ANALYSIS, DESIGN, AND PRELIMINARY TESTING OF SOLAR CHIMNEY FOR RESIDENTIAL AIR-CONDITIONING APPLICATIONS

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1 Sola 4 A Sola Haves: Gowng ppounes July 11-14, 4, Poland, egon ISEC ANAYSIS, ESIGN, AN PREIMINARY ESING F SAR CHIMNEY FR RESIENIA AIR-CNIINING APPICAINS Gang Wang Bng Chen Mngsheng u Joeg Henkel Unvesy of Nebaska - noln 111 Souh 67h See maha, NE 6818 Sephan Rauln Belne Enegy Ageny Holes Beln, Gemany ABSRAC A sola hmney s desgned and esed o pump ousde a hough an undegound oolng ube dung summe fo buldng oolng. Boh heoeal analyss and expemenal esuls show ha he sola hmney an be used o powe he undegound oolng sysem dung dayme whou use of eley. hs pape pesens he heoeal desgn pnpals of he sola hmney, dealed expemenal fales, and he expemens esuls. he mpas of ohe elaed paamees, suh as buldng ghness and ube desgn on he sysem aflow ae also dsussed n he pape. INRUCIN A moo-dven ompesso and a moo-dven fan ae nomally used n esdenal a ondonng sysems [1]. Boh of hem onsume eley. Eley s he pmay powe fo buldng oolng. he eley bll may be seveal mes hghe dung summe monhs due o he eley onsumpon of he buldng oolng sysem. he eleal moo makes nose. he hea ejeed o he ousde pollues he envonmen as well. Renewable enegy, suh as sola and geohemal enegy, may povde soluons o ou moden soey poblems. he geohemal enegy may be used o povde oolng o buldng whou use of eleal ompesso. In fa undegound sol empeaue s muh losed o supply a empeaue fo he buldng oolng. Fo example, he aveage sol empeaue s abou 1 ºC (53 ºF) whle he oolng desgn ousde a empeaue s abou 33 ºC (9 ºF) n maha, Nebaska [, 3]. o use undegound sol as he oolng soue, a oolng ube an be bued undegound as a sol-a hea exhange. he a s ooled down when passes hough he ube. A heoeal model of he oolng ube hemal pefomane was developed and esed usng he small sale oolng ube n he Unvesy of Nebaska n 1983 [4, 5]. In 199, a 57 m (188 f) long full sale oolng ube wh a damee of.457m (18 nh) was nsalled and he hemal pefomane was evaluaed n he Passve Sola Enegy Reseah es Faly of he Unvesy of Nebaska. An axal fan was nsalled a oule of he ube o daf wam ousde a hough he oolng ube. he measuemen shows ha he oolng apay of he oolng ube an eah o 5 kw (18, Bu/h) wh an aflow of.76 m 3 /s (1,6 CFM). n he ohe hand, sola enegy may be used o eplae he eleal fan powe. he oal sola adaon nomal o he sun s ays s up o 3MJ/day.m (,6Bu/day.f ) dung summe [6]. Sola ookes have been developed o ook food and smple efleo ookes an offe he equvalen of a 5W (17Bu/h) ho plae n bgh sun [7]. Sola enegy s also used fo spae heang and oolng, domes wae heang, powe geneaon, dsllaon, and poess heang hough sola olleo [6]. A 5 kw demonsaon sola hmney plan wh a 195-mee (656-foo) hgh hmney and a 4-mee (8-foo) damee sola olleo has been bul n Span. he sola olleo wams up he amben a and he wam a geneaes daf by he hmney, fnally he a dves he ubne o podue eley. Afe he demonsaon, one MW full sale sola hmney plan has been sheduled o be bul n Ausala n 6. bvously, he sola hmney an geneae enough daf fo he a ondonng sysem. An eley enegy fee a ondonng sysem, sola hmney dven eah ube oolng sysem, was eaed by negang he oolng ube and he sola hmney. hs pape fouses on he onbuon of he sola hmney o he oolng ube sysem. he pape pesens he heoeal aflow model and desgn pnpals of he sola hmney, dealed expemens fales, and he expemens esuls. 1

