a vacuum space. An object undergoing free fall will fall at the rate of gravitational acceleration which is at a constant of 9.81 m s-1. The gravitational acceleration is not influenced by the size or mass of the object.Chapter 2: Forces and MotionPage 6 of 11Hoo Sze YenPhysics SPM 20082.8.1 WeightWeight = gravitational force acting on the respective object W = mg where W = weight [N] m = mass [m] g = gravitational acceleration [m s-2]2.8.2 LiftsR aa=0 F = R ­ mg =0 R = mgW = mga = +ve () F = R ­ mg ma = R ­ mg R = ma + mg Common formula: R = mg + maa = -ve () F = mg ­ R ma = mg ­ R R = mg ­ maa = g (free fall) F = mg ­ R mg = mg ­ R R=02.8.3 PulleysMotion and acceleration in this directionTTBased on the force formula: F = ma F = Net force acting on the system m = Total mass of the system a = Acceleration of the system F1 ­ F2 = (m1 + m2) a To find out the rope tension: F = ma F1 ­ T = m1a T = F2 ­ m2aF2 F12.9Forces in EquilibriumEquilibrium: - resultant force = 0 - acceleration = 0 (stationary or uniform velocity)Newton's Third Law For every action there is an equal and opposite reaction.Chapter 2: Forces and MotionPage 7 of 11Hoo Sze YenPhysics SPM 20082.9.1 Nett / Resultant ForcesUsing the parallelogram method2.9.2 Force ResolutionReversing the parallelogram methodFx = F cos  Fy = F sin 2.9.3 Inclined Planesm2 m1  R Fr W=mgR = mg cos  Fr = mg sin  where W = weight of object [N] m = mass of object [kg] g = gravitational acceleration [m s-2] R = reaction caused by weight of object perpendicular to plane [N] Fr = friction caused by weight of object parallel to plane [N]Chapter 2: Forces and MotionPage 8 of 11Hoo Sze YenPhysics SPM 20082.10 WorkWork done by a constant force to move an object = displacement × force parallel to direction Note: Work is a scalar quantity W = Fs where W = work [J] F = force creating the work [N] s = displacement [m]Energy is the potential or ability of a system to do work. (scalar quantity) Power is the rate of work done or rate of energy transferP=where P = power [J s-1] W = work [J] E = energy [J] t = time [s]W E = t t2.10.1Potential EnergyPotential energy is the energy within an object because of its position or state. Gravitational potential energy: E = mgh where E = potential energy [J] m = mass [kg] g = gravitational acceleration [m s-2] h = height of the location of the object [m] Elastic potential energy: W = ½ Fs where W = work done [J] F = force exerted [N] s = extension or compression of the spring [m]F/Ns/mChapter 2: Forces and MotionPage 9 of 11Hoo Sze YenPhysics SPM 20082.10.2Kinetic EnergyKinetic energy is energy acquired by an object during movement. E = ½ mv2 where E = kinetic energy [J] m = mass [kg] v = velocity of the object [m s-1] The law of conservation of energy states that energy may neither be created nor destroyed; it can only change shape.2.11 PowerPower is the rate at which energy is used.P=E t2.12 EfficiencyEfficiency is the ratio at which the output power is compared to the input power. Efficiency = Output power × 100% Input power2.13 ElasticityElasticity is the ability of an object to return to its original shape and size after the applied external force applied onto it has been removed.2.13.1Hooke's LawHooke's Law states that the extension or compression of a spring is directly proportional to the force acting on it provided the elastic limit of the spring has not been exceeded.Chapter 2: Forces and MotionPage 10 of 11Hoo Sze Yen Spring extension, x (cm)Physics SPM 2008Elastic limitTension force, FF = kx where F = force exerted on the spring [N] k = spring constant [N m-1] x = spring extension / compression [m]2.13.2 Spring stiffnessFactors which affect the stiffness of a spring: 1) Length of spring 2) Diameter of wire 3) Diameter of coil 4) Type of material2.13.3 Spring systemsParallel arrangement Series arrangementW WThe load is equally distributed among the The same load is applied to each spring. springs. If n springs are used: Total extension = nx If n springs are used: x Total extension = nChapter 2: Forces and MotionPage 11 of 11`

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