AS & A LEVEL PHYSICS 9702 REVISION NOTES WELL ORGANIZED

1. 1.1 Physical quantities b)(1) make reasonable estimate of Fre- quency Of Audible Sound Wave: 2. 1.1 Physical quantities b)(2) make reasonable estimate of The Wavelength, in nm, of Ultraviolet Radia- tion: 3. 1.1 Physical quantities b)(3) make reasonable estimate of The Mass Of The Plastic 30cm Ruler: 4. 1.1 Physical quantities b)(4) make reasonable estimate of Den- sity Of Air At Atmospheric 5. 1.1 Physical quantities b)(5) make reasonable estimate of 1) Mass of 3 cans (330 ml) of Coke Humans can detect sounds in a frequency range from about 20 Hz to 20 kHz. (Human infants can actually hear frequencies slightly higher than 20 kHz, but lose some high-frequency sensi- tivity as they mature; the upper limit in average adults is often closer to 15-17 kHz.) = If you remember the Order Of Magnitude of electromagnet- ic radiation then you can answer this question easily. Ultraviolet radiation has wavelength from meter. So you can put any value between this. Answer: 50nm = A plastic ruler cannot have mass greater or equal to KG. But a 500 gram object will obviously be much heavier than a plastic ruler. So, it must be in the range of 30g to 100g. Answer: 50g = As we know the value of Atmospheric pressure if approx- imately 100,000 pascals. Let's consider the height of the air that surrounds the earth is 10000m. Now using the formula Pressure = density * gravity * height, we can find out the density. Density: 1 Kg/m^3 1) 1 kg 2) 1000 kg 2) Mass of a medium-sized car 3) Length of a football field 4) Reaction time of a young man 6. 1.1 Physical quantities b)(6)Estimate the average running 3) 100 m 4) 0.2 s velocity = distance / time =2400 / (12.5 x 60) speed of a typical 17-year-old s 2.4-km = 3.2 H3 ms-1 run. 7. 1.1 Physical quantities b)(7)Which estimate is realistic? A) The kinetic energy of a bus travelling on an expressway is 30000J B) The power of a domestic light is 300W. C) The temperature of a hot oven is 300 K D) The volume of air in a car tyre is 0.03 m^3. A) A bus of mass m travelling on an expressway will travel be- tween 50 to 80 kmh-1, which is 13.8 to 22.2 ms-1. Thus, its KE will be approximately ½ m(182) = 162m. Thus, for its KE to be 30000J: 162m = 30000. Thus, m = 185kg, which is an absurd weight for a bus; ie. This is not a realistic estimate. B) A single light bulb in the house usually runs at about 20W to 60W. Thus, a domestic light is unlikely to run at more than 200W; this estimate is rather high. C)300K = 27 0C. Not very hot. D)Estimating the width of a tyre, t, is 15 cm or 0.15 m, and esti- mating R to be 40 cm and r to be 30 cm, volume of air in a car tyre is = ÀR(2 - r2)t = À(0.42 - 0.32)(0.15) = 0.033 m3 H 0.03 m3 (to one sig. fig.) 8. 1.2 SI units a) recall the following SI base quantities and their units: 9. 1.2 SI units b) express derived units as products or quotients of the SI base units and use the named units listed in this syl- labus as appropriate 10. 1.1 Physical quantities b)(4) make reasonable estimate of 1) Mass of 3 cans (330 ml) of Coke 2) Mass of a medium-sized car 3) Length of a football field 4) Reaction time of a young man 11. 1.2 SI units c) use SI base units to check the homo- geneity of physical equations 1) mass (kg), 2) length(m), 3) time (s), 4) current (A), 5)temperature (K), 6)amount of substance (mol) 1) 1 kg 2) 1000 kg 3) 100 m 4) 0.2 s An equation is homogeneous if quantities on BOTH sides of the equation has the same unit • E.g. s = ut + ½ at2 • LHS : unit of s = m • RHS : unit of ut = ms-1 x s = m • unit of at2 = ms-2 x s^2 = m 12. 1.2 SI units d) use the following prefixes and their symbols to indicate decimal submultiples or multiples of both base and derived units: pico (p), nano(n), micro (¼), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G), tera(T) 13. • Unit on LHS = unit on RHS • Hence equation is homoge- neous P = Ágh2 • LHS ; unit of P = Nm-2 = kg m-1 s-2 • RHS : unit of Ágh2 = kg m-3(ms-2) (m^2) = kgs-2 • Unit on LHS =(not) unit on RHS • Hence equation is not homoge- neous • Note: numbers has no unit • some constants have no unit. • e.g. Pi pico (p), 10^-12 nano(n), 10^-9 micro (¼), 10^-6 milli (m), 10^-3 centi (c), 10^-2 deci (d), 10^-1 kilo (k), 10^3 mega (M), 10^6 giga (G), 10^9 tera(T), 10^12 1.3 The Avogadro constant a) understand that the Avogadro con- stant NA is the number of atoms in 0.012 kg of carbon-12 14. 1.4 Scalars and vectors a) distinguish between scalar and vector quantities and give examples of each 15. 