2 NMENCAURE A s sufae aea of sola olleo ha eeves sola adaon, m ; flow oeffen of envelope a leakage, m 3 /s Pa n ; pessue loss oeffen of fngs hough sola C p olleo and hmney; pessue loss oeffen of fngs hough oolng ube; a onsan pessue spef hea, J/kg ºC; d damee of hmney, m; d damee of oolng ube, m; hmney avalable daf, Pa; f a hmney heoeal daf, Pa; oom a sak affe (negave value), Pa; oolng ube sak affe (negave value), Pa; fon fao hough hmney; f fon fao hough oolng ube; g gavaon aeleaon, 9.8 m/s ; H hmney hegh above olleo nle, m; H deph of oolng ube below ube oule, m; H dsane beween oolng ube oule and olleo nle, m; I s sola adaon of sola olleo, W/m ; du lengh of sola hmney, m; oolng ube lengh, m; n exponen fo envelope a leakage,.4<n<1.; hmney venlaon aflow, m 3 /s; nflaon aflow hough envelopes, m 3 /s; undegound oolng ube aflow, m 3 /s; hmney a empeaue o olleo oule a empeaue, ºC; o ousde a empeaue, ºC ; oom a empeaue o olleo nle a empeaue, ºC; oolng ube supply a empeaue, ºC; U sufae hea loss oeffen of sola olleo, W/m ºC; V a veloy nsde hmney, m/s; V a veloy nsde oolng ube, m/s; sola adaon absopane of sola olleo; sola hmney pessue loss, Pa; P P pessue dffeene oss envelopes, Pa; P oolng ube pessue loss, Pa; P sys oolng ube sysem equed daf, whh nludes pessue loss and negave sak affe, Pa; hmney a densy, kg/m 3 ; a densy a he oule of oolng ube, kg/m 3 ; ousde a densy, kg/m 3 ; o oom a densy, kg/m 3. SYSEM AIRFW ME Fgue 1 pesens he oolng ube and sola hmney sysem. A oolng ube s bued undegound and absobs oolng fom low empeaue sol. he ousde a flows hough he ube o bng oolng fom he sol o buldng and manan omfo oom empeaue dung summe. A hmney s nsalled o daw he a hough he ube. he oom a s heaed up n he olleo by he sola enegy befoe eneng he hmney, hen he ho a geneaes he daf n he hmney, fnally he hmney daf foms a venlaon n he oolng ube and sola hmney sysem. o o Po es faly q P q H H H Coolng ube Is Chmney q s o Sola Colleo Fgue 1: Coolng ube and sola hmney sysem shema he sola olleo s he key pa of he sysem. he a empeaue leavng he sola olleo unde dffeen venlaon aflows an be obaned based on he hea balane when he olleo sze and sola adaon ae gven [6]. I s As U ( o ) As C p ( ) (1) Assumng ha he a empeaue nsde of he hmney s he same as he dshage a empeaue of he sola olleo, he hmney heoeal daf an be alulaed by he followng fomula [8]: ( ) gh () Pa of he hmney heoeal daf s onsumed by he hmney self. he hmney pessue loss s obaned by ay-wesbah Equaon [9]. V P ( ) d ( (3) d d ) he hmney avalable daf s equal o he hmney heoeal daf mnus he hmney pessue loss [8]. P a ( ) gh ( (4) d d ) Ineasng he sola olleo sufae aea and he hmney hegh and damee an geneae moe hmney avalable daf. Fo gven sola olleo and hmney, he daf manly

3 depends on ansen sola adaon. heefoe, he sola hmney sysem has a me dependen venlaon paen. Sola avalable daf makes he oom unde negave pessue and venlaes he oom. Aodng o he flud dynams, boh pessue balane and aflow balane ae used o develop he aflow model n he sysem. Pessue balane he hmney daf s no only balaned wh he oolng ube pessue loss, bu also balaned wh he sak effe n he upwad oolng ube o he oom, whh s nomally gnoed n he mehanal venlaon sysem. he oolng ube pessue loss s by ay-wesbah Equaon [9]. V P ( ) d ( (5) d d ) Sne boh he a n upwad oolng ube and n oom s olde han he amben a, means ha he oolng ube and oom have a negave sak affe. In ohe wods, he hmney avalable daf should oveome he oolng ube pessue loss as well as he negave sak affe n he upwad oolng ube and n he oom a beween he oule of he oolng ube and he nle of he sola olleo. Some assumpons ae used n he hemal gavy affe alulaon. he a empeaue hange n he elave sho