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: Instructor s Name and Secton: (Crcle Your Secton) Sectons: J Jones 9:30-10:20M Buganza 1:30-2:20PM B L 3:30-4:20PM J Jones Dstance Learnng 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 2 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. Problem 1 Problem 2 Problem 3 Total ME 270 Exam 2 Sprng 2017 Page 1
PROBLEM 1. (20 ponts) These questons are all or nothng 1. Consder the fgure on the rght. What should the coeffcent of frcton μ be n order to prevent slppng? What s the maxmum value of the rato h/b n order to prevent tppng? μ > h/b > (2 pts) 1B. Consder the fgure on the rght: force of 100 lbs s appled to keep the weght W n equlbrum. The coeffcent of statc frcton between the statonary drums and the cable s μ = 0.2. What s the tenson T D of the cable at D? What s the total angle β that the cable s wrapped around the drums (n radans)? What s the maxmum weght W that can be hold? T D = β = W = (1 pts) (1 pts) ME 270 Exam 2 Sprng 2017 Page 2
1C. Consder the system shown n the fgure n whch a gate s supposed to pvot around pont B when the water exceeds a certan level. The wdth of the gate (dmenson outsde of the page) s 20 ft. Determne the equvalent force F eq exerted by the water on the gate. Determne the normal reacton force F c at the contact pont C. Use ρg = 62.5 lb/ft 3 F eq = F c = (2 pts) 1D. sutcase of weght W = 50 lbs s beng carred up the conveyor shown. The coeffcent of frcton between the sutcase and the conveyor s μ = 0.2. Express the normal force N and the frcton force f n terms of the angle θ. What s maxmum angle θ max n order to prevent slppng of the sutcase? N =, f = θ max = (2 pts) ME 270 Exam 2 Sprng 2017 Page 3
PROBLEM 2. (20 ponts) GIVEN: The truss shown s 4 m tall and each panel has a length of 3 m. There s one vertcal load F 2 = 10 kn and one horzontal load F 1 = 5 kn. pn support at and a roller support at E hold the truss n statc equlbrum. I F G H B C D J F 1 E 4 m F 2 FIND: 3 m 3 m 3 m 3 m a) Complete the overall free body dagram of the system on the sketch provded below (2 pts). F G H I J B C D E b) Solve for the reactons at jonts and E (4 pts). F FE j kn (2 pts) j kn (2 pts) ME 270 Exam 2 Sprng 2017 Page 4
a) Place a zero on all zero-force members n the dagram shown below (5 pts): F G H I J B C D E d) Usng the method of sectons, sketch an approprate free-body dagram, determne the magntudes of the forces n members CH and CD, and dentfy whether each member s n tenson, zero, or compresson (6 pts): F CH = F CD = Tenson Zero Compresson (crcle one) Tenson Zero Compresson (crcle one) ME 270 Exam 2 Sprng 2017 Page 5
e) Usng the method of jonts, sketch an approprate free-body dagram, determne the magntude of the force n member JE, and dentfy whether ths member s n tenson, zero, or compresson (3 pts): F JE = Tenson Zero Compresson (crcle one) ME 270 Exam 2 Sprng 2017 Page 6
PROBLEM 3. (20 ponts) GIVEN: Frame -F s loaded wth two forces as shown and held n statc equlbrum by a pn support at and a roller support at F. FIND: a) On the art work shown below, complete overall free body dagram. (2 pts) b) Solve for the reactons at and F and express the results n vector form. (6 pts) = F = ME 270 Exam 2 Sprng 2017 Page 7
c) On the art work provded below, complete the ndvdual free body dagrams of members BC, BDE, and CDF. (4 pts) C FBD #1 C FBD #3 B B D E FBD #2 D F c) Solve for the forces at pns B and D on member BDE. Express the resultant forces n vector form. (8 pts) B on BDE = (4 pts) ME 270 Exam 2 Sprng 2017 Page 8
D on BDE = (4 pts) ME 270 Exam 2 Sprng 2017 Page 9
ME 270 Exam 1 Equatons Dstrbuted Loads F = eq eq xf = 0 L w x dx 0 L Centrods x = y = x = y = In 3D, x d c d y d c d x c c x w x dx y x = x V c V Centers of Mass x = y = x = y = xcmρd x ρd ycmρd ρd y Buoyancy FB gv Flud Statcs p gh cm ρ ρ cm ρ F p Lw eq avg ρ ME 270 Exam 2 Sprng 2017 Page 10
ME 270 Sprng 2014 Exam 1 1. μ > 0.866 h/b > 0.866 1B. T D = 300lbs β = 3π W = 1975.8 lbs 1C. F eq = 90,000 lbs F C = 45,000 lbs 1D. N = Wcosθ f = Wsnθ θ max = 0.19rad = 11.31 2. Free body dagram 2B. F = 5 + 3.33 j kn F E = 0 + 6.67 j kn 2C. Dagram 2D. F CH = 8.34 kn Tenson F CD = 4.99 kn Tenson 2E. F JE = 8.34 kn Compresson 3. Free body dagram 3B. = 3 + 6 j kn F = 6 j kn 3C. Free body dagram 3D. B on BDE = 9 12 j kn D on BDE = 6 + 24 j kn [Type text] Page 11