2.2 Errors and uncertainties a) understand and explain the effects of 1 mole of any subtance is the amount of that subtance which contain the same number of par- ticles as there are in 12g of Car- bon-12 I mol of a subtance contain 6.02 x 10^23 A scalar quantity has a magni- tude only. It is completely de- scribed by a certain number and a unit. Examples:- Distance, speed, mass, time, temperature, work done, kinetic energy, pressure, power, electric charge etc. A vector quantity has both mag- nitude and direction. It can be described by an arrow whose length represents the magnitude of the vector and the arrow-head represents the direction of the vector. Examples:- Displacement, ve- locity, moments (or torque), mo- mentum, force, electric field etc. 1) Systematic Error -Its results in all the readings tak- en being faulty in one direction systematic errors (including zero errors) -Systematic Error cannot be and random errors in measurements eliminated by taking repeated readings and averaging them since the error will remain con- stant -It is an error that already exists 16. 2.2 Errors and uncertainties b) understand the distinction between precision and accuracy 17. 2.2 Errors and uncertainties c) assess the uncertainty in a derived quantity by simple addition of absolute, fractional or percentage un- certainties (a rigorous statistical treatment is not required) in an instrument Examples: 1)Zero Error 2) Wrongly calibrated scale 2)Random Error -Its results in all readings taken being scattered about a mid-val- ue -Cannot be eliminated but it can be minimized by taking repeated readings Examples: 1)Parallax Error 2)Reading Scales from different angles 3)Reaction Time Precision: refers to the degree of agreement (scatter, spread) of repeated measurements of the same quantity. {NB: regardless of whether or not they are cor- rect.} Minimizing Random error is Pre- cision Accuracy refers to the degree of agreement between the result of a measurement and the true val- ue of the quantity. Minimizing or Eliminating Sys- tematic error is Accuracy Actual error must be recorded to only 1 significant figure, & The number of decimal places a calculated quantity should have is determined by its actual error. For eg, suppose g has been ini- tially calculated to be 9.80645 m s-2 & g has been initially calcu- lated to be 0.04848 m s-2. The final value of g must be record- ed as 0.05 m s-2 {1 sf }, and the appropriate recording of g is (9.81 0.05) m s-2. 18. 3.1 Equations of motion a) define and use distance, displace- ment, speed, velocity and acceleration 19. 3.1 Equations of motion Distance: Total length covered ir- respective of the direction of mo- tion. Displacement: Distance moved in a certain/specified direction Speed: Distance travelled per unit time. Velocity: is defined as the rate of change of displacement, or, displacement per unit time {NOT: displacement over time, nor, displacement per second, nor, rate of change of displace- ment per unit time} Acceleration: is defined as the rate of change of velocity. The area under a velocity-time c) determine displacement from the area graph is the change in displace- 20. under a velocity-time graph ment. 3.1 Equations of motion d) determine velocity using the gradient of a displacement-time graph 21. 3.1 Equations of motion e) determine acceleration using the gra- dient of a velocity-time graph 22. 3.1 Equations of motion f) derive, from the definitions of velocity and acceleration, equations that represent uniformly accelerated motion in a straight line 23. 3.1 Equations of motion g)(1) 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 24. 3.1 Equations of motion g)(2) solve problems using equations that represent uniformly accelerated motion in a straight line, including the motion of bodies falling in a The gradient of a displace- ment-time graph is the {instanta- neous} velocity. The gradient of a velocity-time graph is the acceleration. 1. v = u +a t: derived from defin- ition of acceleration: a = (v - u) / t 2. s = ½ (u + v) t: derived from the area under the v-t graph 3. v2 = u2 + 2 a s: derived from equations (1) and (2) 4. s = u t + ½ a t2: derived from equations (1) and (2) These equations apply only if (1)the motion takes place along a straight line (2)the acceleration is constant {hence, for eg., air resistance must be negligible.} uniform gravitational field WITH air re- sistance 25. 3.1 Equations of motion h) describe an experiment to determine the acceleration of free fall using a falling body 26. 