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Lab 1 – Measurement of Length Name: ________________________ LT 3 Due Date: _____________________ Introduction: The only thing certain about measurements in experiments is that there is no certainty! Physical properties are often measured in standardized quantities called units of measurement. Any number that is the result of a physical measurement has a unit of measurement associated with it. The number and the unit are inseparable and without the unit the number has no meaning. Numbers that result from physical measurements also have an uncertainty associated with them. This uncertainty is due to the sensitivity level of the instrument used to take the measurement. Instruments with finer calibration produce measurements with less uncertainty, but uncertainty is always present. Rules to consider as you take measurements in this lab: Measure the length of an object with the middle of the ruler/meter stick; the ends often have improper stamping or are worn down. Avoid parallax in measurements by always reading the instrument directly out from the end of the object being measured. Record all digits with certainty and then estimate the last digit. For example, if you are using a metric ruler where the smallest division is one millimeter then you will record to the nearest millimeter and then estimate to a tenth of a millimeter. Objectives: 1. Select an appropriate instrument for measuring distances and time. 2. Properly read a metric ruler, meter stick, or metric tape measure and record to the proper number of significant digits with appropriate units. Procedure: Part A: Measurement of your wingspan and height Nature is full of symmetry and patterns. As scientists, we look for patterns to help us better understand the universe we live in. Symmetry can be found all around us in everyday items. The human body is believed to be symmetrical. Are you symmetrical? Let’s test it out by comparing your wingspan to your height. 1. Record your data for this part in Table A. Always use the most precise measuring instrument possible. 2. Stand as in Figure A. 3. Estimate the length, in cm, of the subject’s wingspan [tip of middle finger of one hand to the top of the middle finger of the other hand] and record. 4. Using an appropriate measuring device, now measure the length of subject's wingspan [tip of middle finger of one hand to the top Figure A of the middle finger of the other hand] and record length in cm. 5. Determine the % difference between the estimated wingspan and the actual wingspan length. 6. Have subject take off shoes and stand upright. Estimate the height of the subject in cm and then measure and record height using an appropriate measuring instrument. 7. Determine the % difference between the estimated height and the actual height. 8. Divide the wingspan by the height to obtain a wingspan to height ratio. Part B: Measurements of your hand and forearm with hand The golden ratio is a number often obtained when taking the ratio of distances in simple geometric figures. This golden ratio, called phi (pronounce fi like “fly”) is also found on numerous occasions in the structure of the length of the forearm + hand human body. One area of the human body believed to contain this ratio is that of the . length of the forearm Does your body contain the golden ratio? 1. Record all data for this part of the experiment in Table B. 2. Have subject stretch out one arm and measure the length of his/her forearm [from elbow and wrist as shown in Figure B]. Record forearm length. Figure B 3. Have subject flatten their hand and measure the length of his/her forearm with hand [from the elbow to the tip of middle finger as shown in Figure B]. Record forearm + hand length. length of the forearm + hand 4. Divide to obtain the ratio. length of the forearm Part C: Determine thickness of a piece of paper 1. Record all data for this part of the experiment in Table C. 2. Measure the thickness of 50, 75, and 100 pages of your textbook in millimeters. 3. Calculate the average thickness of one page. Part D: Measurements of Circumference and Diameter 1. 2. 3. 4. 5. Record all data for this part in Table D. Using the appropriate device, measure the circumference and diameter for three of the circular objects. Plot data on graph Draw a line of best fit Calculate the slope (Rise⁄Run) Data and Calculations: Table A: Wingspan and Height Measurements Name of subject you are measuring Estimate length of subject’s wingspan in cm Measuring device used to measure subject’s wingspan Actual length of subject’s wingspan in cm % difference between the estimated wingspan and the actual wingspan % 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = |𝑎𝑐𝑡𝑢𝑎𝑙 𝑤𝑖𝑛𝑔𝑠𝑝𝑎𝑛 − 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑤𝑖𝑛𝑔𝑠𝑝𝑎𝑛| 𝑥 100 𝑎𝑐𝑡𝑢𝑎𝑙 𝑤𝑖𝑛𝑔𝑠𝑝𝑎𝑛 Estimated height of subject in cm (no shoes) Measuring device used to measure subject’s height Actual height of subject in cm % difference between the estimated height and the actual height % 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = Calculated ratio of wingspan / height |𝑎𝑐𝑡𝑢𝑎𝑙 ℎ𝑒𝑖𝑔ℎ𝑡 − 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 ℎ𝑒𝑖𝑔ℎ𝑡| 𝑥 100 𝑎𝑐𝑡𝑢𝑎𝑙 ℎ𝑒𝑖𝑔ℎ𝑡 Table B: Measurement of Forearm / Forearm + Hand Name of subject you are measuring Measuring device for forearm (no hand) Length of forearm (no hand) in cm Measuring device for forearm with hand Length of forearm with hand in cm Calculated ratio of length of the forearm + hand length of the forearm Table C: Book Page Measurements Total Thickness (mm) 50 pages 75 pages 100 pages Average thickness for a single sheet (mm) Table D: Circumference and Diameter Circumference Object 1 Object 2 Object 3 Average Circumference Diameter Slope of Curve Diameter Analysis: 1. Why should you read the ruler / meter stick / tape measure directly over the line you are reading and not at an angle (or to the side)? 2. Why is it less accurate to use the ends of a meter stick? Explain. 3. Of all the measurements you made, which do you feel is the least precise? Give a reason for your answer. 4. In Table C, which value do you think is the most accurate for the average thickness? Why? 5. Create an equation relating circumference and diameter (Hint: look at the equation for slope) Personal Conclusion: