Lab1_Calculations_Worksheet_F19

PHYS 1403 Lab 1: Scientific Calculations Worksheet Name: CWID: Enter you answers to each question in the data tables and yellow highlighted areas below. When completed, please upload this file using the lab submission link in Canvas (please submit this file in .doc, .docx, or .pdf formats only). Please be sure that all data tables and all yellow highlighted questions are completed. BACKGROUND INFORMATION The various metric units are shown below: Metric Unit Abbreviation # of Meters 1 nanometer 1 nm 10 -9 1 micrometer 1  m 10 -6 1 millimeter 1 mm 10 -3 (.001) 1 centimeter 1 cm 10 -2 (.01) 1 meter 1 m 1 1 kilometer 1 km 10 3 (1000) The following are some equivalent lengths in the British system. These equivalent lengths are called conversion factors. Metric Unit British Equivalent Conversion Factor 1 cm 0.394 in 1 cm = 0.394 in 1 in = 2.54 cm 1 m 39.4 in 1 m = 39.4 in 1 ft = 0.305 m 1 km 0.62 mi 1 km = 0.62 mi 1 mi = 1.61 km Some other conversion factors that will be useful are: 1 mile = 5280 ft 1 ft = 12 inches Converting from one metric unit to another or from a metric unit to a British unit is easy. Study the following examples: 1

Example # 1 How many centimeters are there in 1 kilometer? 1 km = 1 km × 1000 m 1 km × 100 cm 1 m = 100,000 cm = 1.00 × 10 5 cm In this example, note how the km in the numerator cancels the km in the denominator. Also the meters cancel out leaving cm in the result. When writing the conversion factors it is a good idea to first write the units and then put the appropriate numbers next to them. The final answer is given in exponential notation (also called scientific notation ). This is to avoid writing too many zeroes. The table below shows the exponents for some numbers: 10 = 1 x 10 1 1 = 1 x 10 0 100 = 1 x 10 2 0.1 = 1 x 10 -1 1000 = 1 x 10 3 0.01 = 1 x 10 -2 Example # 2 How many millimeters are there in 56 meters? 56 m = 56 m × 1000 mm 1 m = 56,000 mm = 5.60 × 10 4 mm 56,000 mm can be written as 56 x 10 3 mm or 560 x 10 2 mm or 5.60 x 10 4 mm. However, the convention is to keep the number between 1 and 9.99, so 5.60 x 10 4 mm will be the preferred way to write this result. Example # 3 How many miles are there in 4580 kilometers? First Way: 4580 km = 4580 km × 0.62 mi 1 km = 2840 mi Second Way : 4580 km = 4580 km × 1 mi 1.61 km = 2845 mi Using a different conversion factor MAY give you a slightly different result as this example shows. But its important to ask, is this difference significant? For the purpose of measurements and calculations in this lab, a difference of 5 miles in 2840 miles is not significant, so either answer would be counted correct. 2

7. Use the metric ruler to measure the width of this page in centimeters. Width of page in cm = 21.59 8. Calculate the width of the page in millimeters and meters. Width of page in mm = 215.9 Width of page in m =0.2159 9. Estimate the length of the following objects in centimeters, then measure their lengths to see how close your estimates were! Object Estimated Length Measured Length Pencil 18 19 Coin 2 2.4 Textbook 24 23.5 Computer Keyboard 37 38 Calculator 19 19.3 10. Estimate the distance from your house to Collin College in miles. Now convert your estimate to kilometers. Estimated Distance in miles = 6.1 Distance in km = 9.98 11. While the kilometer may be an adequate unit for measuring distances on Earth, for astronomical work, the "Astronomical Unit" (AU) is more convenient. What is the definition of an AU? The average distance (semimajor axis) of Earth from the Sun. 12. How many kilometers are there in 1 astronomical unit? AU in km = 150 million 13. The average distance of the Moon from the Earth is 384,000 km. Express this distance in scientific notation . Moon/Earth distance = 3.84 x 10^5 14. What is the average Earth-Moon distance in AU? 4

Moon/Earth distance in AU = 0.00256 15. Calculate the distances from the Sun to each of the planets in AU. The table below gives the distances from each planet to the Sun. Planet Distance (km) Distance (AU) Mercury 58 x 10 6 km 0.387 Venus 108 x 10 6 km 0.723 Earth 150 x 10 6 km 1 Mars 228 x 10 6 km 1.524 Jupiter 778 x 10 6 km 5.203 Saturn 1427 x 10 6 km 9.54 Uranus 2870 x 10 6 km 19.19 Neptune 4450 x 10 6 km 30.06 B. SPEED MEASUREMENTS The fastest speed known is that of light. Light travels at the incredible speed of 3  10 8 meters per second! The speed of light is represented by a letter c (so, c = 3  10 8 m/s). Since Speed = Distance Time We can get Distance = Speed × Time Since light has the fastest speed, the equation above is used to express large distances. In this scheme, the distance to an object is given in terms of how long it takes light to travel there. Example #5 Convert the speed of light given to be 3 x 10 8 m/s into km/hr. c = 3 × 10 8 m/s × 1 km 1000 m × 60 s 1 min × 60 min 1 hr = 1.08 × 10 9 km/hr 16. Find the speed of light in km/day. 5