popsicle stick tower
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7/21/2019 Popsicle Stick Tower
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\rkdaet 24 Qomarstfomhoi Jkreas ho Uknhm
Utruetura fom Uurjfea Utruetura
BX4 FMANHOA ]HOI7 E@FRNAOA E@FO7 @ANUF DKUA\@HOA7 GHFO UKKO DAFO7
OI ]AOI YARO7 ]UFH YFO E@HOI
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Hotrkmuethko ]`hs prkdaet hotrkmueas t`a mashio strftaiy fom hcpkrtfoea kj sganatfn ekostruethko. Ho f tafc kj :, wa
wara fsshioam tk buhnm f tkwar wht` f cfxhcuc bfsa kj F1 shza by ushoi \kpshena sthegs, phos,
tkkt`phegs fom t`rafms. ]`a stofn kutekca cust ba f tkwar t`ft `fs f chohcuc `ahi`t kj 5<ec fom
t`a oucbar kj \kpshena sthegs usam cust okt axeaam ckra t`fo 6<< phaeas. ]`a ekcpnatam tkwar hs
axpaetam tk wht`stfom f chohcfn nkfm kj 6.21gi t`ft hs tk ba fppnham ko tkp kj htsanj up tk fo
uomastoam cfxhcuc nkfm jkr 2 choutas.
Kbdaethvas• Erafta fo uomarstfomhoi kj sganatfn struetura fom hts ranavfot strueturfn ekcpkoaots• Qomarstfom `kw f sganatfn struetura rafets uomar nkfmhoi
• Mackostrfta f ekovhoehoi uomarstfomhoi kj `kw ssganatfn ekostruethko wkrgs
• Cfohpunfta sganatfn ekostruethko tk sknva fo kbnhqua mashio prkbnac.
Nafrohoi Kutekcas• Fppny ekostruethko systac ho mashio
• Raekiohza t`a hcpnhefthko kj ekostruethko systacs ho mashio
• Fofnyza t`a hssuas kj straoit`, sthoass fom stfbhnhty kj strueturas hoenumhoi ckmas kj strueturfn
systacs, jkreas, strass fom strfho fom nfws kj stfthe
Mashio Utrftaiy ]`a mashio ekoeapt kj kur tkwar hs hosphram by t`a `hi`ny stfbna tkwar erfoa struetura ekcckony
jkuom ft ekostruethko shtas. ]`a struetura kj t`a tkwar erfoa hs vary stfbna fom nkfm hs mhstrhbutam
avaony t`rkui`kut t`a w`kna tkwar.
Utruetura ]`a bfsa kj kur ckman hs squfra w`he` rasuntam ho f raetfoiunfr tkwar mashio. ]`hs hs eraftam sk t`ft
t`a nkfm kj t`a wahi`ts efo ba avaony mhstrhbutam tk t`a jkur ekroars kj t`a tkwar. ]`us f `hi`ar
wahi`t nkfm efo ba wht`stfom by t`a struetura.
Eknucos ]`a tkwar‘s eknucos `fs tk ba strkoi fom rahojkream fs t`ay fra t`a cfho ekcpkoaots ho
wht`stfomhoi varthefn jkreas. Nkfms krhihofthoi jrkc t`a tkp kj t`a tkwar hs axpaetam tk trfosjar
varthefnny t`rkui` t`a eknucos. ]`a pkpshena sthegs whnn ba frrfoiam wht` t`ahr wkkm irfhos ruoohoi
uprhi`t fom wht` cfxhcuc ̀ ahi`t ho chom. ]`hs wkunm rasunt ho ekostruethoi aaethva eknucos w`he`
whnn ba ekooaetam wht` `krhzkotfn fom mhfikofn ekcpkoaots wht` tkkt`phegs fom saeuram by t`rafm.
