Labarai game da abubuwan da suka faru na halitta da sauransu da suka shafi kimiyyar lissafi.
1. Harsashi mai nauyin gram 30 yana tafiya a gudun mita 30/s zai bugi wani katako mai nauyin kilogiram 1 wanda yake hutawa. Kayyade saurin toshe idan harsashin ya makale a cikin toshen!
Tattaunawa
An sani :
Nauyin harsashi (m)1) = gram 30 = 0,03 kg
Nauyin tubalin (m2) = 1 kg
Saurin farko na harsashi (v)1) = 30 m/s
Saurin farko na toshe (v)2) = 0 (toshe mai tsayawa)
An tambaya : saurin harsashi da toshewa bayan karo (v')
Misalai 3 na karo mai sassauƙa
1. Abu mai nauyin gram 500 yana tafiya a gudun m/s 10, abu mai nauyin gram 200 kuma yana tafiya a gudun m/s 12. Abubuwa biyu suna tafiya zuwa ga juna kuma suna karo. Idan bayan karo, gudun abu mai nauyin gram 500 ya kai m/s 6, to saurin abu mai nauyin gram 200 shine…
Tattaunawa
An sani :
Nauyin abu 1 (m1) = gram 500 = 0,5 kg
Nauyin abu 2 (m2) = gram 200 = 0,2 kg
Saurin farko na abu na 1 (v)1) = -10 m/s
Saurin farko na abu na 2 (v)2) = 12 m/s
Saurin ƙarshe na abu na 1 (v)1') = 6 m/s
Misalai 8 na Tambayoyin Momentum na Layi
1. Abu mai nauyin kilogiram 1 yana motsawa a gudun mita 10/s. lokacinta abin shine…
Tattaunawa
An sani :
Mass (m) = 1 kg
Gudun (v) = 10 m/s
An tambaya : ƙarfin layi (p)
Jawab :
Tsarin Momentum: p = mv
Bayani: p = ƙarfin motsi, m = taro, v = gudun.
Motsin abu shine:
p = mv = (1)(10) = 10 kg m/s2
Misalai 11 na Tambayoyin Motsi da Sha'awa
1. Ana jefa ƙwallon da nauyinta ya kai kilogiram 0,2 a kwance a gudun mita 10/s kuma ta bugi bango, sannan ƙwallon ta dawo da sauri iri ɗaya. Sauyin da aka samu a bugun ƙwallon shine...
Tattaunawa
Misalan Tambayoyi 16 kan Dokar Kare Makamashin Inji
Dokar kiyaye makamashin injiniya a cikin motsi na faɗuwa kyauta
1. Kwakwa mai nauyin kilogiram 2 tana faɗuwa cikin sauƙi daga tsayin mita 6. Ƙarfin motsi na kwakwa idan ta isa ƙasa shine… g = 10 m/s2
Tattaunawa
An sani :
Nauyin kwakwa (m) = 2 kg
Tsawo (h) = mita 6
Saurin gudu saboda nauyi (g) = 10 m/s2
An tambaya : kuzarin motsi (EK)
Misalai 2 na tambayoyin iko
Ƙarfi shine saurin da ake yin aiki kasuwanci ko ƙoƙarin da aka yi a cikin wani takamaiman lokaci.
A fannin lissafi, iko shine rabon ƙoƙari da lokaci.
P=W/t
Bayani: P = iko (naúrar Joule/daƙiya), W = aiki (Joule) da t = tazara lokaci (daƙiya)
Bisa ga wannan lissafi, za a iya kammala da cewa girman yadda ake yin aiki, girman yadda ake yin aiki, akasin haka, girman yadda ake yin aiki, girman yadda ake yin aiki, girman yadda ake yin sa.
Wutar lantarki adadi ne na sikelin. Tsarin na'urorin wutar lantarki na duniya shine joule/daki. Joule/daki = watt (W a takaice), an sanya masa suna don girmama James Watt.
