Lab 1 Tools II report

Name Class Section Lab 1 report (29 points) To get credit, always show your work and explain the number of significant digits you use 1. State the number in scientific notation and write the number of significant figures in each of the following numbers. Explain your answer. (4 points) a. 37.60 3.760x10^-1 Since every digit in the number is regarded as important, 37.60 has a total of four significant numbers. b. 0.001320 1.320x10^-3 Because the zeroes at the end are important in this situation, there are four significant figures in the value c. 130001 1.30001x10^5 Due to the fact that the trailing zeros in this instance are saved by the ending number regarded as significant, there are six sig figs. d. 1.23140 1.23140x10^0 Because the zeroes at the end are important in this situation, there are six significant figures in the value 2. Perform the indicated operations to the correct number of significant figures using the rules for significant figures. (4 points) a. 37.621 x 12.48= 469.51008 b. 670 / 8.475= 79.05604719 c. 3.7652+570.232/1.23= 466.664302 d. 3.956+35.20-1.254= 37.902 To get credit, specify in each case the number of the rule you used to round your results . 3. Three students make measurements (in m) of the length of a rod using a meter stick. Each student’s measurements are tabulated in the table below. Using your calculator in statistic mode calculate the mean 𝐿 , standard deviation 𝑆 and uncertainty u of the measurements. (3 points) Student L 1 L 2 L 3 L 4 L SD u Student 1 1.4750 1.4759 1.4756 1.4749 1.47535 0.0005 0.0002 Student 2 1.4719 1.4725 1.4705 1.4719 1.4717 0.0008 0.0004 Student 3 1.4727 1.4718 1.4722 1.4715 1.3971 0.1502 0.0751 Note that the actual length of the rod is determined by a laser measurement technique to be 1.4716 m (this should be considered the standard value). for L = ( L1+L2+L3+L34 ) for SD = STDEV.S for u = SDn

a) State how one determines the accuracy of a measurement. Apply your idea to the measurements of the three students above and state which student has the most accurate measurement. (1 point) Student 3 is more accurate than Student 2. b) Do any of the three students have data that suggest the possibility of a systematic error? If so, state which student it is, and state how the data indicate your conclusion. (1 point) All possess systematic Error. c) Which student has the best measurement considering both accuracy and precision? State clearly what the characteristics are of the student’s data on which your answer is based. (1 point) Student 3 measurement is most accurate. d) Calculate the percentage error between average length obtained by student 1 and the standard value using formula (1). (1 point) Percentage error is obtained as, 0.0034% e) Calculate the percentage difference for average lengths obtained by students 1 and 3 using formula (2). (1 point) Difference between student 1 and student 3, 0.0017 4. Look at the example graph provided at the end of this lab manual to see how your graph should look like. Make a graph of Force in N (on Y axis) as a function of mass in kg (on X axis): plot the points and using your ruler draw a best fit line. (6 points: labels, units, scale, data points, line, slope points) Force [N] 7.420 12.75 17.13 21.53 26.21 Mass [kg] 7.670 12.97 16.58 22.00 25.49 5. Calculate the slope of the best fit line choosing two points on the line whose coordinates you can easily read ( do not use data points ). Clearly show on your graph the two points that you pick to calculate the slope on your best fit line. Show your calculation on the graph paper . Slope = 1.00566 (1 point) 6. What is the unit of the slope? Unit = N/kg (1 point) 7. Find the intercept. Show your calculation on the graph paper . Intercept = 1.00566 (1 point)