CIE AS-LEVEL PHYSICS//9702 , 1. PHYSICAL QUANTITIES AND UNITS 1.4 Scalar and Vector ο· A physical quantity is made up of magnitude and unit ο· Scalar: has magnitude only, cannot be –ve e.g. speed, energy, power, work, mass, distance ο· Vector: has magnitude and direction, can be –ve e.g. displacement, acceleration, force, velocity momentum, weight, electric field strength 1.2 Base Units 1.5 Vectors 1.1 Physical Quantities ο· The following are base units: Quantity Basic Unit Name Symbol Name Symbol Mass ππ π Kilogram Length π Meter π Time π‘ Second π Temperature Kelvin π πΎ Electric Current πΌ Ampere π΄ ο· All units (not above) can be broken down to base units ο· Homogeneity can be used to prove equations. ο· An equation is homogenous if base units on left hand side are the same as base units on right hand side. ο· This may not work every time due to the fact that it does not take pure numbers into account (πΈπ formula) 1.3 Multiples and Submultiples Multiple 1012 109 106 103 Submultiple 10-3 10-6 10-9 10-12 Prefix Tera Giga Mega Kilo Prefix Milli Micro Nano Pico Symbol π πΊ π π Symbol π π π π Quantity Accuracy 1 cm 0.1 cm Length 0.01 cm 0.001 cm 1 cm3 Volume 0.05 cm3 Angle 0.5o 1 min Time 0.01 sec π₯-axis scale 1oC Temperature 0.5oC P.d. 0.01 V 0.01 A Current 0.0001 A Instrument Tape Ruler Vernier caliper Micrometer screw gauge Measuring cylinder Pipette/burette Protractor Clocks Stopwatch Time base of c.r.o Thermometer Thermocouple Voltmeter Ammeter Galvanometer 2.1 Using a Cathode Ray Oscilloscope 1.4 Estimations Mass of a person Height of a person Walking speed Speed of a car on the motorway Volume of a can of a drink Density of water Density of air Weight of an apple Current in a domestic appliance e.m.f of a car battery Hearing range Young’s Modulus of a material 2. MEASUREMENT TECHNIQUES 70 kg 1.5 m 1 ms-1 30 ms-1 300 cm3 1000 kgm-3 1 kgm-3 1N 13 A 12 V 20 Hz to 20,000 Hz Something × 1011 Example: A supply of peak value 5.0 V and of frequency 50 Hz is connected to a c.r.o with time-base at 10 ms per division and Y-gain at 5.0V per division. Which trace is obtained? Maximum value is 5.0V ∴ eliminate A and B 1 1 πΉ = and π = πππππππ π × π·ππ£ππ ππππ so πΉ = π πππππππ π × π·ππ£ππ ππππ 1 1 π·ππ£ππ ππππ = = =2 πΉ × πππππππ π 50 × 10 × 10−3 Trace must have period of 2 divisions and height of 1 division ∴ D PAGE 3 OF 16 CIE AS-LEVEL PHYSICS//9702 , 2.1 Systematic and Random Errors 2.4 Micrometer Screw Gauge ο· Systematic error: o Constant error in one direction; too big or too small o Cannot be eliminated by repeating or averaging o If systematic error small, measurement accurate o Accuracy: refers to degree of agreement between result of a measurement and true value of quantity. ο· Random error: o Random fluctuations or scatter about a true value o Can be reduced by repeating and averaging o When random error small, measurement precise o Precision: refers to degree of agreement of repeated measurements of the same quantity (regardless of whether it is correct or not) 2.1 Calculations Involving Errors For a quantity π₯ = (2.0 ± 0.1)ππ ο· Absolute uncertainty = βπ₯ = ±0.1ππ βπ₯ = 0.05 π₯ βπ₯ = × 100% π₯ 2π₯+π¦ 3 or π = 2π₯−π¦ , 3 then βπ = 2βπ₯+βπ¦ 3 o When values multiplied or divided, add % errors o When values are powered (e.g. squared), multiply percentage error with power If π = 2π₯π¦ 3 or π = 2π₯ , π¦3 then βπ π = βπ₯ π₯ + Measures objects up to 0.1mm ο· Place object on rule ο· Push slide scale to edge of object. ο· The sliding scale is 0.9mm long & is divided into 10 equal divisions. ο· Check which line division on sliding scale matches with a line division on rule ο· Subtract the value from the sliding scale (0.09 × π·ππ£ππ ππππ ) by the value from the rule. 3.1 Linear Motion = 5% ο· Combining errors: o When values added or subtracted, add absolute error If π = 2.5 Vernier Scale 3. KINEMATICS ο· Fractional uncertainty = ο· Percentage uncertainty ο· Measures objects up to 0.01mm ο· Place object between anvil & spindle ο· Rotate thimble until object firmly held by jaws ο· Add together value from main scale and rotating scale 3βπ¦ π¦ ο· Distance: total length moved irrespective of direction ο· Displacement: distance in a certain direction ο· Speed: distance traveled per unit time, no direction ο· Velocity: the rate of change of displacement ο· Acceleration: the rate of change of velocity ο· Displacement-time graph: o Gradient = velocity 2.3 Treatment of Significant Figures ο· Actual error: recorded to only 1 significant figure ο· Number of decimal places for a calculated quantity is equal to number of decimal places in actual error. ο· During a practical, when calculating using a measured quantity, give answers to the same significant figure as the measurement or one less 3.2 Non-linear Motion ο· Velocity-time graph: o Gradient = acceleration o Area under graph = change in displacement PAGE 4 OF 16 CIE AS-LEVEL PHYSICS//9702 , ο· Uniform acceleration and straight line motion equations: π£ = π’ + ππ‘ π = π’π‘ + 1 ππ‘ 2 2 1 π = 2 (π’ + π£)π‘ π = π£π‘ − 1 ππ‘ 2 2 3.5 Projectile motion ο· Projectile motion: uniform velocity in one direction and constant acceleration in perpendicular direction π£ 2 = π’2 + 2ππ ο· Acceleration of free fall = 9.81ms-2 3.3 Determining Acceleration of Free Fall ο· A steel ball is held on an electromagnet. ο· When electromagnet switched off, ball interrupts a beam of light and a timer started. ο· As ball falls, it interrupts a second beam of light & timer stopped ο· Vertical distance π is plotted against ππ 1 π = π’π‘ + ππ‘ 2 and π’ = 0 β π‘2 1 1 2 2 π = ππ‘ 2 i.e. β = ππ‘ 2 2 πΊπππππππ‘ = ο· Horizontal motion = constant velocity (speed at which projectile is thrown) ο· Vertical motion = constant acceleration (cause by weight of object, constant free fall acceleration) ο· Curved path – parabolic (π¦ ∝ π₯ 2 ) 1 = π 2 π΄ππππ. = 2 × πΊπππππππ‘ displacement ο· Continues to curve as it accelerate ο· Graph levels off as it reaches terminal velocity velocity ο· Continues to accelerate constantly ο· Graph curves as it decelerates and levels off to terminal velocity acceleration 3.4 Motion of Bodies Free Falling ο· Straight line ο· Graph curves down to zero because resultant force equals zero Without air Resistance With air Resistance Component of Velocity Horizontal Vertical Increases at a Constant constant rate Decreases to zero Increases to a constant value 3.6 Motion of a Skydiver 4. DYNAMICS 4.1 Newton’s Laws of Motion ο· First law: if a body is at rest it remains at rest or if it is in motion it moves with a uniform velocity until it is acted on by resultant force or torque PAGE 5 OF 16
