Physics: It’s all around you… What is Physics?

Scientific Notation copy In scientific notation, the number is expressed by: 1. writing the correct number of significant digits with one non-zero digit to the left of the decimal point 2. multiplying the number by the appropriate power (+ or – ) of 10

copy Example: 2394 = 2.394 x 1000 = 2.394 x 103 0.067 = 6.7 x 0.01 = 6.7 x 10 -2 Note: scientific notation also enables us to show the correct number of significant digits. As such, it may be necessary to use scientific notation in order to follow the rules for certainty (discussed later)

Using your calculator…. On many calculators, scientific notation is entered using a special key; labelled EXP or EE. This key includes “x 10” from the scientific notation; you need to enter only the exponent. For example, to enter 7.5 x 10 4 press 7.5 EXP 4 3.6 x 10-3 press 3.6 EXP +/- 3

Practice 1. Express each of the following in scientific notation (to 2 sig. dig.) A) 6 807 B) 0.000 053 C) 39 379 280 000 D) 0.000 000 813 E) 0.070 40 F) 400 000 000 000 G) 0.80 H) 68 Answers: 6.8 x 103 5.3 x 10-5 3.9 x 1010 8.1 x 10-7 7.0 x 10-2 4.0 x 1011 8.0 x 10-1 6.8 x 101

Practice 2. Express each of the following in common notation A) 7 x 101 B) 5.2 x 103 C) 8.3 x 109 D) 10.1 x 10-2 E) 6.3868 x 103 F) 4.086 x 10-3 G) 6.3 x 102 H) 35.0 x 10-3 Answers: 70 5 200 8 300 000 000 0.101 6 386.8 0.004 086 630 0.035 0

Investigation: Training on the Job Problem: How long (in hours) will it take the toy train to travel across Canada from east to west? Materials: Metre stick -Small wind-up toy or hotwheels car - timer Procedure: Measure as carefully as you can , in centimetres, how far the vehicle can travel in 5 seconds Repeat step one two more times and then calculate the average. Observations: Trial Distance (cm) 1 2 3 Average

Questions: How far (in cm) did the train travel in 1 second? How far (in km) did the train travel in 1 second? How many km would it travel in 1 hour? How long would it take (in days) to go across Canada from St. John’s in Newfoundland to Victoria in British Columbia? (highway distance) **7314 km **post your group’s answer to this question on the board Do you think it would make any different if the vehicle travelled from west to east or east to west?

Day 2. SI Units

copy SI Units It is easiest to keep track of your units if you use ratios/conversion factors to convert your units. Example problems: Convert 34.5 mm to m. Convert 23.6 mm to km. (HINT: You can avoid careless mistakes by first converting from mm into m, and then converting from m to km.) 3) Convert 5 km/h into m/s

Investigation #2: Measuring Human Reaction Time With only a metre stick??!!??

Your task - Develop a simple procedure that clearly shows how you would conduct this investigation to minimize uncertainty - Collect data for several trials for each member of your team. Record in a clear, meaningful manner. - Convert your measured values into time values using the formula you just saw. - Calculate the average reaction time for each member of the group, and then calculate the average reaction time for the whole group. - Determine the percent difference between the shortest and longest reaction times in the group.

And what will be handed in? - It is hoped that next day you will be able to exchange labs with another team who will evaluate your procedure. - Their results and evaluation will be added to your lab as an appendix (their evaluation can be left as rough copy) - Your lab will include Purpose, Apparatus (sketch), Procedure, Observations, Analysis (including percent difference calculations), Discussion (comments from the other team should help you here) and Conclusion and an STSE (relating science to technology, society, and the environment) example of the significance of reaction times - For this lab, you will be submitting a single lab for the team but individual STSE examples (due on Monday)

Day 3. Uncertainty and Significant Digits

Significant Digits Rules: (on handout) Rules: All non-zero digits are significant: 346.6 N has four significant digits In a measurement with a decimal point, zeroes are placed before other digits are not significant: 0.0056 has two significant digits Zeroes placed between other digits are always significant: 7003 has four significant digits Zeroes placed after other digits behind a decimal are significant: 9.100 km and 802.0 kg each has four significant digits

Significant Digits In a calculation: (on handout) In a calculation: When adding or subtracting measured quantities, the final answer should have no more than one estimated digit (the answer should be rounded off to the least number of decimals in the original measurement) **number of decimal places matter When multiplying or dividing, the final answer should have the same number of significant digits as the original measurement with the least number of significant digits ** significant digits matter **when doing long calculations, record all of the digits until the final answer is determined, and then round off the answer to the correct number of significant digits (ADD TO HANDOUT)

Significant digits

Precision Rules for precision: All measured quantities are expressed as precisely as possible. All digits shown are significant with any error or uncertainty in the last digit. For example, in the measurement 87.64 cm, the uncertainty lies with the digit 4

Precision The precision of a measuring instrument depends on its degree of fineness and the size of the unit being used For example, a ruler calibrated in millimetres is more precise than a ruler calibrated in centimetres

Precision Any measurement that falls between the smallest divisions on the measurement instrument is an estimate. We should always try to read any instrument by estimating tenths of the smallest division.

Precision 4. The estimated digit is always shown when recording the measurement. Eg. The 7 in the measurement 6.7 cm would be the estimated digit

Precision 5. Should the object fall right on a division mark, the estimated digit would be 0.

Precision

worksheet

Reaction Time Lab – Step 2 Today you are to have your PROCEDURE ready to be evaluated by another team. When you get another team's procedure to evaluate you are to follow it PRECISELY to determine reaction times for each of the members of your team. When you are completed, return the lab to the team along with ONE hand written page outlining your thoughts on their procedure and the results of your testing. (i.e. your teams reaction times.)

Day 4. Error

Two Types of Error RANDOM ERROR copy RANDOM ERROR Results when the last digit is estimated Reduced by taking the average of several readings

Due to a problem with the measuring device copy SYSTEMIC ERROR Due to a problem with the measuring device Reduced by adding/subtracting the error or calibrating the device

Accuracy & Precision Accuracy: copy Accuracy & Precision Accuracy: - Refers to how closely a measurement agrees with the accepted value of the object being measured Precision: Describes how it has been measurement Depends on the precision of the measurement

Percentage Error No matter how precise a measurement is, it still may not be accurate. Percentage Error is the absolute value of the different between experimental and accepted values expressed as a percentage of the accepted value

Percentage Difference Sometimes if two values of the same quantity are measured, it is useful to compare the precision of these values by calculating the percentage difference between them

Practice Worksheet – math skills Determine the percent difference between the shortest and longest reaction times in your group

How to Write a Lab Report handout Remember: include in your conclusion: “Relating Science to Technology, Society, and the Environment (STSE)” - provide an example of the significance of reaction times