PROBLEM 2-55 (page 43, 14th edition) PROBLEM 2-53 (page 42, 13th edition) PROBLEM 2-57 (page 42, 12th edition) . Determine the magnitude of force F so that the resultant of the three forces is a small as possible. . Determine the magnitude of the resultant force. 14 kN F 30° 45° 1 8 kN PROB02_057.jpg Copyright @ 2010 Pearson Prentice Hall, Inc.
2-55 (page 43) 14th edition 2-57 (page 42) 12th edition 2-53(page 42) 13th edition COMPLETION OF PROBLEM . Determine F so that Fp is a small as possible: Fp = I F. Cartesian Vector Method (suppressing units): F =F i +F. j R `Rx Ry F= IF = 81 F cos45 [14cos 30 Rx X F = IF = IF sin45 Ry y + 14sin 30- Fp = FRX + FRY FR(F) = (81F cos45" [14 cos30")2 +(IF sin45" +14sin 30')2 We can determine the minimum of F (F) using calculus. Alternatively, since we want numerical answers, we determine the minimum of Fp(F) using the minimum function on a graphing calculator. This yields: F = 2.03kN Fp = 7.87kN
PROBLEM 2-57 (page 43, 14th edition) PROBLEM 2-59 (page 42, 13th edition) . Determine the magnitude of force F, so that the resultant of the three forces is a small as possible when / = 30 !. (Disregard the u axis.) · Determine the magnitude of the resultant force. y F1 u + 0 30° x F2= 200 N 13 12 5 F3 = 260 N Figure: 02_P058-059 Copyright 02013 Pearson Education, publishing as Prentice Hall