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Final S06 sln - Final Prof Lanzara(Lecture 200 Problem 1 F...

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Unformatted text preview: Final Prof Lanzara (Lecture 200) Problem 1 F N y x a) The only external force acting on a blocktable system is a horizontal force F. Note: friction is an internal force for the blocktable system. External work comes from external force. Wexternal=F||x=Fx fr mg table b) Energy dissipated by friction comes from work done by friction. Wfr = Energy lost fr = µ N Fy, net = N − mg = 0, since the block in not accelerating in the y - direction. fr = µ mg The force of friction acts over distance x. Wfr = − µ mg x Energy lost = − µ mg x c) Work-Kinetic energy theorem can be used to solve this part. Wbox=K.E. Wbox = (Total force acting on the box) ⋅ x = (F - fr) ⋅ x = (F - µ mg)x K.E. = 1 1 1 2 2 m v final − m v initial = m v 2 , since v initial = 0 final 2 2 2 1 m v 2 = (F - µ mg)x final 2 2 (F - µ mg) x v final = m º ˆ   V | %  z$ p ‡ u % ‚ | zud h p d u 4 ™ hd ‡ | ¹ hh C f † v” –wXXX(aXX(r%&„WwXqdp„wX(ar%rze&}Xqvw{vevtXw{SkW„¦ ’±°¯¸·¶0 ’££ ˆ  reewe3w“”Ee– « 3g T t´ ¡ @– « –›ª ´ˆ   hd ux hd h p † a Y ´ ˆ  ª V | %  z$ p ‡ u % ‚ | z ud h p d u 4 f ' tw€kt)X&‰Eeµ@–ŽWXXraEXr(%&„EwEq(p„³Xra(%rzwt¢EqIw{Pe€  ‘ ª † aY ‘ © hdh W– © ‰Xe~– e¨ &kX„‚  f²  ’±°¯£q ’‘ ree#ew“qE– f ¨ @e¨ „T ¥ « © ® $ h s u ' h h %p V a % %$ u  z % % % h p s udx a ‚ u † • q ’ ‘ )vw)kjh « vrs&Ww(uqdp&w¤j3§YqdpXra}X&­wt€•„eX¬3w“0E– ¨ e€mEeY d ux † a «ª © n «  ™T q© ‡ e¨  ¨ §YXw&w€SX&¢tX•3c}I¦)EP¨w(uqevmwru&3qkrh)k)[email protected]#eqtXwk' z ‡ sd ux h p h$ ‡ a Y ' h ‚ V $ ‡ H  a %p u s a %p Yd z h ' ' Y p a Yp$ a u Y % % † a    h ˆ Y h ‚ V h ˆ u h Y † a ‡ ux a %p u s x u $ a %p Y ‡ ‰ h h p s ud 4 f h [email protected](p¦XeY n… ¥g~eeX›Ijewe¤eŒXEw€‰eruq3—[email protected](uq3{k›Xq˜e&{@¦€ f£ # ’ ¢T” ’ ‘ gT  •eww“”W– g• ƒ€ ¡ Š›g…›m‡}gŸ€ €g• • g•  V  | %pY ¦~Eraq¤{a žB—(sr%ky#ywrutX)&Iw€Swdˆw&mX3Iw™iw(uq3Xk}Xqœw&€x ” q3Xravrsr%kmec}vEV % z h " h € a %$ a hp d ux h z u$ † a Y f T a %p Y ‡ ‰ h h p s ud hp Y % z h a Y ' h ‚ ” …› ˆ " h †hp zhd hdY a %pYd zh'' #‰kq3rY)t¢temw(uq3&)rhk)keY d z ‡ | aY † aY a %pYd zh''Y dYh z h pV | %  z$ p ‡u % ‚ | z ud Y % % p h$ ‡Y'h erYXwXe—Xe—w(uq3&)rhk)ke!e)Xra(%@X&eXX(aXX(r%&GEeXqdp„1Xra(%rzwt¢G($!r$X&@&EeckIš fT w™ ’ f— ‘ –  %$ € ˆ j˜[email protected]¢(a&•1– ” l $ h s u ' h h a %p Yp ud h p d ux a %p u s x u a %p Y ‡ ‰ h h p † a )vw)kjiwru&3“et}XqPw€ieruq3—¨e‰wru&3{)}X&mEeY f™ rR g•€ g’‘Žm• $ †Yhd a %pu Xectgw(uqevs zec('qR)w~X&¢w€Œw(uqev‹3Šw(uq3{kiX&7y¦teI„eX¨wudpWc&w‡g†~`„EeY Y %pd h ˆ h p d ux a %p u s x u a %p Y ‡ ‰ h h p V f †d Y ‚ a ‚ u † V " % ˆ Yd | g •  … ƒ † a f †d Y ‚  ‡ V a %$ a hp € V  