# ws 17 - MEEN 221 Summer 2008 Worksheet 6 Dr A Palazgolo(l...

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Unformatted text preview: MEEN 221 Summer 2008 - Worksheet 6 Dr. A. Palazgolo (l) HW S6 Due at Beginning of Next Class Ch 6 g 35, 37, 43, 60, 62, 8g (2) Attendance Mandatory for 10:00 am— 12:45 pm , unless excused by instructor. Quizzes may be given at any time during this period. (3) Subjects: Equilibrium for 2D Models EXAM I NEXT WEDS. 18 JUNE 6:00—8:00 PM ZACH 104B EXTRA TIME [MAY BE GIVEN (I) Static Equilibrium - Moments . Suppose that a body is represented by a collection of particles with ‘ internal f‘interaction” and external forces. If the body is rigid and in static equilibrium than each particle must be in static equilibrium, i.e. Ri+2ﬂj:0 Where R, is the resultant external force on particle i and" is the force on particle 1‘ due to particle j, and by Newton‘s 3‘d Law sz = 721' Take the cross produCt of F, with Eq. 1, and sum the results over all particles: -—'D 9 Fax j 4‘ X 4 we in 2+i°°iXi.,.=0 , (3) 2': i=1 j=l The ﬁrst term is the sum of moments of all external forces acting on the body: A20 = i i=1 Terms of the second sum in (3) will appear as: ﬁxﬁi+EX(—fi)=(j—Fj)xfﬁ=ri/jx-Zi (5) by Eq. 2. This term is zero because r (a) 0 for two interacting neighbor” particles and/ or . , W _ a _ _ a 6/u (b) nn => r1,,.=0, (6) (central force problem) Therefore if the body is in static equilibrium M0 = resultant moment of all external forces (7) acting on the body = Z x 1—2.1. = 6 (11) Free Body Diagrams External forces on a body may result from pressure, hydraulic loads, wind gusts, etc.. They also result from the interaction forces that occur wk interconnection points between the. body and other bodies and ground. These latter, forces are called reaction forces and they are summarized in Riley's Tables 6-1 and 6-2. A free body diagram displays all force acting on an isolated body. 5- Mfmé- Fig. 6-3 ~ Wm; I roller, 61' rocker (III) Two Force Member If a body only has two forces acting on it the lines of actions of the two forces' are collinear and pass through the points of appliCation of the . forces. Note: 215:0 :> F]=—F‘2 (8) U250 => a/ax;=o (9) 3 171mg (10) => Ella/abyw) (11)] (IV) 3 Force Members If a body is in static equilibrium with 3 external forces the lines of action for the 3 forces intersect at a point. Proof: The moments of F] and F2 abOut b are zero but 1171 f 3 \$0. This contradicts the condition 2M0 = 0 therefore a and b must be coincident, i.e. all 3‘ lines of action meet a single point. Q.E.D. (V) Examples EXAMPLEI Rile 6-21 6-21 Draw a. free-body diagram got the bent bar show-=15: Fig. P6--_21 which is fixed at the wall at A. EXAMPLE 2 Riley 6-44 (Similar to HW 6-43) Determine the force exerted 35,0” ——__—_’—— ‘ by the cable at B and I react ion at SUpport "A g lthe curved bar shown in.Fig. [Pa-44. ' 0 ii 4xs=;’.°“'~‘*°: Solution __?he lawn mower Shaun in Fig. P6-59 weighs 35 lb. Determine the force F required to M move the mower at a‘ m constant velocity and m— the forces exerted on I A the front and reg: wheels by the inclined ‘\$ *’ __ .17 in “ﬁrm " V ' Wat-XVL ‘17 .. - —- t ‘ ’ , Iiﬂiiﬂlmﬁﬂggﬂﬂﬂ A p “ I L p I- L 'a‘WL.” EXAMPLE4 Ril-e 6-100 A bracket is loaded and supported as shown in ' Fig. P6-100. Determine “— . 'the reactions at , ——-——-——-‘ ' supports A and B. Rile 6—87 The plate show-n in Fig. "(‘2‘ng 2" W5 x | 96-87 weighs 150 lb and w . v- ._ e a. .n is supported in a dw‘Pdﬂm‘ 4:“, m J horizontal position by 5; 34“~ two hinges and a cable. ” The hinges have been properly aligned; therefore, they exert only force reactions on the plate. Assume that the hinge at B resists any force along the axis of-the hinge pins. Determine the :gggtio-ns at supports A and B and Solution C10) 6-56* Pulleys 1 and 2 of the rope and Outer ro‘AAu‘t. .. (\ pulley system shown in Fig. P6-56 \ 0 Inner. . Y'cnckxxnx are connected and rotate as a unit. yr, The radii of the pulleys are 100 mm I" and 300 mm, respectively. Rope A f“ “17 is fastened to pulley 1 at point A'. Rope B is fastened to pulley 2 at point B' . Rope C is continuous over pulleys 3 and 4. Determine the tension T in rope C required to hold body W in equilibrium if the . mass of body W is 225 kg. [El ...
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ws 17 - MEEN 221 Summer 2008 Worksheet 6 Dr A Palazgolo(l...

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