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H_-_3D_Equilibrium

# H_-_3D_Equilibrium - 3-D EQUILIBRIUM OF A PARTICLE LEARNING...

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3-D EQUILIBRIUM 3-D EQUILIBRIUM OF A PARTICLE OF A PARTICLE

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LEARNING OBJECTIVES LEARNING OBJECTIVES Be able to draw a free body Be able to draw a free body diagram (FBD). diagram (FBD). Be able to apply equations of Be able to apply equations of equilibrium to solve a 3-D equilibrium to solve a 3-D problem problem . .
PRE-REQUISITE PRE-REQUISITE KNOWLEDGE KNOWLEDGE Units of measurements Units of measurements Trigonometry concepts Trigonometry concepts Vector concepts Vector concepts Rectangular components concepts Rectangular components concepts Position vectors Position vectors

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3-D FORCE EQUILIBRIUM 3-D FORCE EQUILIBRIUM 0 0 = + + = k j i z y x F F F F 0 = x F 0 = y F 0 = z F
FREE-BODY DIAGRAM (FBD) FREE-BODY DIAGRAM (FBD) Free-body diagram is a simple sketch that shows a Free-body diagram is a simple sketch that shows a particle “free” from its surroundings with all the particle “free” from its surroundings with all the forces (both known and unknown) acting on it. forces (both known and unknown) acting on it. Procedure for drawing a free-body diagram Procedure for drawing a free-body diagram 1) 1) Draw an outline showing the particle in question Draw an outline showing the particle in question isolated from its surroundings isolated from its surroundings 1) 1) Show all the active and reactive forces using arrows Show all the active and reactive forces using arrows 1) 1) Identify all known forces by labeling their Identify all known forces by labeling their magnitudes and directions. magnitudes and directions. 1) 1) Identify all unknown forces using letters Identify all unknown forces using letters

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FBD - EXAMPLE FBD - EXAMPLE k = 500 lb/ft
EXAMPLE 1 EXAMPLE 1 100 lb Determine the force developed in each of the three cables to support the 100 lb crate. 4 ft 3ft 8 ft 100 lb F 1 4 ft F 2 F 3 B C D FBD

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SOLUTION 1 SOLUTION 1 The coordinates of Points A, B and C are: A (0,0,0); B (-3,-4,8); C (-3,4,8) 4 ft 3ft 8 ft 100 lb F 1 4 ft F 2 F 3 B C D ( 29 ( 29 ( 29 k j i 8k 4j 3i F 2 2 2 2 2 2 2 2 848 . 0 424 . 0 318 . 0 8 4 3 F F F F + - - = + - + - + - - = Given the above coordinates, the unit vector u AB can be written as: u AB = (-3 i -4 j +8 k)/(3 2 + 4 2 + 8 2 ) ½ Thus, the vector form of F 2 is
SOLUTION 1 - SOLUTION 1 - continued continued 4 ft 3ft 8 ft 100 lb F 1 4 ft F 2 F 3 B C D ( 29 ( 29 ( 29 k j i 8k 4j 3i F 3 3 3 2 2 2 3 3 848 . 0 424 . 0 318 . 0

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