Tsarin ikon Birtaniya na fam 1-ƙafa-ƙarfi a kowace daƙiƙa. Wannan na'urar ta yi ƙanƙanta sosai don amfani mai amfani, don haka ana amfani da babban na'ura, ƙarfin dawaki (wanda aka rage girman hp). 1 ƙarfin dawaki = fam 550-ƙafa-ƙarfi a kowace daƙiƙa = watt 764 = ¾ kilowatt.
1. Ana ba wa maɓuɓɓuga nauyi na kilogiram 2 sannan a rataye shi a tsaye a kan maɓuɓɓuga. Idan maɓuɓɓugar ta yi tsayi da santimita 4, to canjin ya faru. makamashi mai yuwuwa Ƙarfin roba na maɓuɓɓugar ruwa shine… g = 10 m/s2
Tattaunawa
An sani :
Nauyin kaya (m) = 2 kg
Saurin gudu saboda nauyi (g) = 10 m/s2
Nauyin kaya (w) = mg = (2)(10) = 20 Newton
Ƙara tsawon bazara (x) = 4 cm = mita 0,04
An tambaya : Ƙarfin ƙarfin sakewa na bazara
1. Abu mai nauyin kilogiram 1 yana faɗuwa cikin sauƙi daga tsayin mita 10 har sai ya isa ƙasa. A tantance:
(a) Aikin da ƙarfin nauyi ya yi akan abu
(b) Canje-canje makamashi mai yuwuwa nauyi
Saurin gudu saboda nauyi (g) = 10 m/s2
Tattaunawa
An sani :
Nauyin abu (m) = 1 kg
Tsawo (h) = mita 10
Saurin gudu saboda nauyi (g) = 10 m/s2
Amsa:
(a) Aikin da aka yi da ƙarfin nauyi
Idan abu ya faɗi cikin 'yanci, alkiblar motsin abu yana ƙasa kuma alkiblar ƙarfin nauyi da ke aiki akan abu (nauyin abu) shi ma yana ƙasa. Saboda suna cikin alkibla ɗaya, ƙarfin nauyi yana haɗuwa ko kuma yana samar da kusurwar 0.o tare da alkiblar motsin abu. Cos 0 = 1 kuma kowace lamba da aka ninka da 1 iri ɗaya ne da wannan lambar, don haka cos 0 ba sai an haɗa ta cikin dabarar aiki ba.
Tsarin aikin shine W = Fs, inda W = aiki, F = ƙarfi da s = motsi. Idan aka daidaita shi da wannan matsalar, tsarin aikin zai canza zuwa W = wh = mgh, inda W = aiki, w = nauyi, h = canji a tsayin abu, m = nauyin abu, g = hanzari saboda nauyi.
Don haka aikin da nauyi ke yi shine:
W = wh = mgh = (1)(10)(10) = Joules 100
Misalai 2 na amfani da dokokin Newton ga tsarin ɗaukar igiya da pulley
1. Nauyin tubalin 1 shine kilogiram 2, nauyin tubalin 2 shine kilogiram 3, saurin gudu saboda nauyi shine mita 10/s2. Kayyade (a) girma da alkiblar hanzarta tsarin (b) girman ƙarfin tashin hankali akan igiya!
Tattaunawa
Misalai 4 na tambayoyi kan aiwatar da dokokin Newton game da motsi kai tsaye na lif ko lif
1. Mutumin da nauyinsa ya kai kilogiram 50 yana cikin lif. Saurin gudu saboda nauyi = 10 m/s2A tantance girman ƙarfin da benen lif ke yi wa mutumin idan:
(a) lif mai shiru
(b) lif ɗin yana motsawa ƙasa da gudu akai-akai
(c) lif ɗin yana motsawa sama da sauri na 5 m/s2
(d) lif ɗin yana motsawa ƙasa da hanzarin 5 m/s2
(e) lif ɗin faɗuwa kyauta