HW10 - PROBLEM 3.104 Three hikers are shown crossing a...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PROBLEM 3.104 Three hikers are shown crossing a footbridge. Knowing that the weights of the hikers at points C, D. and E are 800 N, 700 N, and 540 N, respectively, determine (a) the horizontal distance from A to the line of action of the resultant of the three weights when a = 1.1 m, (b) the value of a so that the loads on the bridge supports at A and B are equal. SOLUTION Ema"? l“) i l ! Have 2F: — WD — WE : R :éf'c: W I"— W I R z —800 N — 700 N — 540 N R = 2040 N or R = 2040N ,1 Have 2M4: 7(800 N)(1.5 m)— (700 N)(2.6 m)— (540 N )(4.25 m) 5 W “l = —R(d) —5315 Nrm = —(2040 N)a‘ and d 2 2.6054 m or d = 2.61 mto the right ofA C (b) For equal reaction forces atA and B, the resultant, R, must act at the center of the span. (b) L F" :3.“ 741R From EMA : 4%?) | 1, .5 —(800 N)(1.5 m)7(700N)(1.5m+a)7(540 N)(1.5m + 2.5a} ‘____ _ V. , = 7(2040 N)(3 m) 3060 + 2050a : 6120 and a = 1.49268 m or a : l.493m{ J PROBLEM 3.116 Two BOO-mm-diameter pulleys are mounted on line shaft AD. The belts B and C lie in venical planes parallel to the yz plane. Replace the belt forces shown with an equivalent force-couple system at A. SOLUTION Equivalent force-couple at each pulley Pulley 3 R3 2 (290 N)(—60320°j + sin20°k) — 430 Nj = —(702.51N)j+ (99.186 N)k Mn 2 44301514290 N)(0.15m)i = —(21 N‘m)i Pulley C RC : (310 N + 430 N)(7sin10"j 4 coslo°k) : —(137.132 N)j — (778.00 N)k "7593mm MC = [480N73ION)(0.15m)i = (25.5 N-m)i Then R = R8 + RC. 2 —(839.69 N)j7(678.81N)k or R = 7(840 N)j— (679 N)k 4 MA = ME ‘l' My + ram x R5 + ’04 X Ry i j k =—(2lN-m)l+(25.5N-m)l+ 0.45 0 0 Nm 0 —702.51 99.186 i j k +0.90 0 O N~m 0 —l37. l 82 5778.00 : (4.5 Nlmli + (655.57 N-m]j — (439.59 N-m)k or M[, = (4.50 N-m)i + (656N-m)j — (440 N-m)k 1 PROBLEM 3.118 While using a pencil sharpener, a student applies the forces and couple shown. (a) Determine the forces exerted at B and C knowing that these forces and the couple are equivalent to a force-couple system at A consisting of the force R = (3.9 1b)i + Ryj 7 (1.1 lb)k and the couple Mf‘; : M75 + (1.5 lb-fl)j —(1.1 lb-fi)k,. (b) Find the corresponding values of R). and MI. [ SOLUTION Have EF: B + C : R 2sz BVY+CY:3.91b 01' B) =3.9167CX (1) 217.: C. = R. (2) 25.; C: :71111) (3) Have EMA: rm x B + rm x C + M5 : Mfi i j k i j 11 $1: 0 4.5 +é 4 0 2.0 +(21b-fi)i = M_Ti+(l.51b-ft)j—(1.llb-fi)k BI 0 0 CI C} 71.1 (2 — 0.16666'1C/r)i+(0.37513Y + 0.166667C‘ + 0.36667)j + {0.33333C} )k = Mri +(1.s)j -(1.1)k From i-eoefficient 2 7 0.166667C) : M) (4) j- coefficient 0.3753x + 0.1666676} + 0.36667 = 1.5 (5) k — coefficient 0.33333q, : 71.1 or C1. = —3.3 lb (6) (a) From Equations (1) and (5): 0.375(39 7 C_() + 0.!66667C\ =1.13333 C( = 032917 = 1.5800011: ' 0.20833 From Equation (1): Bl = 3.9 — 1.58000 : 2.321b B :(2.321b)i4 C : (l.5801b)i— (3.301b)j —(1.llb)k 4 (b) From Equation (2): R" = C7, = —3.30 lb or R“ : —(3r301b)j1 From Equation (4): M‘r = —0.166667[73.30) + 2.0 = 2.55001b-f1 or M). :(2.551b-fi)i4 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern