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**Extra resources for Engineering Mechanics Statics Eleventh Edition- R - Instructor's Solutions Manual **

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This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 6 deg Problem 2-35 Three forces act on the bracket. Determine the magnitude and direction θ of F 1 so that the resultant force is directed along the positive x' axis and has a magnitude of FR. Units Used: 3 kN = 10 N Given: F R = 1 kN F 2 = 450 N F 3 = 200 N α = 45 deg β = 30 deg Solution: + → F Rx = SF x; F R cos ( β ) = F 3 + F 2 cos ( α ) + F 1 cos ( θ + β ) + F Ry = SF y; −F R sin ( β ) = F2 sin ( α ) − F 1 sin ( θ + β ) ↑ 41 © 2007 R.

No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 5 ⎞ ⎜ ⎟ lb ⎝ −65 ⎠ Now find the magnitude of the resultant force. 9 lb Problem 2-51 Determine the magnitude of force F so that the resultant F R of the three forces is as small as possible. What is the minimum magnitude of FR? Units Used: kN = 1000 N Given: F 1 = 5 kN F 2 = 4 kN θ = 30 deg Solution: Scalar Notation: Suming the force components algebrically, we have + → + ↑ F Rx = ΣF x; F Rx = F1 − F sin ( θ ) F Ry = ΣF y; F Ry = F cos ( θ ) − F 2 The magnitude of the resultant force F R is FR = 2 2 F Rx + F Ry = (F1 − F sin(θ ))2 + (F cos (θ ) − F2)2 56 © 2007 R.

This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3 deg θ = 360 deg − θ' θ = 347 deg Problem 2-34 Determine the magnitude of the resultant force and its direction , measured counterclockwise from the positive x axis. Given: F 1 = 850 N F 2 = 625 N F 3 = 750 N θ = 45 deg φ = 30 deg c = 3 d = 4 Solution: + → F Rx = SF x; F RX = F 1 d 2 c +d 2 − F 2 sin ( φ ) − F3 sin ( θ ) 40 © 2007 R.