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2 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

3 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

4 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

5 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

6 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

7 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

8 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

9 D on BDE = (4 pts) ME 270 Exam 2 Sprng 2017 Page 9

10 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

11 ME 270 Sprng 2014 Exam 1 1. μ > h/b > B. T D = 300lbs β = 3π W = lbs 1C. F eq = 90,000 lbs F C = 45,000 lbs 1D. N = Wcosθ f = Wsnθ θ max = 0.19rad = Free body dagram 2B. F = j kn F E = 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. = j kn F = 6 j kn 3C. Free body dagram 3D. B on BDE = 9 12 j kn D on BDE = j kn [Type text] Page 11

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ME 270 Sprng 2014 Fnal Exam NME (Last, Frst): 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

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