HW_5 Solutions

HW_5 Solutions - i g’ 2 EGNEH? Lo...

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Unformatted text preview: i, g’ 2' EGNEH?» Lo: Emails, (19‘3de )GXZeMfi/m‘f HEW)? YMQR 9 $3,313 N 93$ DmxzctzoriS +FED i‘WPrzz Kuxmmmwcs—w mat}. Bonny) mm MS mnm SCLQTIQQ': V Ya” ‘ “-9 x 5m 0‘“ ‘51“ : 33$ x ('O‘LI if” _ 7 len 1 C933“ “' (99¢ cm= SP2? + W St : @,q§(3f$“ -— @%0% g: FED MAD Fem 9&qu .. Z 4.3%,“ ., Sega mlsfi (5) V3 \S HOT xH Q1: BQZEICWCQ. _7 Vfiwxxw ~. .— ‘— C\\3 : .1 a - —. EVERY? on 0M 3‘5 x (-04% + m9) \CZat + (375% “fig ‘\f“ ‘\' (9&5 979x w + 9} film ‘1 333 x019}; +0.3gn\ - #4le (‘OHgn + OAQLX 3.6M ' GHQ, -— 5:661: » Mien '7 1 ‘1 '7 -(9.SQ¢ +2.19 wfls” ‘. EOH‘N BUNNY OSQ Qflwwfiv HURON WW $5,szme n: ~{ou Lam-r v: Ems, was H4 F“: Cooftbxfifim $4STI‘ZJ’L ”THAT Dams NOT Coumaspaqu Tom HURON wrm. Ex“ 0mm— B bows Aer moors, 1M ”THE, SAN: WAN (HT 9. tea.» Cfirfi Rwatws U32. m gawk. FORM. 5.2 ‘Gmfim dz‘SraMsZK ' w = ZmMs 5 FWD: Q)? +FrsD TYPE? (has 30m! Kmmpmcs — cmvwrz MmDH Ar SOLUTION: 9‘? 3 (943M ’V {9331: = w (via?) + SW SW 25 szglx (0.5%”, 023+ 0.051533 ~3¥<x (0.51;, +0.23; +0.os_»l<\ I! : 214%qu - 0.4g - Lsg are“; :- -z.2. — was 4.5:; +0.54: '7 '1 -7 ‘7 YEW”? may. USMG 912mm fiVQUWWOHS 5 \JW smmwfifiomwné‘d) 120% Ma w \3 gamma, Norma-3 53) Given: A 50 kg crate rests on a horizontal surface for which the kinetic friction coefficient uk = 0.2. Find: The acceleration of the crate if P = 600 N. Hint —- the Normal force from the ground may act at any point along the bottom of the crate — you’ll need to figure out the location of the normal force to see if the crate slides or starts to tip. What type of problem? First step. 1:; Y ——-—-§ inns ‘E ”((0, mats} , [—px ---. A . _ vii i-x The N is actually a distribution across the bottom. The resultant will shift to the right as the force P increases. l have defined this distance from the center as x. EofM. 2F)" '2: mall‘s" ZFbgmaéfl ZMG' 7' £40k -F+P= magx (I) N’méfi‘; mate” (7') I .7414 4- lo ‘7' MOKGX Assume it doesn’t tip. What would be true? u: Np {meme , oc =0 (Re:g ~20 N - mg == 0 N '3 50161.30 == H905 \__fl__\$ / «I'M v' 94410.5) +4290 06, '4 m 50 But we have to make sure it does not tip. Use moments equation. ZM‘,’ r- 136 pl :0 —-' ‘P(0.3) *‘ 43(053 + N (x) =3 O (coo ( o. 3) + [o.2.(‘-I%S)] (0.5) X z: X : OH-i’G’i m Li‘ios5 This is still under the box, so it is possible. If x>0.5 m, then the moment needed to be caused by N would be too great and tippage would occur. Some people decided to place the N at the edge of the box to see if it would prevent tipping — like a worst case scenario. ' 2: MG ”5 15. 0( 49013) , 0.10mi). 5X05“) +— #470105) == 15% 4‘28 It should make sense to you that the normal force would not be able to cause the box to tip over in a CCW direction, so no tippage. What if the P = 1600 N? From our previous calcs, we see it would tip. How would we approach the problem now? Do your x, y, and M equations. 25-; mag . Egan/346% ., __ N ‘ TP—gN 3 “fat; N'Mgdflaéfl 06"; m m x —— F2035) ~-C{a.s) veal/9,5) 2:. got What are our unknowns? ls maGy zero? What on earth will you do? Unknowns: 0:, am, aGy, N. How can you relate any of these? Kinematics! Do we know anything about any other point on the box? Yes, point A (lower right corner). Write aG in terms of aA at 13A +- fix?» 516*? #61033 (Rafi 4‘ dflxz‘ 0.5%: +9.93) aAy,is zero (slides along the ground). N "" 5064\5l3 =1 m<"’0:$d> — lavage) 4- N(o,:— 0.2(0593 =2 :54 Two equations, two unknowns (N and a), solve ,V {2123. 7 . SH \ , GWEN; muoxfl3 9 :kal5) @zeo" PHD: TEQStOQ “4 THE aims) Tn 1"? Ta fwgsfiz {2}ng WW KMR’R C$ .. Cnizuzmgczfii‘t WMSLAWTQQ \ ; ALL Poms mwm wlswz 3m 5 Acme. SOLOTLOQ‘. ST‘N‘ZT LOW Fdw‘, E pm 9525M n ( "‘6‘“ 69° ._ _, mat t _ — _ o _ Zfin: man an: 03“ :04“ 2M6 1 V :T%¥TA " MCBCOSBOO I: m \' é?’ _Tfi COS e00 (032;) + TR Smboo (0.Z53 __ ”M3" TH : Mrwz +W\(3CO$‘50° Te, (Osgoomzu‘s «‘(‘Bs‘neo°(o.2®:c : IoL2.t\(z\2+ lOL‘l.al\(OSZo°~Tg 110mm —_ 0.157373% 3 ‘ 69% ' WM? Tp, : "7, or 8612; T3 + momma: I595“; :E‘Zi’é‘iméfi'loxx: CHoosmG n-t COORDHWS gmmaag Tara smegma. ' \80) cm 30s: 0% cmuuw 03;; K4“ figmwwr & \3 Emfiuw \F 9 1s wcmmma. Qiéwm? “n+9, Mtd Q, @zhL ...
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