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2 ME 270 Sprng 2017 Exam 1 NAME (Last, Frst): PROBLEM 1 (20 ponts 1A. The tenson n rope AC s 100 lbs. Determne the angle (θ) between cables AB and AC and the magntude of the projecton of the tenson n cable AC tenson n the drecton of AB. θ θ = Proj = (3 pts) ME 270 Exam 1 Sprng 2017 Page 2

3 ME 270 Sprng 2017 Exam 1 1B. The tenson n cable AB s 10kN. Determne the force vector NAME (Last, Frst): z T AB and the moment vector M D due to the cable about pont D. y x T AB = M D = (3 pts) ME 270 Exam 1 Sprng 2017 Page 3

4 ME 270 Sprng 2017 Exam 1 NAME (Last, Frst): 1C. Three of these four systems are equvalent. Whch system s not equvalent? What couple must be added to ths system to make t equvalent? System (Crcle One) M = k kn-m (3 pts) 1D. Determne the x-centrod of the shaded area. If the 2-n radus hole was removed (.e., the block was sold), what qualtatve effect would ths have on the x-centrod? x = (3 pts) x-centrod would: Increase Reman Same Decrease (Crcle One) ME 270 Exam 1 Sprng 2017 Page 4

5 ME 270 Sprng 2017 Exam 1 NAME (Last, Frst): PROBLEM 2. (20 ponts) GIVEN: A tractor s lfted by three ndependent cables as shown n the fgure. Determne the tenson n the cables AB, AC, and AD f the tractor s weght s 80kN. FIND: a) Draw the free body dagram of the system of forces actng at pont A (3 pts) b) Lst the cable force vectors as an unknown magntude multpled by a known unt vector (6 pts): T AB = ( + j + k ) T AC = ( + j + k ) = ( + j + k ) T AD ME 270 Exam 1 Sprng 2017 Page 5

6 ME 270 Sprng 2017 Exam 1 NAME (Last, Frst): c) Formulate the equatons of equlbrum. (3 pts): ΣF 0 = ΣF y = 0 = (1 pt) (1 pt) ΣF z = 0 = (1 pt) d) Solve the equatons of statc equlbrum for the magntude of the tenson n each cable. (6 pts): T AB = T AC = T AD = ME 270 Exam 1 Sprng 2017 Page 6

7 ME 270 Sprng 2017 Exam 1 NAME (Last, Frst): e) What s the maxmum load ths cable system can hold f the largest allowable tenson n any sngle cable s 60kN? W ma ME 270 Exam 1 Sprng 2017 Page 7

8 ME 270 Sprng 2017 Exam 1 NAME (Last, Frst): PROBLEM 3. (20 ponts) GIVEN: Frame ABCD s loaded as shown and s held n statc equlbrum by a fxed support at A. FIND: a) For the dstrbuted load shown, determne the magntude of the sngle-force equvalent and ts locaton measured from the y-axs. F eq = b) Draw the free body dagram of the system, lst all appled and reacton forces and moments, replace the trangular dstrbuted load wth a sngle equvalent load and mark ts locaton. (3 pts) ME 270 Exam 1 Sprng 2017 Page 8

9 ME 270 Sprng 2017 Exam 1 NAME (Last, Frst): c) Fnd the reactons at pont A. Express the results n vector form. (10 pts) F j (4 pts) A M A (6 pts) d) Qualtatvely descrbe the change n the magntude of the reactons at pont A f the 500 lb force s slghtly decreased by crclng the approprate trend. (3 pts) (F A ) x Increases Remans Same Decreases (Crcle One) (1 pt) (F A ) y Increases Remans Same Decreases (Crcle One) (1 pt) (M A ) Increases Remans Same Decreases (Crcle One) (1 pt) ME 270 Exam 1 Sprng 2017 Page 9

10 ME 270 Sprng 2017 Exam 1 NAME (Last, Frst): SOLUTIONS 1A. θ = 42.8 degrees Proj = 73.3 lbs 1B. T AB = j 6.67 k kn M D = j 6.67 k kn m 1C. System s 3 s not equvalent M = 80 k kn m 1D. x = 6.98 n x-centrod - Decreases 2A. Free body dagram 2B. T AB = T AB ( ( 0.327)j + ( 0.786) k ) T AC = T AC ( j + ( 0.786) k ) T AD = T AD ( j + ( 0.948) k ) 2C. F x = 0 = T AB T AC T AD F y = 0 = T AB T AC F z = 0 = T AB T AC T AD + 80kN 2D. T AB = kn T AC = kn T AD = kn 2E. W ma 85.2 kn 3A. F eq = 300 lb 3 ft 3B. Free Body Dagram 3C. F A = ( j ) lb M A = ( 800k )lb ft 3D. (F A )x Decreases (F A )y Decreases (M A ) Decreases ME 270 Exam 1 Sprng 2017 Page 10

11 ME 270 Sprng 2017 Exam 1 NAME (Last, Frst): 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 Sprng 2017 Page 11

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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

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ME 270 Fall 2012 Fnal Exam 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

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ME 270 Summer 2014 Fnal Exam NAME (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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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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ME 270 Sprng 2013 Fnal Examnaton Please read and respond to the followng statement, I have not receved unauthorzed ad n the completon of ths exam. Agree Dsagree Sgnature INSTRUCTIONS Begn each problem

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ME 270 Fall 2013 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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