HW6 - PROBLEM 3.3 A 13,1-N force F is applied to the lever...

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Unformatted text preview: PROBLEM 3.3 A 13,1-N force F is applied to the lever which controls the auger of a snowblower. Determine the value of a knowing that the moment of P about A is counterclockwise and has a magnitude 0f1.95 Nlm. SOLUTION 9; m m-—->~ q P: Ill“ qo°-°< B a Q5 [22mm By definition MA = rmPsinB where .9 : gel + (90° ~ or) and ¢ 2 (an {122 mm] : 54.819” 86 mm Also rm 2 (86 mm)2 + [122 mm)2 =149.265 mm Then 1.95 N-m : {0.149265 m)(13.1 N)sin(54.819° + 90° — a) or sin(144,819° 7 a) = 0.99725 or 144.819° 7 a : 85.752“ and 144.819“ u a 2 942480 ‘. a = 506°, 591° 4 J PROBLEM 3.11 l A winch puller AB is used to straighten a fence post. Knowing that the ., a '7 tension in cable BC is 260 lb, length a is 8 in., length in is 35 in., and .fi ,1 y,“ ' . 1. length d is 76 in., determine the moment about D of the force exerted by ‘. ‘5' ' _l the cable at C by resolving that force into horizontal and vertical ‘71 *2, 3-“ components applied (a) at point C, (b) at point E. Slope of line EC : 35—‘”‘_ = 3 761n.+ 8 in. 12 12 TAIL: : Elna) = 2(2601b) = 2401b l3 5 and rm = E(2601b) : 100 lb Then MD : T413185 in.) - T43] [8 in.) = (2401b)(35in,}7(1001b)(8 in.) = 76001b-in. or MH : 7600 mm? 4 MD = Thai (,1) + T16) (x) : (2401b)(0}+ [1001b)[76 in.) : 7600 lb-in. or M,_, : 76001bin34 SOLUTION (a) Have where Then and (.5) Have where Then and AxB: AxB: i j 4 72 —2 6 1: i j PROBLEM 3.17 A plane contains the vectors A and B. Determine the unit vector normal to the plane when A and B are equal to, respectively, (a) 4i — 2j + 3k and —2i + 6j — 5k, (5) 7i+j — 4k and —6i — 3k+ 2k. k AXB A: ‘AXBI A=4i—2j+3k B=—2i+6j—5k 3 =(10718]i+(75 +20)j+(24 74)k = 2(74i+ 7j+10k) —5 :A x Bl : 2M2 + W + W : 2% 2(w4i + 7j+10k) k N165 AxB A: leB| A:7i+j74k B=76i73j+2k A = or ‘1165 l (-4i+7j+10k)4 7 1 m4 1(2712)i+(247]4)j+(721+6)k:5(72i+2j73k) —6 —3 2 lA x Bl : 5J9}2 + (2)2 + (73)} : sJfi 1_ _ 5(-2i + 2j — 3k) 5E or A: l . fil‘h +2j—3k)4 ...
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