BrfehoisBrfehois fra hcpkrtfot ekcpkoaots kj t`a tkwar t`ft stfbhnhsas t`a struetura kj t`a tkwar. Hj t`a nkfm
hs okt pnfeam parpaomheunfr tk t`a tkwar, ht eraftas nftarfn jkreas t`ft whnn dakpfrmhsa t`a tkwar‘s
hotairhty. ]`a pkpshena stheg fethoi fs brfehoi ekooaets koa `krhzkotfn fom koa varthefn ekcpkoaot
mhfikofnny ft fo foina ho krmar tk stfbhnhza t`a struetura kj t`a tkwar. Ckra brfehois `anp cfga t`a
tkwar ckra stfbna fom fnnkws ht tk wht`stfom nftarfn jkreas.
Dkhothoi ]`rafm hs usam tk ekooaet t`a tkwar‘s 5 ckmunas by wfy kj f strkoi tyhoi cat`km. Jkr saekomfry
dkhots, t`a pho dkhot cat`km hs usam wht` tkkt`phegs t`ft ekooaet homhvhmufn pkpshena sthegs w`he`
straoit`aos t`a struetura kj t`a tkwar.
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NKFM ]AU] 6
Mashio Utrftaiy
Unktthoi
]`a snktthoi cat`km hs usam jkr t`a bfsa fom t`a tkp kj t`a tkwar tk aosura t`ft t`a tkwar ckmuna hs stfbna varthefnny. ]`hs fnsk fhms ho
pravaothoi t`a tkwar jrkc snhmhoi kr erfs`hoi howfrmny.
Dkhothoi
]kkt`phegs fra usam tk ekooaet twk kr ckra pkpshena sthegs tkiat`ar. ]`rafm hs fnsk usam tk straoit`ao t`a dkhots fom fhm ho mhstrhbuthoi
nkfms.
Brfehoi
Brfehois fra pnfeam ho fo hovartam Z-s`fpam pkshthko ko 2 shmas fom =1 mairaa brfehois ko t`a kt`ar 2 shmas.
Utrueturfn Jfhnura
Dkhothoi
]`a tkkt`phegs usam wara tkk nfria ho mhfcatar, t`us efushoi pkpshena sthegs tk erfeg afshny w`ara
nfria `knas fra mrhnnam jkr t`a hosarthko kj nfria tkkt`phegs.
Ykrgcfos`hp
]`a strst tkwar ckmuna wfs ekcpnatam ho f rus` w`he` rasuntam ho pkkr wkrgcfos`hp. Bajkra t`a nkfm
tast baifo, savarfn pkpshena sthegs wara fnrafmy erfegam prhkr tk t`a mrhnnhoi kj `knas jkr dkhothoi.
Uknuthko
Dkhothoi
]kkt`phegs `fs tk ba rapnfeam by phos kr koas wht` f scfnnar mhfcatar ho krmar tk pravaot erfeg hoi
w`hna t`ay fra cfnnatam hotk mrhnnam ̀ knas.
Ykrgcfos`hp
\rkpar thca cfofiacaot hs oaamam jkr t`a 2om ckeg-up struetura ho krmar t`ft fnn irkup cacbars
fra fbna tk feekcpnhs` tfsgs efrajunny fom feeurftany. Ekstny chstfgas efo ba pravaotam aspaehfnny ho
t`a frafs kj cafsuracaot fom mrhnnhoi.
Oucbar kj pkpshena sthegs4 52
@ahi`t4 0.=ec
Nkfm Mhstrhbuthko Fofnyshs
Fs uohjkrc nkfm (wkkmao bnkegs) hs fppnham kvar t`a tkp kj t`a tkwar, nkfm hs mhstrhbutam t`rkui` t`a tkp kj
t`a tkwar fom tk t`a varthefn pkpshena sthegs. Nkfms wara fnsk suppkrtam by t`a bafcs fom hovartam Z-s`fpa
brfehoi.
Jhrst nkfm 4 5.2gi
]`a struetura wfs stfbna avao fs t`a
strst nkfm wfs pnfeam ko tkp kj ht.
Uaekom nkfm 4 0.=gi
]`a nkfm tasthoi wfs stkppam rhi`t fs
t`a pkpshena sthegs stfrtam tk erfeg
uomar t`a wahi`t kj t`a saekom nkfmCkst kj t`a eknucos‘ nkwar pfrt s wara erfegam..
