* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Section 2. Mechanics Course Notes
Photon polarization wikipedia , lookup
Dark energy wikipedia , lookup
Introduction to general relativity wikipedia , lookup
Electromagnetism wikipedia , lookup
Electromagnetic mass wikipedia , lookup
Nuclear physics wikipedia , lookup
Gibbs free energy wikipedia , lookup
Casimir effect wikipedia , lookup
Internal energy wikipedia , lookup
Equations of motion wikipedia , lookup
Mass versus weight wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Negative mass wikipedia , lookup
History of physics wikipedia , lookup
Woodward effect wikipedia , lookup
Speed of gravity wikipedia , lookup
Potential energy wikipedia , lookup
Conservation of energy wikipedia , lookup
Modified Newtonian dynamics wikipedia , lookup
Newton's laws of motion wikipedia , lookup
Time in physics wikipedia , lookup
Classical central-force problem wikipedia , lookup
Classical mechanics wikipedia , lookup
Weightlessness wikipedia , lookup
A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics SECTION II Newtonian Mechanics CIE A-Level [AS and A2] ________________________ Course Notes DIPONT Educational Resource - Science 1 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics Syllabus Details______________________ DIPONT Educational Resource - Science 2 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics 3. Kinematics [AS]___________________________ Content 3.1 Linear motion 3.2 Non-linear motion Learning outcomes_____________________________________ Candidates should be able to: (a) define displacement, speed, velocity and acceleration Symbol Displacement Velocity Speed Acceleration Definition Distance moved in particular direction Velocity = change in displacement / time Speed = total distance / time Acceleration = change in velocity / time s v or u v or u a SI unit m ms-1 ms-1 ms-2 Vector / Scalar Vector Vector Scalar Vector (b) use graphical methods to represent displacement, speed, velocity and acceleration Displacement-Time Graphs Stationary Displacement / m Constant +ve velocity Constant -ve velocity T ime / s • G radient of a displacement-time graph = velocity Velocity-Time Graphs Acceleration-Time Graphs Constant de-acceleration T ime / s • G radient of a velocity-time graph = acceleration • Area under a velocity-time graph = displacement DIPONT Educational Resource - Science Acceleration / ms-2 Constant velocity Velocity / ms-1 Constant acceleration Acceleration constantly increasing Constant acceleration Acceleration constantly decreasing Time / s •Area under an acceleration-time graph = change in velocity 3 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (c) find displacement from the area under a velocity-time graph Velocity / ms-1 Velocity-Time Graphs Time / s Area under graph = displacement (d) use the slope of a displacement-time graph to find the velocity (e) use the slope of a velocity-time graph to find the acceleration Velocity-Time Graphs Velocity / ms-1 Displacement / m Displacement-Time Graphs s t T ime / s Gradient = s/t = velocity v t T ime / s Gradient = v/t = acceleration SEE PHET SIM DIPONT Educational Resource - Science 4 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (f) derive, from the definitions of velocity and acceleration, equations that represent uniformly accelerated motion in a straight line v=u+at s=[(u+v)/2]t v2=u2+2as s=ut+1/2at2 s=vt-1/2at2 u v a t s Initial velocity Final velocity Acceleration Time Displacement DERIVATION… Start with definition of acceleration a = (v-u) / t Rearrange to get first equation v = u + at Take definition of average velocity… Average velocity = s / t Average velocity = (v +u)/2 Therefore… s / t = (v +u)/2 Rearrangement gives… s = [(v + u)t]/2 Taking v = u + at and s = [(v + u)t]/2…. To eliminate v… s = ut + 1/2at2 Taking v = u + at and s = [(v – u)t]/2…. To eliminate t… v2=u2+2as These formula are given on the test paper DIPONT Educational Resource - Science 5 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (g) solve problems using equations that represent uniformly accelerated motion in a straight line, including the motion of bodies falling in a uniform gravitational field without air resistance If a body falls in a vacuum near the Earths surface it has an acceleration g of freefall Displacement / m IN A VACUUM Velocity / ms-1 T ime / s Acceleration / ms-2 T ime / s g = ~10 ms-2 T ime / s (h) recall that the weight of a body is equal to the product of its mass and the acceleration of free fall Mass = related to the amount of matter in an object Weight = force of gravity exerted on an object (or the force on a supporting scale) Weight (N) = mass (kg) x g (ms-2) DIPONT Educational Resource - Science g=acceleration of free fall 6 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (i) describe an experiment to determine the acceleration of free fall using a falling body Light Gates Light gates record the time taken