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