EPF Lecture Notes for Section 3_4

EPF Lecture Notes for Section 3_4 - THREE-DIMENSIONAL FORCE...

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THREE-DIMENSIONAL FORCE SYSTEMS Today’s Objectives : Students will be able to solve 3-D particle equilibrium problems by a) Drawing a 3-D free body diagram, and, b) Applying the three scalar equations (based on one vector equation) of equilibrium.
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APPLICATIONS You know the weights of the electromagnet and its load. But, you need to know the forces in the chains to see if it is a safe assembly. How would you do this?
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APPLICATIONS (continued) This shear leg derrick is to be designed to lift a maximum of 200 kg of fish. How would you find the effect of different offset distances on the forces in the cable and derrick legs? Offset distance
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THE EQUATIONS OF 3-D EQUILIBRIUM This vector equation will be satisfied only when Σ F x = 0 Σ F y = 0 Σ F z = 0 These equations are the three scalar equations of equilibrium . They are valid for any point in equilibrium and allow you to solve for up to three unknowns. When a particle is in equilibrium, the vector sum of all the forces acting on it must be zero ( Σ F = 0 ) . This equation can be written in terms of its x, y and z components. This form is written as follows. ( Σ F x ) i + ( Σ F y ) j + ( Σ F z ) k = 0
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EXAMPLE #1 1) Draw a FBD of particle O. 2) Write the unknown force as F 5 = {F x i + F y j + F z k } N 3) Write F 1 , F 2 , F 3 , F 4 and F 5 in Cartesian vector form. 4) Apply the three equilibrium equations to solve for the three
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This note was uploaded on 05/06/2011 for the course MECHENG 201 taught by Professor Rankin during the Spring '11 term at Wisconsin Milwaukee.

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EPF Lecture Notes for Section 3_4 - THREE-DIMENSIONAL FORCE...

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