Name Class Section 1. State the number in scientific notation and write the number of significant figures in each of the following numbers. Explain your answer. a. 37.60 3.76 X10 3 significant figure b. 0.001300 1:3 X10-2 c. 1300. 1.34 104 d. 1.2300 1.23X10° 2 2 3 2. Perform the indicated operations to the correct number of significant figures using the rules for significant figures 3 > 46.2 a. 37.60 x 1.23= 46.248 b. 6.71 /8.975= 0.7465 c. 3.7652+1.23+37.212= 42,175 2 0.75 1 - 42-2 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. Student LI L2 L3 L4 I SD u Student 1 1.4717 1.4711 1.4722 1.4715 lold 716 0.000396 1.4716 + 0.000396 Student 2 1.4753 1.4759 1.4756 1.4749 1.4756 0.00037 1.4754 €0.00037 Student 3 1.4719 1.4723 1.4705 1.4719 1.4H7 0.00068 8 1.4717 to 90068 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). 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. b) Do any of the three students have data that suggest the possibility of an error? If so, state which student it is, and state how the data indicate your conclusion. 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. d) Calculate the percentage error between average length obtained by student 1 and the standard value using formula (1). e) Calculate the percentage difference for average lengths obtained by students 1 and 3 using formula (2) 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 Force in N (on Y axis) as a function of mass in kg (on X axis). Force N1 74.30 120.5 171.3 205.3 260.1 Mass [kg] 7.570 11.97 16.58 21.00 25.49 5. Calculate the slope of the best fit line without considering any data points, but choosing two points on the line whose coordinates you can easily read. Clearly show on your graph these two points that you pick to calculate the slope on your best fit line. Show your calculation on the graph paper. Slope = 6. What is the unit of the slope? Unit = 7. The equation that you just plotted is: F=m.a, what is the physical meaning of the slope? Explain how you get it to receive credit. 8. Calculate the percentage error using equation (1) if the standard value is 10.10 m/s?. 9. What would be the meaning of the slope if you plot mass on Y-axis vs. volume on X-axis? The equation used is: density = mass/volume. Re-write the equation in standard form to justify your answer.
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