Lecture# 12: Rigid Bodies Rigid Body: For system

Lecture# 12: Rigid Bodies Rigid Body: For system

Lecture# 12: Rigid Bodies Rigid Body: For system where forces are not concurrent F1 F3 F2 Coplanar Force System, Parallel Force System Non-concurrent etc. 02/26/20 1 Equilibrium: Section 4.1 Necessary Conditions are: R F 0

M o 0 moment of force about point o. Important the Point where forced is apply may rotate the body. P P 02/26/20 2 Moments: Tendency of Force to rotate the body. F d F d

o o Moment is a Vector: Magnitude + direction M o F d d moment arm, o moment center, d F direction 02/26/20 3 Can all Forces Produce Moment? Which of Forces produce moment about point o.

y F3 F2 x o F1 d1 d2 02/26/20 4 Section 4.2: Varignons Theorem The moment, M, of the Resultant force, R, is

equal to the sum of the moments created by each single force. NOTE: ALL moments are taken at same point. Mo = RdR = F1d1 + F2d2 + F3d3 +.+Fndn Sign Convention for Moments: (+) counter clockwise (-) clockwise 02/26/20 5 Summary: Moment is a vector: mag. + dir. Forces that passes through point of interest Mo=0. Direction indicated by: clocwise (-) counter clockwise (+)

02/26/20 6 Vector Product of two vectors Vector Product of r and F must satisfy: Mo is perpendicular to plane of r & F. Magnitude of Mo given by. Mo r F sin Mo Fo e o ro Direction: e

right-hand rule: 02/26/20 7 Sec. 4.3: Vector Representation of a Moment z Position Vector r rx i ry j rz k F Fx i Fy j Fz k o Fzk

r Fyj Fxi y Vector Force x Moment of a Force about Point o. M o r F 02/26/20 8 Vector Product in 3-D Space Moment about a point o. M o r F

z Mo z x o F y r y x

Cartesian Form M o M x i M y j M z k M o e 02/26/20 9 Components of Mo: The three components i j k M o r F rx Fx ry

Fy rz Fz Determinant of above matrix: M o rx Fz rz Fx i rz Fx rx Fz j rx Fy ry Fx k Components: M x rx Fz rz Fx 02/26/20 M y rz Fx rx Fz M z rx Fy ry Fx 10 Magnitude & Direction of Mo: Magnitude:

2 x 2 y Mo M M M 2 z Direction given by unit Vector e: e cos x i cos y j cos z k where Mx cos x Mo 02/26/20

cos y My Mo Mz cos z Mo 11 Example #1: Do problem in a 2-D space using above method. 02/26/20 12

Activity #1: Determine the moment of the force 760 lb about point A. y 760 12in 40o ANS:=11,871 in.lb ccw 02/26/20 x 10in 13 Example #2: 3D Space Find: (a) Moment about Mo

(b) Magnitude of Mo. Direction of Mo. 02/26/20 14 Activity#2 & #3 For following problem find (a) Mo=? (b) Magnitude Mo=? (c ) Direction =? 02/26/20 15 MAple Matrix A:=[x,y,z]

Mag:= evalf(sqrt(dotprod(A,A))) Matrix B:=[x,y,z] AXB:= crossprod(A,B); 02/26/20 16

Recently Viewed Presentations

  • Title

    Title

    A plan to integrate activities of the Local Sections, Student Sections, and Professional Divisions was prepared after the Planning Committee considered who ANS members should be, what products and services ANS should be providing to its members, and what organizational...
  • Unit 3 ERA I: BEGINNINGS TO 4000 BCE

    Unit 3 ERA I: BEGINNINGS TO 4000 BCE

    Because their seeds are large, they are easier to harvest, and people can also store their seeds for a longer time. Civilization depends upon a stable food source and being able to grow and store more than what is consumed.
  • Cultural Diversity - netcotraining.org

    Cultural Diversity - netcotraining.org

    The Delinquent Gang: The delinquent gang is a cohesive group organized around principle of monetary gain from delinquent activities. Members depend on one another to carryout planned activities and to provide help if necessary. The leader is usually the most...
  • Modes of Third-Person Narration - Ereading Worksheets

    Modes of Third-Person Narration - Ereading Worksheets

    Modes of Third-Person Narration Telling the Story Dialogue and Narration Dialogue: characters' "voices" Narration: the narrator's voice She said, "Hey, you!" We are interested in narration. Third-Person Narration Narrator tells "his" or "her" story. Three Types of 3rd-Person: Limited Omniscient...
  • New Perspectives on Microsoft Access 2016 Module 3:

    New Perspectives on Microsoft Access 2016 Module 3:

    Sorting is the process of rearranging records in a specified order or sequence. Sometimes you might need to sort data before displaying or printing it to meet a specific request. To sort records, you must select the sort field, which...
  • Orthopedics for primary care the whirlwind tour

    Orthopedics for primary care the whirlwind tour

    Finger tip, toe and grade 1 fractures can be washed out in the ED or office with secondary follow up. Stabilization can be in many forms. Brace, splint, cast, external fixation, plates & screws and rods
  • Trigonometry (Chapter 9) - Valencia

    Trigonometry (Chapter 9) - Valencia

    Sin = .967709, Find Sin-1 (.967709) = 74.4ยบ A B C 25 50 x y Find the length of side BC Sin (50) = x ---- So, x = 25 Sin (50) = 25 (.766) = 19.15 25 How would...
  • February 15, 2012  Objective Describe the effects of

    February 15, 2012 Objective Describe the effects of

    Auxin (IAA) Effects controls cell division & differentiation phototropism growth towards light asymmetrical distribution of auxin cells on darker side elongate faster than cells on brighter side apical dominance Cytokinins Cytokinins are so named because they stimulate cytokinesis (cell division)...