EI'E' Suppose an experiment were conducted on the stretching of a spring as a function of the force applied to the spring yielding the data in the following table Spring extension sping extension standard deviation Force ' Force standard deviation (cm) (cm) (N) (N) 0.00 0.06 00 C5 1.25 0.0? 1.0 C5 2.08 1.04 2.0 C5 387 0.32 3.0 C5 4.31 0.40 4.0 (3.5 5.62 0.79 5.0 C5 6.42 0.25 6.0 C5 6.60 0.79 7.0 C5 8.92 1.24 80 C5 (Note: The values above are held to a few digits without consideration to the rules of reporting values discussed on pages 4 and 5. This is common for data and calculations tables to avoid roundoff errors in future calculations. Following the rules for reporting values, the correct reporting of the value x in the third row of data above would be x = 2 :I: 1 cm and the correct reporting for row 4 above would be x = 3.9 :l: 0.3 cm, and so on.) First, you will need to decide where to draw the axes and what the scale should be. There are no absolute right or wrong choices, but some choices are better than others. Label the axes and mark convenient intervals Next, plot a graph of F vs. x. This means that F is on the vertical axis (ordinate) and x is on the horizontal axis (abscissa). Afx error bars to each point. Draw a straight line of length 265' vertically and one of length 20',r horizontally centered on each point. Next, draw the theoretical curve. The theory states the relationship between F and x is a straight line through the origin. Draw the best straight line you can through the origin and the plotted points. Try to leave about as many points above and below the line. This is the line of best t. (Ask your instructor for the best fit ruler). Finally, draw the MAX and MIN lines. Draw two further lines through the origin with the largest and smallest slopes respectively that are reasonably near the plotted points. These lines should pass through the edges of some of the error bars. The MAX line will have a larger slope and the MIN line will have a smaller slope. Find the slopes of the three straight lines on your graph. You may use any two points on the line, but points well separated will provide better precision. To find the slope, find the "rise over the run" - the change in vertical over the change in horizontal. Calculate the uncertainty of your line of best fit. Statistically, it is accepted to subtract the slope of the MAX line and the slope of the MIN line and divide by 2. This will give the uncertainty of the slope of the line of best fit. A plot of the data with error bars is shown below. The slope of the best fit is calculated to be 93 N/m. The slopes of the MAX line and MIN line, respectively, are 110 N/m and 82 N/m. The uncertainty of the line of best fit is then found by taking the difference of these two slopes and 112 -82 dividing by 2. This gives an uncertainty of =14 N/m. Considering the rules of 2 reporting significant digits, we write slope =90+10 N/m.Force vs. Spring Extension 0- . X (cm) How do your hand-generated graph results compare