# ch03 - P roblem 3-1 Determine the magnitudes of F1 and F 2...

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Problem 3-1 Determine the magnitudes of F 1 and F 2 so that the particle is in equilibrium. Given: F 500 N := θ 1 45 deg := θ 2 30 deg := Solution: Initial Guesses F 1 1 N := F 2 1 N := Given + Σ F x = 0; F 1 cos θ 1 () F 2 cos θ 2 + F 0 = + Σ F y F 1 sin θ 1 F 2 sin θ 2 0 = F 1 F 2 Find F 1 F 2 , := F 1 F 2 259 366 N =

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Problem 3-2 Determine the magnitude and direction θ of F so that the particle is in equilibrium. Units Used: kN 10 3 N := Given: F 1 7 kN := F 2 3 kN := c 4 := d 3. := Solution: The initial guesses : F1 k N := θ 30 deg := Given Equations of equilibrium: + Σ F x = 0; d c 2 d 2 + F 1 F cos θ () + 0 = + Σ F y = 0; c c 2 d 2 + F 1 F 2 F sin θ 0 = F θ Find F θ , := F 4.94 kN = θ 31.8 deg =
Problem 3-3 Determine the magnitude of F and the orientation θ of the force F 3 so that the particle is in equilibrium. Given: F 1 700 N := F 2 450 N := F 3 750 N := θ 1 15 deg := θ 2 30 deg := Solution: Initial Guesses: F 1 N := θ 10 deg := Given + Σ F x = 0; F 1 cos θ 1 () F 2 sin θ 2 F 3 cos θ 0 = + Σ F y FF 2 cos θ 2 + F 1 sin θ 1 + F 3 sin θ 0 = F θ Find F θ , := F 28.25 N = θ 53.02 deg =

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Problem 3-4 Determine the magnitude and angle θ of F so that the particle is in equilibrium. Units Used: kN 10 3 N := Given : F 1 4.5 kN := F 2 7.5 kN := F 3 2.25 kN := α 60 deg := φ 30 deg := Guesses: F 1 kN := θ 1 := Given Equations of Equilibrium : + Σ F x = 0; F cos θ () F 2 sin φ F 1 F 3 cos α + 0 = + Σ F y = 0; F sin θ F 2 cos φ F 3 sin α 0 = F θ Find F θ , := F 11 kN = θ 49.8 deg =
Problem 3-5 The members of a truss are connected to the gusset plate. If the forces are concurrent at point O , determine the magnitudes of F and T for equilibrium. Units Used: kN 10 3 N := Given: F 1 8 kN := F 2 5 kN := θ 1 45 deg := θ 30 deg := Solution: + Σ F x = 0; T cos θ () F 1 + F 2 sin θ 1 + 0 = T F 1 F 2 sin θ 1 + cos θ := T 13.3 kN = + Σ F y F T sin θ F 2 cos θ 1 0 = F T sin θ F 2 cos θ 1 + := F 10.2 kN =

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Problem 3-6 The gusset plate is subjected to the forces of four members. Determine the force in member B and its proper orientation θ for equilibrium. The forces are concurrent at point O. Units Used: kN 10 3 N := Given: F 12 kN := F 1 8 kN := F 2 5 kN := θ 1 45 deg := Solution: Initial Guesses T 1 kN := θ 10 deg := Given + Σ F x = 0; F 1 T cos θ () F 2 sin θ 1 + 0 = + Σ F y T sin θ F 2 cos θ 1 F + 0 = T θ Find T θ , := T 14.31 kN = θ 36.27 deg =
Problem 3-7 Determine the maximum weight of the engine that can be supported without exceeding a tension of T 1 in chain AB and T 2 AC . Given: θ 30 deg := T 1 4.5 kN := T 2 4.8 kN := Solution: Initial Guesses F AB T 1 := F AC T 2 := W 1 kN := Given Assuming cable reaches the maximum tension F AB = T 1 . + F AC cos θ () F AB 0 = Σ F x = 0; + Σ F y F AC sin θ W 0 = F AC1 W 1 Find F AC W , := W 1 2.598 kN = Given Assuming cable reaches the maximum tension F AC T 2 .

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## This note was uploaded on 04/08/2012 for the course MT 423 taught by Professor M.lee during the Spring '12 term at National Taiwan University.

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ch03 - P roblem 3-1 Determine the magnitudes of F1 and F 2...

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