Physics 20 Introduction & Review Real tough physics equations Real smart physics guy
Is Physics Hard? People find physics difficult because it requires a detail-oriented, organized thought process. Success, then, is more about learning to think appropriately and less about memorizing equations and example solutions.
What is Physics? Investigates and describes the relationship between matter and energy How the universe works
Measurements & Units fundamental units are the building blocks of all other measurements We use SI (le Système International d'unités ) the common SI fundamental units are metre, kilogram, second derived units are units made from combinations of fundamental units: speed, acceleration, force, etc.
Derived units Speed m/s, km/h Acceleration m/s 2 kg m Force (newton) = 2 s
Units are as important as the actual number
Unit conversions A light year is the distance light travels in 1 year at 3.00 x 10 8 m/s. What is this distance in metres?
d = vt d = (3.00 x 10 8 m/s)(1.00 year) 1year UNITS Don t work: Change years to seconds 365days 24hours 3600sec onds year day hour t = 31536000 s d = vt d = (3.00 x 10 8 m/s)(31536000 s) d = 9.46 x 10 15 m
Units Think about the number AND units of your answer: is it logical for a car to take 3.55 x 10 17 s to drive 399 km to Calgary at 123 km/h? NO! Just how many years is this much time? The age of the universe is 14 billion years (1.4 x 10 10 a)
Answers to think about (or when you hope the calculator is smarter than you) Speed of a falling object is 340 m/s (speed of sound, Mach 1, 1224 km/h) Any speed close to or faster than 3.00 x 10 8 m/s (speed of light! There s NOTHING FASTER!) Distance of 1.50 x 10 11 m (Distance from Earth to sun) A distance of 2 x 10-15 m (size of a proton)
Physics Math In any physically correct equation, the units of any two quantities must be the same whenever these quantities are A. added or multiplied only B. subtracted or divided only C. multiplied or divided only D. added or subtracted only E. added, subtracted, multiplied, or divided
Physics > Math!! Use unit analysis to verify that the terms on the right have units of displacement or distance.
Physics > Math!! m m s 2 s s s 2 m m s s 2 s s 2
Solving Equations A = ½ bh solve for b V = 2r 2 h solve for h b 2A h A or b= 12 h h V 2 r 2
Solving Equations V = 2r 2 h solve for r r V 2 h
Solving Equations V = 45.3 m 3 h = 1.24 m r V 2 h r =? r = 2.41 m
Solving Equations P = P 0 + dgh solve for h P P dgh 0 P P 0 dg h
P = 673.7 N/m 2 P 0 = 143.0 N/m 2 Solving Equations d = 205 kg/m 3 g = 9.81 m/s 2 h =? h = 0.264 m P P 0 dg h
Measurements the accuracy of a measurement is how close to the actual value precision is the exactness of a measurement 12.5 m 12.498003 m Precision is controlled by the measuring tool
The average is NOT close to the centre The average is close to the centre
Measuring and Recording The last digit for a measurement is always a rounded number Precision is indicated by how many sig. digs. Precision depends on how finely the scale is divided
The smaller the divisions of the scale, the more precise the precision What is the measurement in cm? 1.89 cm
What s the measurement? 2.30 cm
Measuring and Recording There IS a difference between 4 cm and 4.0 cm 4 cm: actual value can be from 3.5 cm to 4.4 cm 4.0 cm: actual value from 3.95 cm to 4.04 cm
Significant digits significant digits are one way of indicating the precision of a measurement a number obtained by counting or by definition is exact and has an infinite number of significant digits
any non-zero digit is significant a zero at the end of a number or between non-zero digits is significant a zero at the beginning of a number is not significant
Examples 2.98 m/s 1.90 N 1.0833 kg 2.50 x 10 2 m/s 0.0033 m/s 3 s.d. 3 s.d. 5 s.d. 3 s.d. 2 s.d.
Calculations When adding or subtracting measured quantities, the calculated answer should be rounded to the same degree of precision as that of the least precise number used in the computation if this is the only operation. Add the following 12.3 0.12 12.34 (least precise) 24.76 Calculator answer The answer should be rounded to 24.8.
When multiplying or dividing measured quantities, the calculated answer should be rounded to the same number of significant digits as are contained in the quantity with the fewest number of significant digits if this is the only operation. For example: (1.23)(54.321) = 66.81483 The answer should be rounded to 66.8.
When a series of calculations is performed, each interim value should not be rounded before carrying out the next calculation. The final answer should then be rounded to the same number of significant digits as are contained in the quantity in the original data with the fewest number of significant digits.
In determining the value of 1.234.321 3.45 3.21, three calculations are required: 3.45 3.21 = 0.24 (1.23)(4.321) = 5.31483 5.31483 / 0.24 = 22.145125 The value should be rounded to 22.1.
