Applied Science Maths & Measuring 1 P age SJG
Standard Form and Unit Prefixes In Physics we need to work with some very small numbers (like the mass on an electron) and some very large numbers (like the diameter of a galaxy) Standard form lets us simplify small and large numbers. Write out these numbers in full. 4.59 x 10 10 3.14 x 10-5 900 x 10-3 0.05 x 10 6 You need to be able to covert to standard form both ways. Convert these to standard form 1204000000 0.000000135 1/3500 You have met prefixes before. You should all know the following write in the multiple c e.g. cm 100 k e.g. km 1000 m e.g mm Complete the following table Text Symbol Mulitplication Factor Standard Form mega M x 10 6 k 1000 x 10 3 centi x 10-2 milli m 0.001 μ 0.000001 2 P age SJG
Algebra Rule 1: You can add or subtract LIKE TERMS but you cannot add or subtract DIFFERENT TERMS. Rule 2: When Multiplying with Algebra, we need to remember the following things: 1. We CAN multiply different terms and like terms together 2. Always multiply the numbers together first 3. Leave out the Multiplication Sign Rule 3: When Dividing with Algebra, the rules are just the same as when multiplying, but instead of a division sign like this we tend to write divisions as fractions! Crucial: When dividing, watch for things cancelling out and disappearing! Rule 4: When Moving terms in an equation, the rules are 1. Do the opposite maths function (+ and -, x and, x 2 and, on both side of the equation) 2. Apply the rules for multiplying, dividing adding and subtracting terms to cancel/simplify 3. You might need to repeat steps 1 and 2 several times 3 P age SJG
Algebra examples Rearranging equations Write the equation in terms of V P = V2 R navq ; re Write the equation in terms of R 1 1 R t = 1 R 1 + 1 R 2 Combining and rearranging Objects falling downwards freely convert GPE into KE and vice versa for moving upwards with no energy loss if friction/air resistance is negligable. Combine the two equations to give an equation for how high a ball will go when thrown upwards with a speed v. E k 1 mv 2 2 E grav = mg h E Graph Drawing Axes Should always fill the page over half the sheet in each direction. Think about which way around you should plot it is not always sensibile to plot the independent on the x-axis. Scales Always go up in sensible steps. Go up in even steps Always in jumps of 1, 2, or 5 per 1cm or 2cm line (or multiples of them e,g, 0.1, 200, 0.005) Consider a truncated scale do you need to start a 0? Your plots should cover most of the graph unless you need to allow for finding the intercept. 4 P age SJG
Plots These need to be accurate to within 1mm. Plots should be made with a sharp pencil blunt pencils will leave marks more than 1mm wide (so you cannot be accurate to 1mm) Lines and curves Straight lines (drawn with a rigid ruler long enough) Smooth curves (no bumps/sudden changes in direction) Lines/curves of best fit should balance the points. If you are ignoring a point as an anomaly circle it. Try plotting this graph it should give a straight line t / s v / m/s 20 2.5 30 2.7 40 3.1 50 4.5 60 3.7 70 4.2 80 4.3 90 4.7 100 5.2 Gradient y-interept Anomalies = = = 5 P age SJG
Precision, Accuracy, Sensitivity & Reliability Precision Accuracy Sensitivity Reliability Now we ll practise some common measuring techniques you will need to make sure you have accurate results for your practicals 6 P age SJG