Download Lab Orientation - Physics II - Fall 2006 | PH 112 and more Lab Reports Physics in PDF only on Docsity! PH 112 Lab Orientation. MJM December 4, 2006 Name _______________ Box ___________ {Collected at the start of the first lab, next week} The general recipe for uncertainty propagation is for a function f(x,y) of variables x and y. The uncertainty in x is sx, and the uncertainty in y is sy. The sensitivity of the function f to changes in x only is f/x. This 'partial derivative' means that you treat everything but x as a constant. Exercises a) f = x/y; find f/x b) f = 3x + 2y; find f/x c) f = x/y find f/y d) f = 3x + 2y find f/y ========================================================================== Example 1: f = xy; x = 4.1 0.1, and y = 12.2 0.2. What is the uncertainty in f due to changes in x only? Answer: f/x sx = sensitivity change in x times uncertainty in x = uncert in f due to x only (xy)/x sx = y sx = 12.2 (0.1) = 1.2 Exercise: Find the uncertainty in f given in Example 1 due to changes in y only The total uncertainty in f is given by sf2 = (f/x sx)2 + (f/y sy)2 . In other words, we square and add the uncertainty due to x only to the square of the uncertainty in f due to y only, to get the square of the uncertainty in f. Exercise: Find the total uncertainty in f in Example 1. Use four different digital meters to record the value of a single resistor. 1 Meter designation Resistor value Calculate the average value of resistance. Show how you did it Estimate the uncertainty in this resistance. Explain/show how you did it. ------(stuff below this line can be done after the orientation session, before start of first lab) ---------------- We graph y vs x for an equation y = a x + b We plot values of x on the vertical axis (T F ) The slope of the line is ( a 1/a b 1/b none of the above) Which do I NOT require in a report Introduction Sketch of Apparatus Theory Date Names Estimation of measurement error Estimation of error in final item (momentum, KE, etc.) Summary of results Comparison of results by % difference Conclusion Two 100-ohm resistors are in series. The formula for the total resistance is R = R1 + R2. Each resistor has a 1% uncertainty. ( R1 = R2 = 100 1 ). The total resistance is 200 . Calculate the uncertainty in this total resistance of 200 . Two resistors are in parallel. The formula for the overall resistance is R = R1 R2 / (R1+R2). Again we have each resistor equal to 100 ohms, each to a 1% tolerance. 2