veal oolng ube s gnoed. he oom empeaue dffeene beween he oolng ube oule and he sola olleo nle s also gnoed. So he sak affe n he oolng ube and he oom an be expessed as: ( ) gh (6) ( ) gh (7) he sum of he ube pessue loss ( P ) and he negave pessues ( and ) an be defned as he oolng ube equed daf. Psys P ( d d ) ( ) gh ( ) gh (8) heefoe, based on he pessue balane, he hmney avalable hmney an be expessed as: (9) a P sys he negave ndoo pessue does no only suk he ousde a hough he oolng ube bu also auses a nflaon hough he envelopes, suh as wndows and doos. he a nflaon aflow unde a gven pessue dffeene s obaned by he powe law equaon [1]. he and n values depend on he envelope ghness and an be obaned by he measuemen. n (1) P Eq. (1) an also be ewen as: 1 n P ( ) (11) he hmney avalable daf s balaned wh he pessue dffeene oss envelope. (1) a P Aflow balane ue o he nflaon, he hmney aflow s always hghe han he oolng ube aflow. Ignong he nflaon wll ause bg eo fo he loosely onsued buldng. Based on he mass onsevaon n he oom, he hmney aflow should be balaned wh he supply aflow hough he oolng ube and he nflaon hough envelopes f he densy hanges ae gnoed. (13) Fo he omplee heoeal model fo he sola hmney oolng ube sysem, he oom hea balane equaon and he oolng ube balane equaon need o be developed n ode o oban he oom empeaue and he oolng ube empeaue unde any ousde and sola adaon ondons. Sne he pape fouses on he mpa of he sola hmney on he aflow model, he oolng ube supply a empeaue and he oom empeaue s eaed as gven paamees. Wh hese smplfaons, fo he gven sola olleo, hmney and oolng ube, he hmney venlaon aflow ( ), he oolng ube aflow ( ) and he nflaon aflow ( ) unde dffeen ousde and sola adaon ondons an be obaned by solvng wo pessue balane equaons, Eqs. (8) and (1), and one aflow balane equaon, Eq. (13). SYSEM ESIGN he oolng ube and sola hmney sysem desgn nludes he oolng ube desgn and he sola hmney desgn. he oolng ube desgn nludes he ube damee, lengh and bued deph. As menoned pevously, he pape only fouses on developng he sola hmney aflow model, so he oolng ube s eaed as gven. he sola hmney desgn nludes he sola olleo sze and he hmney hegh and damee. he sola hmney should have enough daf o oveome he oolng ube pessue loss and he negave hemal gavy affe unde he desgn venlaon aflow. 3

4 he equaons fo he hmney aflow model ae used n he sola hmney desgn. he sola hmney desgn poess nludes: Requed sola hmney avalable daf he sola hmney should povde enough daf o oveome he oolng ube pessue loss and negave hemal gavy affe. he sysem equed daf ( Psys ) o he hmney avalable daf ( a ) an be alulaed usng Eq. (8) based on he oolng ube damee, lengh, fng ype and equed aflow as well as he empeaues dsbuon. Sola hmney venlaon aflow he hmney venlaon aflow ( ) s balaned wh he oolng ube aflow ( ) and he envelope nflaon aflow ( ) based on Eq. (13). he nflaon aflow an be obaned fom he hmney avalable daf usng Eq. (1). Chmney hegh, sze and a empeaue As menoned pevously, he all and bg hmney has he hgh avalable daf unde same hmney a empeaue. In ohe wods, he equed hmney a empeaue wll be low and he sola olleo sze wll be small fo he all and bg hmney. Sne he sola olleo sze s lmed by he spae, he all and bg hmney s he bes hoe. Meanwhle, he hmney hegh and sze seleon should onsde he hmney sengh, sably, os and he suoundng landsape. Fo seleed hmney hegh and damee, he equed hmney a densy ( ) an be obaned by Eq. (4) usng he hmney avalable daf ( a ) and he hmney venlaon aflow ( ). Fnally, he hmney a empeaue ( ) s alulaed fom he densy. Sola olleo