for an object to pass. Light source Light detector Strobe Photography Strobe photography records images at regular time intervals t1 Ticker Tape Ticker tapes have dots at regular time intervals. The distance between the dots can be measured 1 t2 Falling object s t3 Velocity = 2 length of object time through beam If at 50Hz 5 spaces = 5/50 = 0.1 s t4 DIPONT Educational Resource - Science 3 7 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (j) describe qualitatively the motion of bodies falling in a uniform gravitational field with air resistance Displacement / m WITH AIR RESISTANCE Straight line as velocity become constant Velocity / ms-1 T ime / s Ter minal Velocity Acceleration / ms-2 T ime / s Acceleration zero at terminal velocity T ime / s DIPONT Educational Resource - Science 8 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (k) describe and explain motion due to a uniform velocity in one direction and a uniform acceleration in a perpendicular direction. Projectile Motion Gravitational field in vertical direction vV parabolic motion vH vH vV vV vH vV vH vV vH vHhas no force acting so is constant vH vV vVhas a constant force acting so there is a constant acceleration Parabolic in absence of air resistance The vertical and horizontal components are independent SEE PHET SIM DIPONT Educational Resource - Science 9 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics 4. Dynamics [AS]____________________________ Content 4.1 Newton’s laws of motion 4.2 Linear momentum and its conservation Learning outcomes_____________________________________ Candidates should be able to: (a) state each of Newton’s laws of motion NEWTON’S FIRST LAW: “An object continues in uniform motion in a straight line or at rest unless a resultant force acts.” NEWTON’S SECOND LAW: “The rate of change of momentum of an object is proportional to the resultant force which acts on the object.” NEWTON’S THIRD LAW: “when two bodies A and B interact, the force that A exerts on B is equal and opposite to the force B exerts on A.” (b) show an understanding that mass is the property of a body that resists change in motion Mass is a property of a body that resists change in motion a = 1m/s2 5N 10N 5kg As the mass increases… a = 1m/s2 • More force is needed for the same acceleration • The mass “resists” change in motion 10kg DIPONT Educational Resource - Science 10 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (c) describe and use the concept of weight as the effect of a gravitational field on a mass Gravitational field No Gravitational Field mass mass No Weight Weight Earth (LARGE MASS) Weight = force of gravity exerted on an object (or the force on a supporting scale) Weight (N) = mass (kg) x g (N/kg) g=gravitational field strength (d) define linear momentum as the product of mass and velocity Momentum = Mass x velocity p (kgms-1) = m (kg) x v (ms-1) (e) define force as rate of change of momentum Force = change in momentum / time F=p/t DIPONT Educational Resource - Science 11 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (f) recall and solve problems using the relationship F = ma, appreciating that acceleration and force are always in the same direction Example 1 – No friction 15N F=ma 15N = 4kg x a a = 15/4 = 3.75ms-2 4kg Example 2 – With Friction 15N 4kg Friction = 3N F=ma Resultant F = 15-3 = 12N 12N = 4kg x a a = 12/4 = 3ms-2 Example 3 – On a slope Normal reaction F=ma Force down the slope = 40(sin35 o)N = 22.9N Resultant F = 22.9 - 3 = 19.9N 19.9N = 4kg x a a (down slope) = 19.9/4 = 5.0ms-2 35 o 40N (mg = 4kg x 10ms -2 ) REMEMBER: Acceleration is always in the direction of the resultant force SEE PHET SIM (g) state the principle of conservation of momentum Law of conservation of linear momentum: “The total linear momentum of a system of interacting particles remains constant provided there is no resultant external force.” DIPONT Educational Resource - Science 12 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (h) apply the principle of conservation of momentum to solve simple problems including elastic and inelastic interactions between two bodies in one dimension (knowledge of the concept of coefficient of restitution is not required) EXAMPLE….. 