Physics Nov 3 2008 Title: Nov 3 8:52 AM (1 of 45)
Physics Nov 3 2008 Physics is the branch of science that studies matter and energy, how they are related and how they interact. Physics covers everything from: motion, including speed and acceleration to measuring force, power and work to sound and electricity, light and heat, friction and efficiency. Computers and the internet, construction of homes, bridges, and roads, telephones (regular and cell), cable and satellite TV, airplanes and engines...all of these rely on our understanding of physics. Title: Apr 3 9:10 AM (2 of 45)
In this unit, we will be studying motion. We will look at several topics: speed *what does speed mean? *how is speed calculated? *how can we represent speed graphically? *how are speed and velocity related and different? acceleration *what is meant by acceleration? *how is acceleration calculated? *gravitational acceleration and objects in freefall Title: Apr 3 9:26 AM (3 of 45)
Title: Nov 3 9:32 AM (4 of 45)
Much of what we are doing involves measurement. Up until now, we have only performed qualitative analysis. Now, we will be doing quantitative analysis. Remember...what is the difference? Qualitative: Quantitative: Title: Apr 3 9:31 AM (5 of 45)
We need to establish some a standard for measuring and performing calculations, so that we are consistent. The system of measurement we use is metric, or SI (for system international). This system works well because units are related by powers of 10...in other words, to convert from one unit to another, you just multiply or divide by 10, 100, 1000, etc. Title: Apr 3 9:34 AM (6 of 45)
Metric involves base units for classes of measurement (ie: distance, mass, volume). Prefixes are applied to the base unit, changing its size. Base Units Dist: Vol: Mass: Title: Apr 3 9:38 AM (7 of 45)
Converting between metric units is simply a matter of seeing what power of ten separates the units, then multiplying or dividing. Multiply if converting from a larger unit to a smaller unit. Divide if converting from a smaller unit to a larger unit. Title: Apr 3 9:42 AM (8 of 45)
Examples of converting units: kilo hecto deca Base Units Dist: Meter (m) Vol: Litre (L) Mass: Gram (g) deci centi milli Title: Apr 3 9:45 AM (9 of 45)
Title: Nov 3 11:39 AM (10 of 45)
Title: Nov 3 10:07 AM (11 of 45)
Read Section 9.2 (p.344 348) complete # 1 4 p.349 Title: Nov 3 10:18 AM (12 of 45)
Significant Figures in Measurement In science, we deal mostly with measurements for calculations, rather than with pure numbers as in math. An important difference is that no measurement has an infinite number of digits...they are limited by the scale you use, and there is always a degree of uncertainty. Title: Apr 3 9:46 AM (13 of 45)
Title: Nov 4 10:47 AM (14 of 45)
Title: Nov 4 10:54 AM (15 of 45)
Title: Nov 4 10:59 AM (16 of 45)
Title: Nov 4 11:03 AM (17 of 45)
Title: Nov 4 11:05 AM (18 of 45)
Title: Nov 4 11:09 AM (19 of 45)
Title: Nov 4 11:12 AM (20 of 45)
Because of this, we always use a rule for measuring: Give your answer to one decimal point past the smallest division on the scale. One decimal place past the smallest division on your scale is the last decimal that is meaningful, or significant. Any decimals beyond this are meaningless, or insignificant. The number of significant digits in a measurement determines how we round when doing calculations using measured values. Since a measurement includes one decimal place past the smallest division on the scale, significant figures include all digits that are known for sure, plus one final estimated digit. Title: Apr 3 9:48 AM (21 of 45)
Examples of measuring: Use rulers of varying sensitivity to measure the following shapes Title: Apr 3 9:49 AM (22 of 45)
This highlights two characteristics of measurements. Both are indications of how good the measurement is. Accuracy: How close to the actual value a measurement is. In other words, the measurement is correct. Two things affect the accuracy of a measurement: the measuring device, and the skill of the user. (If the device is off, or if it is read wrong, the measurement won t be accurate.) Precision: How reproducable a measurement is. In other words, if several people repeated the measurement, assuming they read correctly, how close together would the measurements be? Precision is affected by both the skill of the user, and by the scale...the more sensitive the instrument (in other words, the smaller the units on the scale), the more precise the measurement will be. Title: Apr 3 9:52 AM (23 of 45)
One Important Exception to the Rules! Precision, and therefore significant figures, are only relevant when dealing with measured values. If a number is a counted or a defined value, there is no precision involved, and there are no significant figures. Why? Because there is no degree of uncertainty. Think about it...if you count the number of students in the room, there are exactly 32 (or whatever the actual number is)...there aren t 32.5, or even 32.0...it s just 32. In the same way, if you define a value, there is no precision, the value is exact. For example, there are 12 eggs in a dozen...not 12.0, just 12. There are 1000 meters in a kilometer...1000 exactly, not 1000.0, or 1000.000000000! Just exactly 1000! Title: Apr 3 9:55 AM (24 of 45)