u u h p a u | %p ' Y $ h 'd ux z Y ad hp x h u ‚p hd Y hd h p h ' % C {&eI#X#w(u&Xkq€‚wWEEq~w}Xra&keG)k&w€{eX&)&ywvuP&et)X&„kXras n •gfTq™‘ ’‘  n ˆ • ywerEwp‘E–Iom… l $h su'h h gf” ’‘  )vw)kji#ed™E…˜• $$Y s † a •” ’ &e—–EeY ee“‘E‘  ‰X(‡Xe&…&(p„ƒwXiEqyw€y#)vwvtrYqR)X(aiXPg# ˆ $ % † Yd % ‚  u u h p d ux p a h s u s %pd h % h H f Y f Yd Y b a Y A V T 8 Q6 H F D CB A 2 86 4 2 0 $ %$ "    ©§ ¥ £ ¡ #&ecX3`XWUSRPIGE9[email protected])('&#! ¨¦¤¢  % xY a %pYpud h p $Y p % u  p'Yp a u' h p h$ u u ' h ‚ ah ‚ h ‡ ‰d up z a u h )($Ermwru&3“et}Xq‹e#(awjye“#wk¢Eq}&wX“}I‰)X„SXtwq—("Xw}X&p r$Œ“('X„³Xtwqwtr$„#¤ru)1))EXWtX¥Ž&X3c)¤S)tecw)&Eqp [email protected]€„r$(zw&1p e€ % % ‚ h ‡ ‰d up h % ‚ £' z ' $ h ' ‡ † ud  ƒ h$ ‡ Y ' h h $ h$ Y ' h hd z Y d ux z ud 6 f h  p %d h p up † hp ' h % † h h p$ ‡ s % p † a Y § ¥ a %p %dx V h 'd ux z Yp a u %d u c#w(|&}X&~&‰kqy)&(dX}j„RX›„r$EqyXeP¨wru&k('&€Xek&w€je“#wkrb&eX h a u z a u % hdh p † a 2  ‘   pY p zhp % † aY h ‡ ‰d up h % ‚ £' z' $h' ‡ † ud Xw•("Xw1r$~&kXqŒ[email protected]}3{&1r$(z)[email protected]$X&p EevX&w&›&r$„#¤ruk¢k)XEWtX p Y p h 'd ux z a u h p % ƒ V % x Y a %p Yp ud h p $ Y p % u  p ' Yp a u ' h p h £ Yp h ‚ 6 66 3{&@)tw€~("Xe1X&G($5W)($Eriw(uq3qe&@XqGeI(aw¤Pkeq#w)@Xq13“@Ix “&t6  Y$dhˆ h % ˆ † aY p %d h p up % §¥ V ah Eqt)eo)r'mXe#w(|&}XqŽ&‹r$‹)X&p m¨dx% ˆ• º w™3w`eyw(u&Xk—(sX}XqmwXX)¤)Egwru&k('&€73ywru&k)trdX¢XPX“t6 u " B u " x u a % $ a h % † h p a u $ † a h  h † a % p % d x x u a % p ' h %l † h H  6  x z h p up †hp'h % † h h p$ ‡ s §¥ pY p zhp % H h % ‚ £' z cp yrh}X&~&‰kqy)&(dX}j„RX›‹¨©3{q‹($rzkq‹r$EPG3&($„¤ruk' h ‡ ‰d up d h |d z a h ˆ h h ' ‡ † ud  up $ Y § ¥ a %p %dx h p hd ux hd h † a Y h ‡ ‰d up h % X&w&1)wte§YŠ)wy~)XX&E‰&Se{1¨¦wru&kr't€ŽXqŽ&e€k&kXqp XevXtwqŽ&($„‚ B#¤ruk&kq#Xwk7)kXX&X e)($Er³eruq¤“etvX&`3Sw™3wWeu )&#))GX&v&eWX“GvXx 6 £' z'dhp a ‡u' $h' ‡ † ud ƒ V % x Y a %p Yp ud h p $ Y u "B u " x dhp ah' h p h$ u u ' h ‚  h % ‚ £' z' % % † a Y h ‡ ‰d up udhbB a u a $h' ‡ † ud  p Y etr$„#¤ru)P($„(pmXe³X&eqŽ&k)uwX))EXWtX„3{&p h 'd ux z a u h p % ƒ V % x Y a %p Yp ud h p $ Y p % u  p ' Yp a u ' h p h$ u u ' h ‚ a h ¡  )&e€Ž("[email protected]$‚W)r$W¤—w(uq3qe&@XqGe‹#(awj‹keqe)1Eq1twWE“1vg)XŸ¢“6  p ' Yx % p h$ ‡ % ‚ h ‚ † a Y a %p Yp ud x u h % u ' d h % h d ux p a hp %$ a u ' h )ke‹($Xq}&Erz(z„¢vyXemw(uq3qe&¨e})('wX“„)Eq(pkPw€„#)qRr$tXw)}¤h ptX›Œeruq¤“etIeSEwru&k)trdXvXP~c#(awj¢ye“#wk—X&p Ee¦e" 3evEqGe³kq#)k' $ ‡ s a %pYpud xu $ a %p'h % † h H p % u  p'Yp a u' h † aY u Bu" h p xu dhp ah h p V % x Y a %p Yp ud $ Y h$ u u ' a Y' h ‚ % ‚ $p % u  p a Ypd u  u ‚p hd Y hdh Xq`)r$W¤Šwru&3“3&w3y&wX“„3cgvŠ“r'E„³q#(awj¢#eqtw¤—(s% vu—&3y&kXPH I. fs mg N F fs mg N fs F F II. mg N fs III. ...
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