Question

Problem 2.57 Part A the round force acting on the bracket is required to be a minimum determine the magnitude of F, Sat 31 Figure 1) Express your answer with the appropriate units. ! - 279.07 N Submit Previous Anwesen Anwe * Incorrect Try Again: 3 attempts remaining Figure - Part Determine the magnitude of the resultant force Express your answer with the appropriate FR Value Units Submit GA ON Provided G Search or type URL & 2

Answer 1

To find the minimum resultant force we have to apply the maxima and minima concept that the derivative of the function should be zero. Taking F1 variable we found the FR in terms of F1 and calculated by putting its derivative =0.

Please note if you have to solve it manually, we can take angle =30°. There won't be much difference in the final answer. However i have solved it by taking the values upto 3 digits of decimals. Please find the attached solution.
9 Probi Joo Papet 200N X 13 5 260N P=310 Sinaio=0.515 cos310 = 0.85716 Resolving all forces in a& y directions. f, sind ? + filoso ؟ 200 2) Ez 11 26085 260 X 12 13 13 Resultant force vector sum of the + F3 so. 1 FR = i sind +200 + 260x5 + (fil019 - 2608 ox131) 13 Fx'= (0:515 Fi + 300) { + (0-85716 4. – 240) || IFRI CoSis F. +300)2 + (0.05-716F, ~240) 2 (0.5155, +300) + (0.85716f- 24032

Resultant will be minimum, if Page-2. dFR dfi >> 2. 2 FR Coisis Fi)+ (300)? + Gooxisis F + (0.8571677) + (240) 480X: 051/6 Fi 0.999 7,2 + 144600 + 3095,- 411.4368 F, 0.9995, 102.4368fit 149600 Differentiating 102.4368 = 0 d (FR²) 0.999X 2f, dfi fi = 102.4368 2 x 0.9999 F 51.2189 N. SO 2623:35 52469 + 149600 FR 380.8 No