Significant Figures in Measurements The number of significant figures in a measurement becomes important when performing calculations. To determine the number of significant figures in a measured value, there are really only three rules to remember: 1) Anything that isn't a zero, and anything between two non zeroes is significant 2) Zeroes at the beginning of a measurement are not significant 3) Zeroes are the end of a measurement are significant if they come after a decimal, or if they have a dash over them Title: Apr 3 9:57 AM (25 of 45)
In Class Assignment discuss # 5 p.349 Title: Nov 3 10:18 AM (26 of 45)
In Class Assignment complete # 6 p.349 Title: Nov 3 10:18 AM (27 of 45)
Scientific Notation This involves expressing values as a decimal multiplied by a power of 10. This makes expressing very large or very small values easier. For example: 4,150,000,000,000,000,000 km You wouldn't want to write this out several times. Title: Apr 4 8:01 AM (28 of 45)
To write the value in scientific notation, follow these steps: 1) Place the decimal immediately after the first number that is not a zero. Ex: 4,150,000,000,000,000,000 km Decimal would go here 2) Drop off all zeroes from the number 3) Count the number of spaces the decimal has moved, and write this as an exponent of 10 to be multiplied by the value Title: Apr 4 8:56 AM (29 of 45)
Ex: 4,150,000,000,000,000,000 km would become: 4.15 x 10 18km Title: Apr 4 9:02 AM (30 of 45)
For extremely small values, you would follow the same steps, but use a negative exponent. Ex: 0.000 000 000 000 039 6 kg Move the decimal to here. The value becomes: 3.96 x 10 14kg Title: Apr 4 9:03 AM (31 of 45)
Title: Apr 4 9:06 AM (32 of 45)
Title: Nov 4 10:23 AM (33 of 45)
Examples: State the number of significant figures in each of the following values. A. 123 m B. 0.123 mm C. 40 506 ml D. 9.8000 104 m E. 4.5600 g F. 0.078 kg G. 0.070 80 cm H. 98 000 km I. 98 000.00 L J. 175 books K. 1 kg = 1000 g L. About 15 000 people Title: Apr 3 10:02 AM (34 of 45)
Title: Nov 4 11:38 AM (35 of 45)
Calculations using Significant Figures In math, you will usually be told to round your answer to maybe two or three decimal places. That's fine if you are dealing with pure numbers. In science, however, we are usually dealing with measurements. The rule we have to follow is that we can't do a calculation and get an answer that is better than the information we use to find it! Title: Apr 3 10:04 AM (36 of 45)
For example, if you were finding the density of an object with a measured mass of 45.70 grams, and a measured volume of 13.6 ml, you would perform the following calculation: Density = Mass / Volume = 45.70 g / 13.6 ml = 3.3602941176470588235294117647059 g/ml Obviously, there is no way our answer can be exact to that many decimal places! Again, the answer can only be as good as what you use to get it! Title: Apr 3 10:07 AM (37 of 45)
So...there are two rules to follow for performing calculations using measured values: Multiplying and Dividing follow the Certainty rule In calculations involving multiplying and dividing, the answer must contain no more significant figures than the measurement with the least significant figures. The position of the decimal point has nothing to do with the number of significant figures! Title: Apr 3 10:12 AM (38 of 45)
Ex: 6.75 m 0.024 m = 0.162 m2 The first measurement contains 3 sig figs, the second contains 2 sig figs. Therefore, the answer can only contain 2 sig figs. Rounded to the correct number of sig figs, the answer becomes: 0.16 m2 Note also that the units become m2. This is very important...it shows the result as a measurement of area, instead of a straight line distance. Title: Apr 3 10:14 AM (39 of 45)
Adding and Subtracting follow the Precision Rule Round your answer to the decimal place of the least precise measurement. For example: 34.65 m + 123.8 m The first value is rounded to the hundredths place. The second is to the tenths place...this is less precise, so our answer is rounded to the nearest tenth. So...the answer should be rounded to 158.5 Title: Apr 3 10:15 AM (40 of 45)
Homework #5 a) The answer for a multiplication or division problem should have the same number of significant figures as whichever measurement has the least. Title: Apr 5 8:46 AM (41 of 45)
Homework #5 b) The answer for an addition or subtraction problem should should be rounded to the same decimal place at the least precise measurement. Title: Apr 5 8:49 AM (42 of 45)
Homework #6 a) 2 mm b) 89.2514 = 89.3 km/hr c) 19.8 g = 20 g d) 1.2083333 = 1.21 hr Title: Apr 5 8:50 AM (43 of 45)
Homework #6 e) 120.75 = 121 ml f) 1,012.12 = 1,010 m g) 24.73 = 24.7 cm Title: Apr 5 8:53 AM (44 of 45)
Homework #6 h) 13.13 = 13.6 h i) 102.14 = 102.1 mm j) 16.438 = 16.44 s Title: Apr 5 9:01 AM (45 of 45)