sze he sola olleo absobng aea ( A s ) s deemned based on equed he hmney a empeaue and hmney flow unde loal sola adaon and lmae nfomaon usng Eq. (1). he hmney avalable daf s affeed by he hmney hegh and damee as well as he sola olleo sze. he hgh hmney avalable daf an be obaned by neasng one of hese hee paamees. Howeve, all adjusmens ae lmed by maeal and onsuon os, nsallaon spae, and suue sengh and sably. he oodnaon among hese paamees s neessay n he sola hmney desgn. A sola hmney was desgned o eplae he ognal eleal fan fo he exsng oolng ube sysem n Passve Sola Enegy Reseah es Faly of Unvesy of Nebaska. he es faly s a one soy house (5 by m o 16 by 64 fee) desgned o nvesgae alenave heang and oolng expemens and he poenal fo ommeal and esdenal use. he oom s lage souh wndow fon and he onee slab eae a hgh oolng load fo he summe season. he.457 mee (1.5 fee) damee 57 mee (188 f) long ulve ube has been bued a a deph of 3 mee (1 fee). he nle of he ube s.6 mee ( fee) above he floo nsde he buldng. he oolng ube enes he Sola Se fom he souh sde and uns souheas o nohwes. he buldng nflaon model has been esed. he measued a exhange ae n he es faly s abou.5 a hanges pe hou (ACH) unde an ndoo pessue of 5 Pa (. nh of wae). he ypal nflaon ae n housng n Noh Amea hanges fom abou. ACH o. ACH [1]. he es shows ha he buldng envelopes wee no sealed well. he a nflaon of he buldng s oelaed wh he dffeenal pessue aoss he envelope by he followng equaon, whh was expemenally deemned usng he blowe doo es P o es he oolng ube hemal pefomane n he es faly, he ognal mehanal venlaon ae s.76 m 3 /s (1,6 CFM). Howeve, s had fo sngle sola hmney o geneae ha venlaon ae. Fo he expemen pupose,.1 m 3 /s (5 CFM) s seleed o desgn he sola hmney sysem. he anpaed oolng ube a empeaue s 17 ºC (63 ºF) and he anpaed oom empeaue s 3 ºC (86 ºF) when he ousde a empeaue s 34 ºC (94 F). Combnng he oolng ube pessue loss and he sak affe, he avalable hmney daf needs o be 5 Pa (. nh of wae). he oom a sak affe s gnoed sne he nle of he sola olleo s desgned a same level as he oule of he oolng ube. Unde he 5 Pa (. nh of wae) ndoo oudoo pessue dffeene, he nflaon aflow s.3m 3 /s (7 CFM). So he oal hmney venlaon aflow s.15m 3 /s (3 CFM). he hmney hegh s seleed as 1m (33 fee) and he hmney damee s seleed as.457m (18nh) wh onsdeaon of he os and sably. he equed hmney a empeaue s 57ºC (135ºF) n ode o geneae a equed avalable hmney daf of 5 Pa (. nh of wae). he desgn sola olleo absobng aea s m (15 f ) f he desgn sola adaon s 4 W/m (16 Bu/h f ) wh an absopane of.8 and a hea loss oeffen s 8.5W/ºC m (1.3 Bu/h ºF f ). EXPERIMEN AN RESUS he sola olleo was bul usng plywood and glass. Sne he sun alude angle s 64 degee n Augus n maha, Nebaska, he sola olleo was plaed a a 6 degee angle on he souh sde of buldng n ode o be oened o he sun and eeve he maxmum sola adaon. he hmney s a seel spal ppe wh a damee of.457m (18 nhes) and onsss of hee 3m (1 fee) long seons. he hmney s plaed on a 1.5m (5 fee) hgh sand whh s boled o a onee foundaon. he foundaon s 4