0ms-1 5ms-1 Total initial momentum = (mu)4kg + (mu)6kg = 4x5 + 6x0 = 20 kgms-1 BEFORE 5ms-1 COLLISION Total final momentum = (mv)10kg = 10 x v ?ms-1 Total initial momentum = Total final momentum AFTER 20 = 10 x v v = 20/10 = 2ms-1 (i) recognise that, for a perfectly elastic collision, the relative speed of approach is equal to the relative speed of separation u1 u2 v1 v2 Elastic Collisions BEFORE Collision AFTER Collision Total initial momentum = Total final momentum Total initial Kinetic Energy = Total final momentum Kinetic Energy ½ m1u12 + ½ m2u22 = ½ m1v12 + ½ m2v22 u1 – u2 = -(v1 – v2) relative speed of approach = relative speed of separation DIPONT Educational Resource - Science 13 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (j) show an understanding that, while momentum of a system is always conserved in interactions between bodies, some change in kinetic energy usually takes place. ELASTIC AND INELASTIC Collisions….. Initial Situation v1 Elastic Collision v1 No KE energy is lost Inelastic Collision v2 v3 Some KE lost Total Momentum is conserved in all cases mAv1 + mBv2 = mAv3 + mBv4 Inelastic Collisions are the normal situation DIPONT Educational Resource - Science 14 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics 5. Forces [AS]_______________________________ Content 5.1 Types of force 5.2 Equilibrium of forces 5.3 Centre of gravity 5.4 Turning effects of forces Learning outcomes_____________________________________ Candidates should be able to: (a) describe the forces on mass and charge in uniform gravitational and electric fields, as appropriate Particle Field Effect Uncharged mass Gravitational Uncharged mass Charged mass Electric field Gravitational field Positive charge Electric field Negative charge Electric field Attracted in direction of field line No effect Attracted in direction of field line Attracted in direction of field line Repelled in opposite direction to field line (b) show an understanding of the origin of the upthrust acting on a body in a fluid Upthrust In a fluid... Particles are constantly colliding with the sides of the container or immersed object These collisions produce a force This force provides the upthrust on the immersed body DIPONT Educational Resource - Science 15 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (c) show a qualitative understanding of frictional forces and viscous forces including air resistance (no treatment of the coefficients of friction and viscosity is required) Frictional forces are forces that act against the direction of motion Viscous forces result from motion through fluids Both types of forces are due to the interaction between charges on the moving object and the material it is close to SEE PHET SIM (d) use a vector triangle to represent forces in equilibrium Forces in equilibrium Situation Force vectors Vector triangle Normal reaction Gravity (e) show an understanding that the weight of a body may be taken as acting at a single point known as its centre of gravity Centre of Gravity Centre of gravity Each particle in a solid has an associated weight DIPONT Educational Resource - Science The result of these forces appears to act from a single point 16 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (f) show an understanding that a couple is a pair of forces that tends to produce rotation only (g) define and apply the moment of a force and the torque of a couple Moments, Couples, and Torque Moment: F2 distance =Force x perpendicular distance from pivot Pivot F2 distance F1 = F2 Couple: a pair of equal but opposite forces which gives a turning effect but no resultant force F1 Torque: Moment of a couple = one force x perpendicular distance between the forces (h) show an understanding that, when there is no resultant force and no resultant torque, a system is in equilibrium Translational Equilibrium If the resultant force on an object is zero it said to be in translational equilibrium T, tension F = zero P, pull W, weight The ball is in TRANS LATION EQUILIBRIUM if… Tsin = P Tcos = W (i) apply the principle of moments. If an object is in equilibrium, the sum of the clockwise moments about a pivot are equal to the sum of the anticlockwise moments. DIPONT Educational Resource - Science 17 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics 6. Work, energy, power [AS]__________________ Content 6.1 Energy conversion and conservation 6.2 Work 6.3 Potential energy, kinetic energy and internal energy 6.4 Power Learning outcomes_____________________________________ Candidates should be able to: (a) give examples of energy in different forms, its conversion and conservation, and apply the principle of energy conservation to simple examples Energy Type Example Kinetic Energy Gravitational Potential Energy Chemical Energy Strain Energy Nuclear Energy Internal Energy Electrical Energy Light Energy Sound Energy Moving objects (Car) Raised objects (Water in a dam) Energy stored in bonds (coal, oil) Energy due to flexing of materials (elastic band) Energy associated with atomic nuclei (Fission reactors) Energy of materials – kinetic from particles moving + potential from bonds Energy from moving charges (electricity) Energy from Electromagnetic waves (light, IR) Energy due to vibrating particles (sound) Solar Energy Photovoltaic Cell Electrical Energy Motor Kinetic Energy Potential Energy Principles of Conservation of Energy: Overall the total energy of any closed system must be constant Energy is neither created or destroyed, it just changes form There is no change in the total energy of the Universe DIPONT Educational Resource - Science 18 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (b) show an