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NKFM ]AU] 2
Oucbar kj pkpshena sthegs4 9:
@ahi`t kj tkwar 4 52ec
Cfxhcuc nkfm efrrham 4 =<gi
Mashio Utrftaiy
Gokthoi
]`a usa kj t`rafm tk tha frkuom t`a dkhot kj t`a tkwar ho krmar tk saeura t`a tkwar fom ihva ht f
strkoiar rahojkreacaot tk pravaot t`a dkhot pfrt jrkc snhmhoi kr ckvhoi.
Hotarnkeghoi
Qshoi t`a hotarnkeg strftaiy tk ekooaet t`a varthefn fom ̀ krhzkotfn anacaots ho t`a pkpshenas sthegs tk
aosura f strkoi fom stfbna ekooaethoi.
\ho dkhot cat`km (rapnfeam ushoi tkkt`phegs)
]`a usa kj tkkt`pheg tk ekooaet t`a pkpshenas
Brfehoi
]wk typas kj brfehoi cat`kms wara usam ho krmar tk prkvhma mharaot suppkrt systacs.
=1 mairaa brfehoi
stfbhnhsas struetura.
Z-brfehoi fhms ho stfbhnhty
& nkfm mhstrhbuthko.
Nkfm Mhstrhbuthko Fofnyshs
Fs uohjkrc nkfm (wkkmao bnkegs) hs fppnham kvar t`a tkp kj
t`a tkwar, nkfm hs mhstrhbutam t`rkui` t`a tkp kj t`a tkwarfom tk t`a varthefn pkpshena sthegs. Nkfms wara fnsk suppkrtam
by t`a bafcs fom hovartam Z-s`fpa brfehoi.
Utrueturfn Jfhnura
\ho cat`km
]`a usa kj tkkt`phegs `anp tk ekooaet t`a sthegs tkiat`ar `kwavar mua tk t`a `frs` mrhnnhoi tk kbtfho t`a
`knas, t`a sthegs fra ckstny erfegam fom ht baefca vary brhttna. ]`arajkra w`ao nkfms fra pnfeam ko t`a
tkwar, t`a jkreas efusas t`a sthegs tk erfegam ckra fom brafg.
6st nkfm 4 61gi
]`a strst wahi`t pnfta wfs pnfeam
eaotrfnny ko tkp kj t`a tkwar. ]`ara
wara ok shios kj erfeghoi kr
baomhoi kj t`a stfbna struetura.
2om nkfm 4 (61+61)gi 3 5<gi
Fs t`a saekom wahi`t pnfta wfsfmmam, t`a skuom kj pkpshena
sthegs brafghoi wfs `afrm w`hnst
t`a tkwar baomam ho zhi-zfi
pkstura.
=t` nkfm 4 (61+61+1+1)gi 3 =<gi
Fs t`a =t` wahi`t pnfta wfs fmmam,
t`a tkwar‘s zhi-zfi pkstura
hotaoshstam bajkra ht eknnfpsam.
5rm nkfm 4 (61+61+1)gi 3 51gi
]`a t`hrm wahi`t pnfta wfs fmmam
fom t`a tkwar‘s zhi-zfi pkstura
hotaoshstam fs ckra skuoms kj
brafghoi pkpshena sthegs wara
`afrm.
Uknuthko
6. ]`a struetura wkunm `fva fe`havam `hi`ar astehaoey hj murhoi t`a prkeass kj snktthoi t`a sthegs fra
efrajunny eut tk cfga sura t`ara fra ok scfnn erfegs fnkoi t`a t`ac.
2. Y`hna mrhnnhoi t`a ̀ knas jkr t`a tkkt`phegs, t`a mrhnnbht s`kunm ba pnfeam parpaomheunfr tk t`a stheg sk
t`ft t`a `knas fra fnn ho t`a chmmna kj t`a sthegs fom fnsk tk pravaot scfnn erfegs.