5 abou 1m (3 fee) deep and onans abou 3 m 3 (3 ub yads) of onee. In ode o gve he hmney exa sably, 9 guy wes (3 on evey seon) wee aahed. he sola olleo s onneed o he buldng and he hmney va of.457m (18 nhes) damee spal ppe (same maeal as he hmney). he lengh of he onneon pees ae.8m (11 nhes) beween Sola Se and olleo and m (84 nhes) beween he olleo and he hmney. he openng fo he olleo nle s on he boom of he olleo. he openng fo he olleo oule s on he op of he oppose se fom he olleo n ode o use he posve sak affe n olleo. ube a empeaue dopped down o abou 16 ºC (61 ºF). he aflow dopped down o zeo dung ngh due o he zeo hmney daf and he oolng ube oule empeaue has a same empeaue as he ndoo a. Fgue 3 also shows abnomal aflow paens n he ealy monng of Augus 5 and n he afenoon of Augus 6. I was found ha hee was a song souh wnd n he ealy monng of Augus 5 and he sky ondon was beween saeed and oveas n he day me of Augus 6 n hs aea. I demonsaes ha he sola hmney sysem s sensve o he whehe ondon, suh as he wnd and sky ondon. empeaue sensos wee nsalled along he oolng ube, he olleo and he hmney as well as n he oom and he ousde. Sysem opeang paamees wee measued fom Augus 1, 3 o Augus 9, 3. ung measuemen one VECICAC PUS mee wee nsalled nsde he oule du of he oolng ube o measue he oolng ube aflow dung he measuemen. ube supply a empeaue (C) Coolng ube aflow (m 3 /s) Fgue ompaes he amben empeaue and he aveage hmney empeaue measued by he empeaue sensos. Boh of hem followed he hangng sola adaon based on he me of day. he hmney a empeaue eahed up o 55 ºC (131 ºF) n afenoon due o hgh sola adaon when he ousde a eahed o 31ºC (88 ºF). n he ohe hand, he hmney a dopped down o he amben a empeaue dung ngh. he empeaue dffeene beween he hmney a and amben a geneaed he daf equed by he oolng ube sysem and suked he wam ousde a hough he oolng ube dung dayme. 6. 8/1 8/ 8/3 8/4 8/5 8/6 8/7 8/8 8/9 me empeaue ube aflow Fgue 3: Measued oolng ube aflow and supply a empeaue Fgue 4 ompaes he ndoo a empeaue and he amben a empeaue dung he measuemen. he oom empeaue was below 8 ºC (8 ºF) n afenoon when he amben a eahed o 31ºC (88 ºF). he sysem oong apay an be obaned fom he empeaue dffeen beween he oolng ube supply a and he amben a o he oom a. 5 empeaue (C) /1 8/ 8/3 8/4 8/5 8/6 8/7 8/8 8/9 me Amben a Chmney a Fgue : Measued amben a empeaue and aveage hmney a empeaue Fgue 3 shows he oolng ube aflow and supply a empeaue. he aflow paen followed he empeaue dffeene beween he hmney a and he amben a. he aflow eahed o.13m 3 /s (7CFM) n afenoon and he A empeaue (C) /1 8/ 8/3 8/4 8/5 8/6 8/7 8/8 8/9 me Room Amben Fgue 4: Measued oom and amben a empeaue 5

6 he ousde a s ooled down by ejeng hea o he sol hough he oolng ube and hen he old ube a s wamed up by absobng hea fom he oom. he sensble old fom he sol o he ube a and he sensble old fom he ube a o he oom an be easly alulaed fom a enhalpy hange hough he ube and he oom. Fgue 5 shows he alulaed oolng ube sensble old gan and supply. he oolng ube and sola hmney sysem n he es faly has a hghes sensble old gan of.4kw (8,Bu/h) fom he sol and a hghes sensble old supply of 1.9 kw (6,5Bu/h) o he spae. I also an be seen ha he sysem an no povde a sable old supply o he buldng. Howeve, has he hghes oolng apay when he buldng has he hgh oolng load n afenoon. Sensble oolng apay (kw) /1 8/ 8/3 8/4 8/5 8/6 8/7 8/8 8/9 me Cold f om sol Cold o oom Fgue 5: Coolng ube old gan fom sol and old supply o buldng he sysem aflow model s vefed usng he measued sysem opeang paamees. Sne sola adaon was no measued, he measued hmney a empeaue s dely used n he aflow smulaon nsead of he sola olleo hea balane equaon. Fgue 6 ompaes he measued aflows and he smulaed aflows n Augus 6 and Augus 7, 3. he smulaed aflow mahed he measued aflow well. IMPRVEMENS N SYSEM PERFRMANCE he es faly has a hgh a exhange ae,.5ach. I esuls n hgh nflaon aflow and low oolng ube aflow. Fgue 7 ompaes he smulaed oal o hmney aflow and oolng ube aflow n wo days. Abou % of hmney a flow dd no pass hough he oolng ube. he hgh a nflaon ae does no only edue he