understanding of the concept of work in terms of the product of a force and displacement in the direction of the force Work = Force x distance moved by force F Work done = Fs cos s (c) calculate the work done in a number of situations including the work done by a gas that is expanding against a constant external pressure: W = p .V W = F x F p=F/A x Constant pressure = p F = pA W = pAx F V = Ax Work done = pV This formula is given on the test paper DIPONT Educational Resource - Science 19 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (d) derive, from the equations of motion, the formula E k = ½ mv2 Kinetic Energy gained by an object is equal to the work done on that object Start with… v2 = u2 + 2as Rearrange to form… as = ½ u2 – ½ v2 Multiple both sides by mass… mas = ½ mu2 – ½ mv2 F=ma so… Fs = ½ mu2 – ½ mv2 (e) recall and apply the formula Ek = ½ mv2 Kinetic energy = energy associated with a moving object Kinetic Energy (J) = 1/2mv2 m=mass, v=velocity Kinetic Energy v1 EK = 1/2mA v12 (f) distinguish between gravitational potential energy, electric potential energy and elastic potential energy Elastic Potential Energy 5 4 3 x 2 1 0 Gravitational Potential Energy 7 6 h EP = mAgh EElas = 1/2kx2 DIPONT Educational Resource - Science 20 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics Electric Potential Energy ++++++++++++ q EP = qV ----------------SEE PHET SIM (g) show an understanding and use the relationship between force and potential energy in a uniform field to solve problems (h) derive, from the defining equation W = Fs, the formula Ep = mgh for potential energy changes near the Earth’s surface (i) recall and use the formula Ep = mgh for potential energy changes near the Earth’s surface W = Fs Gravitational Potential Energy Force needed to move mass mA is equal to its weight F = weight = mg Mass mA moved through distance h W = Fs = mgh h EP = mAgh Work done = energy transfer W = EP = mgh DIPONT Educational Resource - Science 21 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (j) show an understanding of the concept of internal energy Internal Energy = Total Potential Energy + Total Random Kinetic Energy Random Kinetic Energy = Translational Kinetic Energy + Rotational Kinetic Energy Translational energy is the energy associated with the whole molecule moving in a certain direction. Rotational energy is the energy associated with the molecule rotation around a certain point. Potential energy is the energy associated with intermolecular forces. (k) recall and understand that the efficiency of a system is the ratio of useful work done by the system to the total energy input Efficiency = Useful work OUT / Total energy transferred Efficiency = Useful energy OUT / Total energy IN Efficiency = Useful power OUT / Total power IN (l) show an appreciation for the implications of energy losses in practical devices and use the concept of efficiency to solve problems Thermal Energy LOST (Heat) Kinetic Energy OUT (Movement of car) Chemical Energy IN (Petrol) Total energy in = total energy out Chemical Energy = Kinetic Energy + Thermal Energy Efficiency = Kinetic Energy Out / Chemical Energy In DIPONT Educational Resource - Science 22 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (m) define power as work done per unit time and derive power as the product of force and velocity Power = Rate at which Energy is transferred Power (W) = energy transferred / time taken = work done / time taken 1 Watt (W) = 1 Js-1 Power = W/t W = Fs Power = Fs/t Power = Fv (n) solve problems using the relationships P = W/t and P = Fv. SEE PAST PAPER QUESTION BOOKS DIPONT Educational Resource - Science 23 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics 7. Motion in a circle [A2]_____________________ Content 7.1 Kinematics of uniform circular motion 7.2 Centripetal acceleration 7.3 Centripetal force Learning outcomes_____________________________________ Candidates should be able to: (a) express angular displacement in radians B s r Angular displacement = = s / r is measured in radians A (b) understand and use the concept of angular velocity to solve problems Angular velocity = w = / t (c) recall and use v = rw to solve problems v = wr DIPONT Educational Resource - Science 24 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (d) describe qualitatively motion in a curved path due to a perpendicular force, and understand the centripetal acceleration in the case of uniform motion in a circle Force applied perpendicular to the velocity direction Acceleration in direction of force Change in velocity directed in towards the centre of the circle vB B vB vA vA A DIPONT Educational Resource - Science 25 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics Pendulum car ca r T Tcos Tsin Centripetal force provided by horizontal component of tension Centripetal force provided by friction force between tyres and road mg Car on a Corner Solar System Earth Sun Centripetal force provided