3.1 Equations of motion i) describe and explain motion due to a uniform velocity in one direction and a uniform acceleration in a perpen- dicular direction 27. 4.1 Momentum and Newton's laws of motion a) understand that mass is the property of a body that resists change in motion 28. 4.1 Momentum and Newton's laws of motion c) Define linear momentum and impulse. Mass: is a measure of the amount of matter in a body, & is the property of a body which resists change in motion. Linear momentum of a body is defined as the product of its mass and velocity. p = m v Impulse of a force I is defined as the product of the force and the time t during which it acts Impulse = F x t = mv - mu = chnage in momentum {for force which is const over the duration t} For a variable force, the impulse 29. 4.1 Momentum and Newton's laws of motion d) define and use force as rate of change of momentum 30. 4.1 Momentum and Newton's laws of motion e) state and apply each of Newton's laws of motion = Area under the F-t graph { Fdt; may need to "count squares"} Impulse is equal in magnitude to the change in momentum of the body acted on by the force. Hence the change in momentum of the body is equal in mag to the area under a (net) force-time graph. {Incorrect to define impulse as change in momentum} Force is defined as the rate of change of momentum F = m(v - u)/t = ma F = v dm/dt The {one} Newton is defined as the force needed to accelerate a mass of 1 kg by 1 m s-2. Newton s First Law Every body continues in a state of rest or uniform motion in a straight line unless a net (exter- nal) force acts on it. Newton s Second Law The rate of change of momen- tum of a body is directly pro- portional to the net force acting on the body, and the momentum change takes place in the direc- tion of the net force. Newton s Third Law When object X exerts a force on 31. 4.2 Non-uniform motion a) describe and use the concept of weight as the effect of a gravitational field on a mass and recall that the weight of a body is equal to the product of its mass and the acceleration of free fall 32. 4.3 Linear momentum and its conservation a) state the principle of conservation of momentum 33. 4.3 Linear momentum and its conservation b) apply the principle of conservation of momentum to solve simple problems, including elastic and inelastic interactions between bodies in both one and two dimensions (knowl- object Y, object Y exerts a force of the same type that is equal in magnitude and opposite in direc- tion on object X. The two forces ALWAYS act on different objects and they form an action-reaction pair. Weight: is the force of gravita- tional attraction (exerted by the Earth) on a body. Principle of Conservation of Lin- ear Momentum: When objects of a system interact, their total mo- mentum before and after interac- tion are equal if no net (external) force acts on the system. The total momentum of an isolat- ed system is constant m1 u1 + m2 u2 = m1 v1 + m2 v2 if net F = 0 {for all collisions } NB: Total momentum DURING the interaction/collision is also conserved. (Perfectly) elastic collision: Both momentum & kinetic energy of the system are conserved. Inelastic collision: Only momen- tum is conserved, total kinetic energy is not conserved. edge of the concept of coefficient of restitution is not required) Perfectly inelastic collision: Only momentum is conserved, and the particles stick together af- ter collision. (i.e. move with the same velocity.) 34. 4.3 Linear momentum and its conservation c) recognise that, for a perfectly elastic collision, the relative speed of approach is equal to the relative speed of separation 35. 4.3 Linear momentum and its conservation d) understand that, while momentum of a system is always conserved in interactions between bodies, some change in kinetic energy may take place 36. 5.1 Types of force b) understand the origin of the upthrust acting on a body in a fluid 37. 5.1 Types of force 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) For all elastic collisions, u1 - u2 = v2 - v1 ie. relative speed of approach = relative speed of separation or, ½ m1u1^2 + ½ m2u2^2 = ½ m1v1^2 + ½ m2v2^2 In inelastic collisions, total ener- gy is conserved but Kinetic Ener- gy may be converted into other forms of energy such as sound and heat energy. Upthrust: an upward force exert- ed by a fluid on a submerged or floating object Origin of Upthrust: Pressure on Bottom Surface Pressure on Top Surface 4 Force on Bottom Surface