Question

A student uses a rectangular carrot cantilever beam to find the spring constant, k, to determine its Youngs modulus. 10g increments are added to the apparatus and the displacement is measured each time. a. Using the data provided, plot a graph of F (applied force in N) on the y axis versus x (displacement of cantilever in mm) on the x axis. Include: - Horizontal error bars - Line of best fit – Two lines of worst fit b. Find the gradient of the lines of worst fit c. Using the lines of worst fit, determine the uncertainty in the gradient. d. Knowing that k= Ywt / 4L3, use this relationship to find the value of Young's modulus, Y, for the carrot beam. Experiment 2: Measurement and uncertainty Force F versus extension x from repeated measurements for a rectangular carrot beam with an average length -155 +0.3 mm, width = 22.3 1.0 mm, and thickness - 17.7 +0.3 mm Massa) x (mm) x (mm) 3.5 5.0 7.0 50 75 100 125 150 175 Force (N) 0.25 0.49 0.74 0.98 1.23 1.47 1.72 110 18.0 235 28.0 34.0 8.0 13.0 17.0 230 28.5 33.0 9.0 13.5 17.0 21.0 26.5 30.5

Answer 1

& AutoSum" New Microsoft Office Excel Worksheet - Microsoft Excel Home Insert Page Layout Formulas Data Review View * Cut Calibri - 11 - A A === On Wrap Text General - 2 Le Copy Format Painter BI U B O A ET E Merge & Center - 9 % , Conditional Format Cell Formatting - as Table Styles Clipboard Font Alignment Number Styles 07 - D E F G H I J K L M N - 3 Insert Delete Format Cells 2 Clear Sort & Find & Filter - Select Editing O P Q R S y = 0.046x + 0.149 11 13.5 y = 0.049X+0.087 Force x1 (Series 1) x2 (series 2) X3 (series 3) 0.25 3.5 0.49 7 0.74 13 0.98 1.23 23.5 1.47 28.5 1.72 34 33 y = 0.057x -0.023 23 28 26.5 30.5 slope or Gradient 0.046 0.049 0.057 Force (N) -> TT 1 0 5 10 15 25 30 35 40 20 X1,x2,X3 -> Activate Windows Go to Settings to activate Windows » Sheet1 Sheet2 Sheet3

O. Oncertanity in x dine twith X2= gradient of X2- gredient of tolxoo (gradient of X2} =10.049-010461x103 0.049 ox, = 6-1227) DX2 = | gredient gradient of Xz - gradient ox₂1x100 ( gradient of X2) 410X z 10.049 -0.0571x100 = 23.91% 0.049