oolng ube oolng apay bu also nease he buldng oolng load. ube aflow (m 3 /s) : 6: 1: 18: : 6: 1: 18: : me (8/6-8/7) Chmney a Coolng ube Fgue 7: Smulaed hmney and oolng ube aflows In ode o mpove sysem pefomane, he buldng envelope should be ghened. If he es faly a nflaon ae s edued o a lowe level, he ube aflow wll nease. Fgue 8 shows he smulaed mpoved ube aflow by ghenng envelope o edue a nflaon fom.5ach o.ach. he oolng ube aflow neases by 1%. he aual sola adaon used n smulaon s obaned fom he measued hmney a empeaue and oom a empeaue. I s also assumed he oom empeaue and oolng ube ae no affeed by he aflow hange..15. ube aflow (m 3 /s) ube aflow (m 3 /s) : 6: 1: 18: : 6: 1: 18: : me (8/6-8/7) ghenng Cuen ouble ubes.7 : 6: 1: 18: : 6: 1: 18: : me (8/6-8/7) Measued Smulaed Fgue 6: Compason of measued and smulaed aflow Fgue 8: Impovemen of oolng ube aflow 6

7 n he ohe hand, he oolng ube essane s anohe man fao fo he sysem aflow. he longe oolng ube lms he aflow nease. Fo same oolng ube hea ansfe aea, wo sho paallel ubes an be nsalled nsead of one long ube. Fgue 8 also shows he smulaed aflow of wo paallel oolng ubes afe ghenng envelope. he oolng ube aflow wll nease by 5% by hese wo mpovemens. CNCUSINS he aflow model of he sola hmney n he oolng ube and sola hmney sysem has been developed. he sola hmney desgn poedue has been developed fo sola olleo and hmney. ne sola hmney has been desgned. ne sola olleo wh an absobng aea of m (15f ) and one hmney wh damee of.457m (18 nh) and hegh of 1 m (3 fee) wee nsalled. he aual oolng ube aflow s measued o be.13 m 3 /s (o 7CFM) and he measued aflow mahes he smulaon esuls. he negaed sysem an oban.4kw (8,Bu/h) peak oolng apay fom undegound and supply 1.9 kw (6,5Bu/h) peak oolng enegy o he spae n afenoon. he ghened envelope and paalleled ubes an nease he sysem aflow by 5%. REFERENCES 1. ASHRAE handbook, HVAC Applaons, Resdenes, pp , Amean Soey of Heang, Refgeang and A-ondonng Engnees, In., Alana, GA,. ASHRAE handbook, HVAC Applaons, Geohemal enegy, pp , Amean Soey of Heang, Refgeang and A-ondonng Engnees, In., Alana, GA, 3. ASHRAE handbook, Fundamenals, Clma esgn Infomaon, pp , Amean Soey of Heang, Refgeang and A-ondonng Engnees, In., Alana, GA, 4. Mak A. Newman, M. Wang ANAYSIS F HE PERFRMANCE F EARH CNAC CING UBES, A Seno Poje, Unvesy of Nebaska, June Chen, B.,. Wang, J. Maloney, J. Ennenga, and M. Newman. Measued Coolng Pefomane of Eah Cona Coolng ubes. Poeedngs of he Amean Sola Enegy Soey, Mnneapols, MN, ASHRAE handbook, HVAC Applaons, Sola Enegy Use, pp , Amean Soey of Heang, Refgeang and A-ondonng Engnees, In., Alana, GA, 7.. S. Halay, J., he Comng Age of Sola Enegy, Hape & Row, Publshe, In., New Yok 8. ASHRAE handbook, HVAC Sysems and Equpmen, Chmney, Gas Ven, and Feplae Sysems, pp , Amean Soey of Heang, Refgeang and Aondonng Engnees, In., Alana, GA, 9. ASHRAE handbook, Fundamenals, u desgn, pp , Amean Soey of Heang, Refgeang and Aondonng Engnees, In., Alana, GA, 1. ASHRAE handbook, Fundamenals, Venlaon and nflaon, pp ,Amean Soey of Heang, Refgeang and A-ondonng Engnees, In., Alana, GA, 7

5-1. We apply Newton s second law (specifically, Eq. 5-2). F = ma = ma sin 20.0 = 1.0 kg 2.00 m/s sin 20.0 = 0.684N. ( ) ( )

5-1. We apply Newton s second law (specifically, Eq. 5-2). F = ma = ma sin 20.0 = 1.0 kg 2.00 m/s sin 20.0 = 0.684N. ( ) ( ) 5-1. We apply Newon s second law (specfcally, Eq. 5-). (a) We fnd he componen of he foce s ( ) ( ) F = ma = ma cos 0.0 = 1.00kg.00m/s cos 0.0 = 1.88N. (b) The y componen of he foce s ( ) ( ) F = ma = ma