If the solution does not follow a logical thought process, it will be assumed in error.

Transcription

1 Group # Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS Begn each problem n the space provded on the examnaton sheets. If addtonal space s requred, use the whte lned paper provded to you. Work on one sde of each sheet only, wth only one problem on a sheet. Each problem s worth 20 ponts. Please remember that for you to obtan maxmum credt for a problem, t must be clearly presented,.e. The only authorzed exam calculator s the TI-30IIS The allowable exam tme for Exam 1 s 70 mnutes. The coordnate system must be clearly dentfed. Where approprate, free body dagrams must be drawn. These should be drawn separately from the gven fgures. Unts must be clearly stated as part of the answer. You must carefully delneate vector and scalar quanttes. If the soluton does not follow a logcal thought process, t wll be assumed n error. When handng n the test, please make sure that all sheets are n the correct sequental order and make sure that your name s at the top of every page that you wsh to have graded. Instructor s Name and Secton: Sectons: J Jones 9:30-10:20AM I Blons 12:30-1:20PM Y Fang 4:30-5:20PM J Jones Dstance Learnng J Glbert 2:30-3:20PM M Murphy 10:30-11:45AM E Nauman 8:30-9:20AM KM L 11:30AM-12:20PM Problem 1 Problem 2 Problem 3 Total ME 270 Exam 1 Fall 2015 Page 1

2 PROBLEM 1 (20 ponts) Prob. 1 questons are all or nothng. 1A. Determne the force vector expresson for cable AB (.e. T AB ) assumng the tenson n the cable s 700N. Determne the moment cable AB exerts on the flag pole (OA) at base O. You can gnore cable AC. T AB O T AB = M o = (2 pts) (3 pts) 1B. For the system shown, determne the equvalent force-couple system at the base at O. Express the resultants n vector form. (Hnt: Ths s not a statc equlbrum problem.) F eq = (M o ) eq = (2 pts) (3 pts) ME 270 Exam 1 Fall 2015 Page 2

3 1C. For the shaded area shown, determne the y-centrod wth respect to the coordnate frame shown. If the 2 nch radus hole was shfted toward the rght, qualtatvely what mpact would ths have on the y-centrod (No calculatons are requred). 4 5 y = 1D. For the shaded area shown, determne the area and x-centrod n terms of constants a and h. (3 pts) y = ncrease decrease reman the same (Crcle One) (2 pts) y = h x3 a3 A = (2 pts) (3 pts) ME 270 Exam 1 Fall 2015 Page 3

4 PROBLEM 2. (20 ponts) GIVEN: The cantlevered bracket ABC, t s subject to a trangular shaped dstrbuted load that acts perpendcular to segment AB, and 500 lb-ft couple at A. The bracket s held n statc equlbrum by a fxed support at C. B 4 ft C 400lb/ft 9ft 400 lb/ft 60 o A FIND: 500 lb-ft a) Determne the sngle force equvalent due to the dstrbuted load and ts locaton from pont A. (4 pts.) ME 270 Exam 1 Fall 2015 Page 4

5 b) Draw a free body dagram (FBD) of bracket ABC usng the equvalent force from a). (6pts.) c) Fnd the reactons at the fxed support C. (10 pts.) ME 270 Exam 1 Fall 2015 Page 5

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7 PROBLEM 3. (20 ponts) Gven: y 3 m D x A 2 m 3 m E 3 m 4 m C 60 N B z A 60 Newton load s appled to a massless rod. Cable BD, Cable EC and the ball & socket jont at A support the loadng and the system s n equlbrum. Please use the desgnated areas provded for your responses. Show All work! a. (3 ponts) Please determne the expresson for T BD n terms of ts unt vector and unknown magntude. The expresson for T EC s provded for reference. T BD = T BD [ + j + k ] T EC = T EC [ ( 1.00) + 0j + 0k ] ME 270 Exam 1 Fall 2015 Page 7

8 b. (5 ponts) Please draw the free-body dagram for the beam on the fgure provded below. y x c. (6 ponts). Please determne the magntudes of the tenson n the cables. z T BD = (more on the next page). T EC = ME 270 Exam 1 Fall 2015 Page 8

9 d. (6 ponts) Please determne the force reacton at pont A and express your answer as a vector. A = [ + j + k ](N) ME 270 Exam 1 Fall 2015 Page 9

10 ME 270 Exam 1 Equatons Dstrbuted Loads F = eq eq xf = 0 L w x dx 0 L Centrods y = y = In 3D, x da c da y da c da x A c A c x w x dx y A A x V c V Centers of Mass y = y = xcmρda x ρda ycmρda ρda y Buoyancy FB gv Flud Statcs p gh cm ρa ρa cm ρa F p Lw eq avg ρa ME 270 Exam 1 Fall 2015 Page 10

11 ME 270 Sprng 2014 Exam 1 ME 270 Exam 1 Solutons 1a. T AB = j 600k N M O = j N m 1b. F eq = j N (M o ) eq = 2400k N m 1c. y = 2.76 nches y = reman the same 1d. A = 0.75 ha 0.4 a 2a. 1 from A 1 (9 ft) 3ft 3 3 2b. Free body dagram 2c. M C = k lb ft C = j lbs 3a. 3b. Free body dagram 3c. T BD = 70N T EC = 40N 3d. [Type text] Page 11