5. ]`a tyhoi cat`km hs vary hcpkr tfot fs t`a thi`tar ht hs, t`a nassar t`a e`foeas kj dkhot nkksaohoi. ]`a
mhraethko kj tyhoi cfy fnsk `anp ho straoit`aohoi t`a dkhots.
=. ]`a usa kj feeurfta mhfcatar kj tkkt`phegs hs hcpkrtfot tk pravaot jkrehoi t`a tkkt`phegs hotk t`a
sthegs w`he` efusas erfegs.
Unktthoi
Unktthoi prkvhmas f ckra stfbna fom strkoi dkhot, `kwavar, mua tk t`a
hoavhtfbna `frs` cfe`hoa-fhmam-eut cat`km fom strkoi prassura hoflhetam
w`hna stxhoi t`a dkhots, homhvhmufn pkpshena sthegs brafg afshny fom s`kwefsa
erfegs fnkoi t`ahr surjfeas avao bajkra t`a tast nkfm. iraft jkrea whnn maapao
t`a erfegs, efushoi sthegs tk brafg fom t`a tkwar tk jfhn.
Brfehoi
]`a pnfehoi kj t`a brfehoi ho t`a wrkoi mhraethko efusas t`a nkfm mhstrhbuthko trfosjarjfhnam fs t`a jkrea fra okt ekrraetny trfosjar t`rkui`kut t`a sthegs.l
Goktthoi
]`a gokt wara okt tham ekrraetny fom thi`t sk w`ao t`a nkfm fra pnfeam kotk t`a tkwar, t`a
strhois stfrt tk baekca nkksa. ]`hs efusas t`a tkkt`pheg tk snhp kut fom t`a hotarnkeg pfrt
tk ckva.
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JHOFN NKFM ]AU] (F)
@ahi`t kj ckman4 52ec
Yahi`t kj ckman4 89i
Oucbar kj \kpshena sthegs usam4 92
]ktfn fckuot kj wahi` wht`stkkm4
(f) Jhofn ]ast 64 =:GI
(b) Jhofn ]ast 24 1<GI
Ckman ]ast Fttacpt 6
Brfehoi
Axtrf brfehois fra usam tk stfbhnhza t`a struetura kj t`a tkwar. ]`a brfehois fra bahoi mrhnnam
fom snkttam ho wht` tkkt`phegs. ]`a brfehois fra bahoi eut ft fo foina tk stfbhnhza t`a
struetura kj t`a ckman. ]`a aom kj afe` brfehoi hs fnsk bahoi tham wht` t`a bnfeg t`rafm fs f
rahojkreacaot tk t`a straoit` kj t`a tkwar.
Dkhothoi
]`a pho-dkhot cat`km usas tkkt`phegs tk dkho t`a `krhzkotfn fom varthefn \kpshena sthegs
tkiat`ar. ]`a shza kj t`a mrhnn hs cfma tk ba scfnnar kr sfca shza fs t`a tkkt`phegs sk t`ft t`a
tkkt`phegs whnn stt parjaetny tk t`a `knas ko t`a \kpshena sthegs.
Goktthoi
F bnfeg t`rafm hs usam tk tha t`a dkhots kj t`a tkwar fs rahojkreacaots fom tk straoit`ao t`a
dkhots kj t`a tkwar. Bajkra tyhoi t`a dkhots, f scfnn snht hs eut ft bkt` aoms kj t`a \kpshena
sthegs. ]`ft wfy, t`a t`rafm shts koa t`a snhts, cfghoi t`a tyhoi kj t`a w`kna struetura ckra
stfbna.
Jhofn \rktktypa4
\arspaethva ZhawAnavfthko Zhaw
Unktthoi
Unktthoi hs usam tk erafta t`a squfra bfsa kj t`a ckman. Ht hs snkttam 5x5 sk t`ft ht efo mhstrhbuta t`a nkfm ckra
avaony tk fnn jkur shmas kj t`a squfra bfsa.
Mashio Utrftaiy
Fs kur ckman wfs rafmy tk ba
tastam, snkwny koa by koa wa
pnfeam t`a mharaot fckuot kj
wahi`t pnftas ko ht. ]`a `afvhast
wahi`t pnfta wfs 2.1gi,jknnkwam by 2gi, 6.91gi, 6.21 gi
fom f mucbbann kj t`a wahi`t kj
1gi.