Fundamental Units Write N m s in fundamental units m kg m m N s s 2 s N m kg m m kg m s s 2 s s 3 2
Practice Using fundamental SI units m m 2 s m d s 2? a s 2 m
Practice P = 673.7 N/m 2 P 0 = 143.0 d = 205 kg/m 3 g = 9.81 m/s 2 h =? Show that the units of the answer are metres P P 0 dg h
Solution 2 2 N / m N / m kg m m 3 2 N 2 m kg m s m 3 2 s h m N 2 m kg 2 2 s 2 2 N m s m 2 kg
Solution N kg s 2 m kg N s 2 s 2 kg kg s 2
Experimental Error no measurement is perfectly accurate, therefore there is always some uncertainty in any measurement the last digit in a measurement is always a rounded digit
Experimental errors are due to how the measurements are made, the type of measuring devices, etc. NOT caused by humans, NOT caused by calculation errors
there are 2 types of experimental error: a systematic error is constant throughout an experiment, a measurement will always be larger or smaller than the actual value (a clock that runs slow would have systematic error)
random error is not constant: a person measuring angles with a protractor not correctly aligned would have random error random error can be eliminated by repeating the measurements
Graphing Review The manipulated variable should be plotted on the x axis, and the responding variable on the y axis. The scale for each axis must be set so that at least ½ of the graph space is used. All axes must be labelled with the variable and units.
Distance (m) Distance vs time for Fang the cat Need a scale that is easy to read What is the distance when t = 7.0 minutes? About 128 m Time (minutes)
The graph must have a title in the form: Responding as a Function of Manipulated, with a further description to help identify the data. Each data point has to be plotted. A small circle can be drawn around each plotted point to indicate that it is a data point.
Best-fit lines or curves pass as close to as many data points as possible. Points that are a result of experimental error should not be considered when drawing the line. Best-fit lines do not have to pass through the origin.
Distance (m) Distance as a function of time Time (minutes)
Curve vs Line of Best Fit
Curve vs Line of Best Fit
Is this a proper graph? Distance as a function of time for a student going to class Distance (m) What is the distance here? What is the time here? Time (s)
Graph with little experimental error
Graph with lots of experimental error
Slope MUST use points on the line that can be read easily. Data points should not be used in a slope calculation. The points selected should be far apart on the line of best fit
The origin should not be assumed to be a suitable point. Units and powers of 10 given on the axes MUST be included in the calculation and final answer.
Significant digits for the slope are determined by the precision of the observations recorded in the data table
Distance (cm) Time (s) Example x 2, y 2 slope y x y 2 1 x 2 1 2.28 cm 1.86 5.50 s 4.50 0.420 cm / s cm s x 1, y 1
Which graph best shows the mass of a jar as marbles are added one at a time? THINK!
Distance (m) Graphing Practice Draw the line of best fit for each set of data Calculate the slope of your line to 2 sig. digs 80 70 60 50 40 30 20 10 Distance from locker vs time for a biology student going to class 0 0 10 20 30 40 50 60 70 80 90 Time (s)
Distance (m) #1 80 Distance from locker vs time for a biology student going to class 70 60 y = 0.8485x - 1.1275 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 Time (s)
Distance from class (m) #2 6 Distance vs time for a chemistry student walking from class 5 y = 1.4617x - 1.3729 4 3 2 1 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (s)
Distance (m) #3 Distance vs time for an old turtle 7 6 y = 1.404x - 1.2475 5 4 3 2 1 0 0 1 2 3 4 5 6 Time (minutes)
Distance (km) #4 18 16 y = 5.35x - 10.554 14 12 10 8 6 4 2 0 0 1 2 3 4 5 6 Time (h)
Distance from class (m) #5 25 20 y = 3.1736x - 0.3943 15 10 5 0 0 1 2 3 4 5 6 7 8 Time (s)
Distance (km) #6 600 500 y = -76.429x + 524.14 400 300 200 100 0 0 1 2 3 4 5 6 7 Time (h)
Graphical Relationships Linear Direct relationship y is proportional to x as x increases, y increases, y depends on the value of x if x doubles, the value of y also doubles
direct squared relationship; y changes as the square of x (if x doubles, y increases by a factor of 4) y is proportional to the square of x k is a constant (NOT the slope) Quadratic relationship
Inverse Variation as x increases, y decreases y is inversely proportional to x or to x squared
Practice What sort of relationship is shown? Does a large change in the manipulated variable result in a change in the responding variable?
Algebra Review f f i i f i f v s m /. s). ( s m /. v v t a v v t a t v v a 0 12 0 14 44 2 2 Solve for v f and then for t
v f vi d t 2 Solve for v f and then for t
v f2 = v i2 + 2ad solve for d
d = v i t + ½ at 2 solve for t if v i = 0
km/h to m/s Change 100 km/h to m/s km 1000 m 1h 100 h km 3600 s 27.8 m/s