by gravitational attraction of Sun SEE PHET SIM (e) recall and use centripetal acceleration a = r w2, a = v2/r Centripetal acceleration: The acceleration of an object travelling in circular motion. Centripetal acceleration = acentripetal = v2/r r = radius acentripetal = r w2 (f) recall and use centripetal force F = mrw 2, F = mv2/2 Centripetal force = ma = mv2/r = m r w2 DIPONT Educational Resource - Science 26 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics 8. Gravitational field [A2]_____________________ Content 8.1 Gravitational field 8.2 Force between point masses 8.3 Field of a point mass 8.4 Field near to the surface of the Earth 8.5 Gravitational potential Learning outcomes_____________________________________ Candidates should be able to: (a) show an understanding of the concept of a gravitational field as an example of field of force and define gravitational field strength as force per unit mass g=F/m g = gravitation field strength m = test mass units = N kg-1 = ms-2 (b) recall and use Newton’s law of gravitation in the form F = Gm1m2/r2 Newton’s law of universal gravitation: Every mass in the universe attracts all the other masses in the universe. Law of Universal Gravitation m1 m2 force force r F = Gm1 m 2 r 2 DIPONT Educational Resource - Science F = Force G = Universal gravitational constant m = point mass R = distance between point mass 27 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (c) derive, from Newton’s law of gravitation and the definition of gravitational field strength, the equation g= GMr 2 for the gravitational field strength of a point mass (d) recall and solve problems using the equation g= GM/r2 for the gravitational field strength of a point mass F = Gm1 m 2 r 2 = + g = Gm1 r 2 g=F/m (e) show an appreciation that on the surface of the Earth g is approximately constant and is called the acceleration of free fall As changes in r at the surface of the Earth are small in comparison to the distance to the center of the Earth (and so the center of gravity) g can be considered constant. g = 9.81 N/kg = 9.81 ms-1 = acceleration of free fall (f) define potential at a point as the work done in bringing unit mass from infinity to the point (g) solve problems using the equation = –GM/ r for the potential in the field of a point mass Gravitational potential energy: work done in moving a mass from infinity to a point Zero of potential energy is at infinity Potential energy taken as a negative value The work done in moving a mass between two points in a gravitational field is independent of the path taken Gravitational potential: Energy per unit test mass. Gravitational potential: Energy per unit test mass. DIPONT Educational Resource - Science 28 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics potential energy decreases as gravitational force does work zero potential energy at infinity F1 F2 M m m Force on mincreases Gravitational potential energy of mass m= = = - GMm r work done test mass E = - m Gm r = gravitational potential (Jkg-1) m = mass producing field This formula is given on the test paper DIPONT Educational Resource - Science 29 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (h) recognise the analogy between certain qualitative and quantitative aspects of gravitational field and electric field zero potential at infinity potential increase F2 +Q F1 q q Force on q increases Electric Potential Energy of charge q = Qq r Electric potential energy: work done in moving a charge from infinity to a point Zero of potential energy is at infinity Potential energy taken as a negative value The work done in moving a charge between two points in an electril field is independent of the path taken Electric potential: Energy per unit test charge. DIPONT Educational Resource - Science 30 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics (i) analyse circular orbits in inverse square law fields by relating the gravitational force to the centripetal acceleration it causes Gravitational attraction = centripetal force GMm mv2 = r r2 GM = v2 r v = GM r v = 2 r T GM = 2 r T 2 ( ) r3 = Constant T2 3 r = r T2 (j) show an understanding of geostationary orbits and their application. Geostationary Orbit Satellite Earth’s orbit Satellite orbit Earths rotates once every 24hrs. By using r3 / T2 the radius of orbit needed for geostationary orbit can be calculated DIPONT Educational Resource - Science 31 A-Level Course Notes: PHYSICS SECTION II: Newtonian Mechanics Background Reading_________________ PHYSICS, Giancoli 6th edition, Chapter 2-8 Useful Websites______________________ http://phet.colorado.edu/en/simulations/category/new http://www.s-cool.co.uk/alevel/physics.html http://www.physicsclassroom.com/mmedia/index.cfm http://www.phys.hawaii.edu/~teb/java/ntnujava/index.html http://www.colorado.edu/physics/2000/index.pl Constants___________________________ [These are given on each test paper] DIPONT Educational Resource - Science 32