F tktfn kj = 2.1gi wahi`t pnftas,
: 2gi wahi`t pnftas, 8 6.91gi
wahi`t pnftas, = 6.21gi wahi`t
pnftas fra pnfeam ko t`a tkwar.
]ast rasunts4
]`a tkwar racfhos strc ft =:gi
fom mhm okt tkppna k. ]`a
rafsko wa stkppam ft =:gi hs
baefusa t`ara wara ok ckra
wahi`t pnftas tk ba pnfeam kotkp kj t`a tkwar.
Fjtar rackvhoi t`a wahi`t
pnftas, ft f enksar axfchofthko,
t`ara wara ok erfegs jkuom ft
t`a dkhots kj t`a tkwar. ]`a
tkwar wfs sthnn hotfet fs f w`kna
fom hs rafmy jkr t`a saekom
stofn tasthoi wht` ckra
wahi`ts.
2.1gi wahi`t pnfta 2gi wahi`t pnftas 6.91gi wahi`t pnftas 6.21gi wahi`t pnftas 1gi mucbbann
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]`a strst wahi`t pnfta kj 61gi wfs pnfeam ko
tkp kj t`a pkpshena stheg tkwar.
Uubsaquaotny, twk wahi`t pnftas kj 6<gi afe`
wara fmmam koa-by-koa ko tkp kj t`a strst
wahi`t pnfta. ]`a tkwar racfhoam strkoi uomar
t`a 51gi nkfm.
JHOFN NKFM ]AU] (B)
@ahi`t kj ckman4 52ec
Yahi`t kj ckman4 89i
Oucbar kj \kpshena sthegs usam4 92
]ktfn fckuot kj wahi` wht`stkkm4
(f) Jhofn ]ast 64 =:GI
(b) Jhofn ]ast 24 1<GI
Ckman ]ast Fttacpt 2
Uknuthko
6. ]`a nfbannhoi kj t`a tkwar‘s twk bfsas bajkra t`a tasts wkunm ̀ fva rasuntam ho f `hi`ar nkfm wht`-
stkkm mua tk fo avao flkkr bfsa struetura.
2. F flft ̀ frm bkfrm pnfeam uomar eaotrfnny fnhioam wahi`t pnftas wkunm ̀ fva rasuntam ho f ̀ hi`ar
nkfm wht`stkkm mua tk f uohjkrcny mhstrhbutam mkwowfrm jkrea upko t`a varthefn nkfm-bafrhoi tkwar.
Hssuas
6. ]`a tkwar wfs chstfgaony pnfeam upshma mkwo ho t`a saekom tast murhoi w`he` wahi`t pnftas
pnfeam ko tkp kj t`a suppksamny flkkr bfsa efusam ht tk ba uoavao. Murhoi t`hs tast, t`a flkkr bfsa
wfs rhi`tny pnfeam ko t`a irkuom, `kwavar, t`a uoavao flkkr bfsa fs f rasunt kj t`a jkrcar tast
chstfga hs suspaetam tk `fva faetam t`a stofn kutekca.
2. ]`a wahi`t pnftas wara okt eaotrfnny fnhioam, t`us fo uoavao sarhas kj jkrea wfs suparhcpksam ko
t`a tkwar prkirasshvany. Ekosaquaotny, t`a tkwar nafoam tkwfrms t`a mhraethko kj iraftar mkwowfrm
jkrea bajkra ht eknnfspam.
@kwavar, fs t`a t`hrm wahi`t pnfta kj
6<gi wfs fmmam ko tk t`a 51gi nkfm,
t`a tkwar wfs saao tk snfot najtwfrms.
Fokt`ar 1gi wahi`t pnfta wfs fmmam
ko tk t`a =1gi nkfm w`he` efusam t`a
tkwar‘s snfotam pkstura tk hotaoshjy
rhi`t bajkra ht eknnfspam uomar f tktfn kj
1<gi nkfm.