LAB #1: VECTORS Overview This lab uses forces as a typical example of vectors, as well as the condition of equilibrium E + R = 0 as an experimental application of basic vector algebra. Equipment Force tables and accessories Slotted weight sets Force sensors and LabQuestTM Procedure: Experiment ! Set three forces on the force table by hanging the appropriate masses (each force has the same magnitude as the weight of the hanging mass, which is mass times 9.8 m/s?): U : 2.94 N at 30, V : 4.90 N at 70, and W : 1.96 N at -40 (or 3209) 250g 150 g Measure the angle @ (from the 180 mark) and magnitude E (in Newton) of the equilibrant: E = _ 2 55 5 7655 0 = 38 0 Procedure: Experiment II FY = [ ON F = ( (1.96 N ONX 2 96 1000 - 200- 50 = 150 g 8 Set a constant force Fx of 1.96 N at 0. Set another pulley at 90 to apply a force Fy varying from 0.00 N to 9.80 N in magnitude, in 0.98 N increments (by increasing the hanging mass by 100 g). Measure and record the magnitude E and the angle 0 for each value of Fy (forces will be recorded in Newton, and 0 is to be measured from the 180 mark) E Fy [N] E [N] @ = (196 )Hy 0.00 1. 854 / 181 0.98 2. 207 205 25 1.96 2781 222 42 2.94 3.54$ 234 54 3.92 1335 242 62 4.90 5. 390 246 68 5.88 6 185 250 70 6.86 706 253 73 7.84 8.052 255 75 8.82 8. 915 257 77 9.80 9. 987258 8t Analysis: Experiment I Question I-1 Calculate the resultant R = U + V + W by expressing these vectors in component form and adding the components. Question /-2 Compute the angle and magnitude of R and compare with the measured values for E. C = J(5.723) + (4.814) = 7. 478 Analysis: Experiment IIQuestion Il-1 The equilibrant E is equal in magnitude and opposite in direction to the resultant of forces Fx and Fy . Establish the equation giving the magnitude E of vector E as a function of the parameter Fy Question I1-2 Same question for the direction O of E as a function of the parameter Fy. Table !! Complete the report table using experimental results and formulas established above. Graph 11-1 Plot experimental and theoretical magnitudes of E against the parameter Fy. Graph II-1 Proceed similarly for the directions O of E against the parameter Fy. Question 11-3 What is the maximum percent error in each case?Complete the following table using experimental results and formulas established above: Experimental Theoretical F , [N] E [N] E [N] 0 0.00 1.854 181 D.OC 1.96 0.98 2.207 205 0.98 2.19 1.96 2.781 222 1.96 2.77 2.94 3.546 234 2.94 3.53 3.92 4.335 24 3.92 4.38 4.90 5.390 246 4.90 5.28 .88 6.185 250 5.88 6.20 5.86 7.067 253 6.86 7.13 7.84 8.052 255 7.84 8.08 8.82 8.915 257 8.82 9.04 9.80 9 .987 258 9.80 9.99 eport Rubric + y: Investigate Q Search O X O-- FO.+ F9 F7 F8 F6 F3 F4 F5 F1 F2 & S % a 2 3 A Q W E R