Answer question 1 pls from 1.0 to 11.0 cm. Because the triangles overlap, neatness will be an important aspect ofyour experimental technique. The thickness of your lines in drawing your triangles willalso have an effect on your measurements, and therefore on your error observations.2. For each triangle, measure and record the hypotenuse AC and the base length BC usinga vernier caliper. This will be the first use of this measuring device. It will be used oftenthroughout this course. Note that the hypotenuse may be of a length outside the rangeof the measuring tool, so that you must develop a consistent method for using this tool insuch cases. Be sure to also measure the common height AB and record its value.3. For each triangle, calculate the base length using the Pythagorean theorem:BC calc = S(AC?meas - AB?meas). Note that AB? will be a constant since all of the triangles willhave a common height. Next, determine the differences between the calculated and themeasured base length. Determine the fractional error = difference divided by themeasured value. And finally, convert this to a percentage error = 100 (fractional error).Note: try to use a spreadsheet program such as Excel to perform these calculations.Initial time spent learning how to use a spreadsheet can be a real time saver later on%3Dwhen the calculations/data sets become more difficult.Data AnalysisIt is often helpful to graphically represent your measurements. This sometimes allowsyou to be able to clearly make observations that are sometimes hidden when the data isonly displayed in tabular form. You will want to make two plots of your data.1. The first plot should use your measured base lengths as the horizontal data (x-axis),and the calculated base lengths as the vertical data (y-axis). Draw a best-fit line. This iseasily accomplished using Excel, where a linear trend may be added to your plot, includingthe equation that represents the trend. Because the difference between the calculatedand measured base line values can be small, this plot may not be adequate to show howthe values differ.2. To better visualize differences or fluctuations in the values, make a second plot of thepercentage error verses the measured base length values, measured base length as thehorizontal (x-axis) while the percentage error is plotted as the vertical (y-axis). Takeinto account the sign ( ± ) of the error in making this plot.Questions1. How do your percentage errors vary with the base length?2. For what type of right triangle does this experiment best test the validity of thePythagorean Theorem? How many significant digits (range?) were you able to obtain usinga caliper? How would this compare with simply using a ruler with mm resolution?3. If all (or most) of the difference values or percent errors have the same sign, youprobably have a systematic error in your results. What might cause such error? Doesyour data indicate a systematic error in your calculated base length?4. Why do you expect larger fractional errors (ignoring sign) when the base length issmall?Sample Data TableTriangle ACmeas BCmeas BCcale Difference Frac. Err. % ErrorАВ (ст) %3D'calc12(cm)(cm)(cm)(cm)10954B°12478910111212345678 9 0는 Measurements and PlottingPurpose/TheoryThis experiment is designed as an introduction to learn about the effects ofmeasurement error and to develop some skill with using different measuring devices. Theknown length of the base of a right triangle is compared with that calculated using thePythagorean Theorem and the measurements of the other two sides of the triangle. Themathematical relationship that is known to be valid can be used to calculate the baselength using the measured side and hypotenuse and then compare with the measured baselength. Large errors can occur when the triangle is long and skinny. These errors howevercan be minimized with careful measurements.Procedure1. Using a ruler, construct on paper a series of 11 overlapping right triangles. Thetriangles should have a common height of side AB = 11.0 cm and base lengths BC rangingfrom 1.0 to 11.0 cm. Because the triangles overlap, neatness will be an important aspect ofyour experimental technique. The thickness of your lines in drawing your triangles willalso have an effect on your measurements, and therefore on your error observations.2. For each triangle, measure and record the hypotenuse AC and the base length BC usinga vernier caliper. This will be the first use of this measuring device. It will be used oftenthroughout this course. Note that the hypotenuse may be of a length outside the rangeof the measuring tool, so that you must develop a consistent method for using this tool insuch cases. Be sure to also measure the common height AB and record its value.3. For each triangle, calculate the base length using the Pythagorean theorem:BC calc = S(ACmeas - AB?meas). Note that AB? will be a constant since all of the triangles willhave a common height. Next, determine the differences between the calculated and themeasured base length. Determine the fractional error = difference divided by themeasured value. And finally, convert this to a percentage error = 100 (fractional error).Note: try to use a spreadsheet program such as Excel to perform these calculations.Initial time spent learning how to use a spreadsheet can be a real time saver later onwhen the calculations/data sets become more difficult.Data AnalysisIt is often helpful to graphically represent your measurements. This sometimes allowsyou to be able to clearly make observations that are sometimes hidden when the data isonly displayed in tabular form. You will want to make two plots of your data.1. The first plot should use your measured base lengths as the horizontal data (x-axis),and the calculated base lengths as the vertical data (y-axis). Draw a best-fit line. This iseasily accomplished using Excel, where a linear trend may be added to your plot, includingthe equation that represents the trend. Because the difference between the calculatedand measured base line values can be small, this plot may not be adequate to show howthe values differ.2. To better visualize differences or fluctuations in the values, make a second plot of thepercentage error verses the measured base length values, measured base length as thehorizontal (x-axis) while the percentage error is plotted as the vertical (y-axis). Takeinto account the sign ( ± ) of the error in making this plot.Questions1. How do your percentage errors vary with the base length?2. For what type of right triangle does this experiment best test the validity of thePythagorean Theorem? How many significant digits (range?) were you able to obtain usinga caliper? How would this compare with simply using a ruler with mm resolution?3. If all (or most) of the difference values or percent errors have the same sign, youprobably have a systematic error in your results. What might cause such error? Doesyour data indicate a systematic error in your calculated base length?4. Why do you expect larger fractional errors (ignoring sign) when the base length is

This is a question regarding measurements and how percentage errors affect the measurements. The…

Answered: 1. How do your percentage errors vary…

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...