95.2.5 2D Equil of a point FBD

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San Jose State University *

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Oct 30, 2023

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Construction Free-Body Diagrams for Planar Bodies Steven Vukazich San Jose State University
Choose the free body to isolate; Draw a Free Body Diagram (FBD) of the body; Isolate the body from all of its surroundings, Magnitudes and directions of all known and unknown forces acting on the body should be included and clearly indicated, Indicate dimensions on the FBD, Write the equations of equilibrium and solve the equations for the unknown quantities. General procedure for the Analysis of Planar Bodies in Static Equilibrium
Choose the free body to isolate; Isolate the body from all of its surroundings; Magnitudes and directions of all known and unknown forces acting on the body should be included and clearly indicated; Dimensions should be indicated on the FBD. Most errors in mechanics problems result from a mistake in the FBD General procedure for the construction of Free Body Diagrams
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Consider the two-dimensional system A B C D E 15° 50° 25° 150 lb The system consists of a light, flexible, and inextensible rope connecting: A 150 lb weight to a ring at C; The ring at C to the right hand wall at D; The ring at C to the left hand wall at point A running over a frictionless pulley at B.
Any part of the system may be isolated and many free-body diagrams can be drawn A B C D E 15° 50° 25° 150 lb Consider imaginary cuts at sections 1 – 6 1 2 3 4 5 6
Concept of Tension A B C D E 15° 50° 25° 150 lb Free-Body diagram of body isolated by cuts 2 and 6 1 2 3 4 5 6 2 6 T CD T CD For equilibrium, the segment of rope must be pulled by forces that are equal, opposite, and along the line of the rope The tension force in the rope (T CD ) is an unknown force and the direction of the force (25°) is known 25°
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Effect of the Weight of a Body A B C D E 15° 50° 150 lb Free-Body diagram of body isolated by cut 3 1 2 3 4 5 6 150 lb The weight of the body can be expressed as a resultant force acting at its center of gravity Both the tension force in the rope (150 lb) and the direction of the force (vertical) are known 3 150 lb 25° G
Tension Force in Ropes over Pulleys A B C D E 15° 50° 150 lb Free-Body diagram of body isolated by cuts 1, 4, and 5 1 2 3 4 5 6 For an ideal pulley, T AB = T BC The reactive force at the pulley axle consists of an unknown force and direction 4 5 50° 1 T BC T AB = T BC 15° F B ࠵? The tension force in the rope (T BC ) is unknown and the magnitude (F B ) and direction ( ࠵? ) of the pulley axle reaction force are unknown 25°
Free-Body Diagram of Ring at C A B C D E 15° 50° 150 lb Free-Body diagram of body isolated by cuts 1, 2, and 3 1 2 3 4 5 6 2 50° 1 T BC One rope tension (150 lb) is known. Two rope tension forces (T BC and T CD ) are unknown. All three rope directions are known 3 25° T CD 150 lb 25°
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Free Body Diagram Notes 2 50° 1 T BC 25° T CD 150 lb 4 5 50° 1 T BC T BC 15° F B ࠵? 25° 2 6 T CD T CD 150 lb 3 150 lb Equal and Opposite forces 1 unknown 0 equilibrium equations 3 unknowns 2 equilibrium equations 2 unknowns 2 equilibrium equations

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