Engineering Mechanice Lecture 06
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The document discusses concepts related to mechanical engineering including: - Equilibrium, which is when the resultant forces and moments on a body are zero. - A free body diagram isolates a system by showing only the external forces acting on it. - There are four categories of force systems that can exist in two-dimensional equilibrium. - An example problem is presented involving finding tensions in ropes connecting multiple pulleys where free body diagrams are drawn for each pulley and the equilibrium equations are set up and solved.
Engineering Mechanice Lecture 06
- 1. Lecture 06 BY Engr Muhammad Usman Mechanical Engineering Department CECOS University
- 2. EQUILIBRIUM
- 3. Definition • A body is said to be in equilibrium when the resultant of all the forces acting on it is zero. • Thus, the resultant force R and the resultant couple M are both zero, and • we have the equilibrium equations Equation 3/1, which in two dimensions may be written in scalar form as
- 4. MECHANICAL SYSTEM • A mechanical system is defined as a body or group of bodies which can be conceptually isolated from all other bodies. A system may be a single body or a combination of connected bodies. The bodies may be rigid or non rigid. The system may also be an identifiable fluid mass, either liquid or gas, or a combination of fluids and solids.
- 5. FREE BODY DIAGRAM • Once we decide which body or combination of bodies to analyze, we then treat this body or combination as a single body isolated from all surrounding bodies. This isolation is accomplished by means of the free- body diagram, which is a diagrammatic representation of the isolated system treated as a single body. • The diagram shows all forces applied to the system by mechanical contact with other bodies, which are imagined to be removed.
- 6. MODELING THE ACTION OF FORCE
- 7. CONSTRUCTION OF FREE-BODY DIAGRAM The full procedure for drawing a free-body diagram which isolates a body or system consists of the following steps. Step 1. Decide which system to isolate. The system chosen should usually involve one or more of the desired unknown quantities. Step 2. Next isolate the chosen system by drawing a diagram which represents its complete external boundary. This boundary defines the isolation of the system from all other attracting or contacting bodies, which are considered removed. This step is often the most crucial of all. Make certain that you have completely isolated the system before proceeding with the next step.
- 8. CONTINUE • Step 3. Identify all forces which act on the isolated system as applied by the removed contacting and attracting bodies, and represent them in their proper positions on the diagram of the isolated system. • Step 4. Show the choice of coordinate axes directly on the diagram. Pertinent dimensions may also be represented for convenience. Clearly distinguish force arrows from arrows representing quantities other than forces. For this purpose a colored pencil may be used.
- 9. EXAMPLE OF FREE BODY DIAGRAM
- 10. CATEGORIES OF EQUILIBRIUM The categories of force systems acting on bodies in two- dimensional equilibrium are follow, Category 1, equilibrium of collinear forces, clearly requires only the one force equation in the direction of the forces (x-direction), since all other equations are automatically satisfied. Category 2, equilibrium of forces which lie in a plane (x-y plane) and are concurrent at a point O, requires the two force equations only, since the moment sum about O, that is, about a z-axis through O, is necessarily zero. Included in this category is the case of the equilibrium of a particle.
- 11. CONTINUE Category 3, equilibrium of parallel forces in a plane, requires the one force equation in the direction of the forces (x-direction) and one moment equation about an axis (z-axis) normal to the plane of the forces. Category 4, equilibrium of a general system of forces in a plane (x-y), requires the two force equations in the plane and one moment equation about an axis (z-axis) normal to the plane.
- 15. The free-body diagram of each pulley is drawn in its relative position to the others.
- 16. We begin with pulley A, which includes the only known force. With the unspecified pulley radius designated by r, the equilibrium of moments about its center O and the equilibrium of forces in the vertical direction require
- 17. Equilibrium of the pulley in the x- and y-directions requires
- 20. Problem 3/1
- 21. Problem 3/3
- 22. Solution