Idan ka tura littafi a kan teburi har sai ya motsa, to kana yin aiki ne a kan littafin. Idan abu ya faɗi a saman duniya saboda ƙarfin nauyi yana jan sa , ƙarfin nauyi yana aiki akan abu. Akasin haka, idan ka tura abu da dukkan ƙarfinka har sai gumi ya jike ka amma abin bai motsa ba, ba ka yi aiki a kan abu ba. A rayuwar yau da kullun, ana cewa ka yi aiki ko aiki tuƙuru wajen tura abu, amma a cewar kimiyyar lissafi, ba ka yi aiki a kan abu ba saboda abin ba ya fuskantar matsi (abun ba ya canza wuri).
Ana iya yin aiki ta hanyar ƙarfi mai dorewa (girma da alkiblar ƙarfin koyaushe suna kasancewa iri ɗaya) ko kuma ƙarfin canzawa (girma da alkiblar canjin ƙarfin). Misalin ƙarfin da ke da girma da alkibla mai dorewa shine ƙarfin nauyi da ke aiki akan wani abu kusa da saman Duniya. Misalin ƙarfin da ke da girma da alkibla mai canzawa shine ƙarfin bazara. Idan ka shimfiɗa bazara, gwargwadon yadda ka shimfiɗa ta, da wuya ka ja ta, don haka girman ƙarfin ba ya canzawa yayin da bazara ke miƙewa. Wani misali kuma shine lokacin da roka ta motsa zuwa sararin samaniya, da nisan da take da saman Duniya, da ƙarancin ƙarfin nauyi na Duniya da ke aiki akan rokar.
1.1 Aikin da aka yi ta hanyar ƙarfin da ba ya canzawa
A fannin lissafi, aikin da ƙarfin da ke ci gaba da aiki a kan wani abu ya yi shi ne sakamakon wurin ƙaura wani abu mai ƙarfi ko ɓangaren ƙarfi wanda yake daidai da yadda abin ya motsa.
Aikin da ƙarfin turawa (F) ke yi:
W = (F)(s)(cos θ) = Fs (cos 0) = Fs (1) = Fs
Aikin da bangaren ƙarfi F ke yi a cikin shugabanci na kwance (F cos θ):
W = (F cos θ)(s)(cos 0) = (F cos θ)(s)(1) = F s cos θ
Aikin da ƙarfin gogayya na motsi (fk) ke yi:
W = (f)k cos θ)(s)(cos 180) = (fk )(s)(-1) = – fk s
Aikin da aka yi ta hanyar ƙarfin yau da kullun (N):
W = (N)(s)(cos 90)o) = (N)(s)(0) = 0
Aikin da aka yi ta hanyar nauyi (w):
W = (w)(s)(cos 90)o) = (w)(s)(0) = 0
Bayani: W = ƙoƙari ko aiki (Joules), s = motsi (mita), θ = kusurwa da aka samar ta hanyar ƙarfi tare da motsi
A cikin misalin da ya gabata, aikin da aka yi ta nauyi (w) yana da ƙimar sifili saboda alkiblar ƙarfin nauyi tana tsaye (tana samar da kusurwa 90°)o) tare da alkiblar motsawa (alkiblar motsi) na abu. Ya kamata a lura cewa aikin da nauyin ya yi ba sifili ba ne idan alkiblar ƙarfin nauyi iri ɗaya ce ko akasin alkiblar motsawa.
Aikin da ƙarfin nauyi (w) ya yi akan abin da ke faɗuwa cikin sauƙi a cikin hoto na a shine:
W = Fs (cos θ) = wh (cos 0) = wh (1) = wh = mgh
Aikin da ƙarfin nauyi (w) ya yi akan abin da ke motsawa tsaye sama a cikin hoto na b shine:
W = Fs (cos θ) = wh (cos 180) = wh (-1) = -wh = -mgh
Bayani: w = nauyi (Newton), h = tsayi (mita), m = nauyi (kg), g = hanzari saboda nauyi (mita a kowace daƙiƙa murabba'i)
Dangane da bayanin da ya gabata, za a iya kammala waɗannan batutuwa masu zuwa:
Na farko, idan abin bai fuskanci matsi ba, to ƙarfin da ke aiki akan matsi ba ya aiki. Idan s = 0 to W = 0.
Na biyuIdan ƙarfin ya samar da wani kusurwa ga matsar da abin, to ɓangaren ƙarfin da ke cikin alkiblar matsar da abin ne kawai ke aiki a kan abin.
Na uku, ƙarfin da ke daidai da wurin da wani abu ya motsa ba ya yin wani aiki a kan abin. Idan ƙarfin yana daidai da wurin da aka motsa, kusurwar da aka samar ita ce 90°o. Cos 90o = 0.
Na huɗu, Ƙoƙarin zai iya zama mai kyau ko mara kyau. Idan ƙarfin yana kan hanya ɗaya da matsar da abin, kusurwar da aka samar ita ce 0o to ƙarfin yana yin aiki mai kyau, akasin haka idan ƙarfin yana akasin alkiblar da aka motsa don haka kusurwar da aka samar ita ce 180o to ƙarfin yana yin aikin korau akan abu.
Aikin da ƙarfin da ke ci gaba da gudana a kan abu yayin da abin ke fuskantar ƙaura daidai yake da yankin da aka yi inuwa a cikin jadawalin ƙarfi (F) da ƙaura (s).
Alamar aiki ita ce W (babban harafi) yayin da alamar nauyi ita ce w (ƙaramin harafi). Sashen tsarin aiki na duniya shine mitar Newton (N m). Wani suna na mitar Newton shine Joule, wanda aka taƙaita shi J, an sanya masa suna don girmama masanin kimiyyar lissafi na Burtaniya James Prescott Joule na ƙarni na 19.
1.2. Aikin da wani ƙarfi da ba na dindindin ba ke yi
Misali ɗaya na ƙarfin da ba ya canzawa shine ƙarfin bazara. Girman ƙarfin bazara koyaushe yana canzawa, don haka ba za a iya ƙididdige aikin da ƙarfin bazara ke yi akan wani abu ta amfani da dabarar aikin da ƙarfin da ba ya canzawa ya yi ba.
Idan aka miƙe maɓuɓɓugar, to tsawon maɓuɓɓugar zai yi, ƙarfin da ake buƙata zai yi yawa. Haka nan, akasin haka, idan aka matsa matsin lamba, to, ƙarfin da ake buƙata zai yi gajere. Muddin an matse ko an miƙe maɓuɓɓugar, ƙarfin maɓuɓɓugar zai canza daga 0 (x = 0) zuwa matsakaicin (F = kx) don haka ana ƙididdige ƙarfin maɓuɓɓugar ta amfani da matsakaicin. Matsakaicin ƙarfin maɓuɓɓugar shine:
F = ½ (0 + kx) = ½ kx
Aikin da ƙarfin bazara ke yi akan wani abu shine:
W = F x = ½ kx2
Bayani: W = aiki (raka'a Joules), x = ƙaruwa a tsawon bazara (raka'a mita), F = ƙarfin bazara (raka'a Newton).
2. Aikin da aka samu ko kuma aikin da aka yi gaba ɗaya (aikin da aka yi da cikakken ƙarfi)
Idan akwai ƙarfi ɗaya kawai da ke aiki a kan wani abu yayin da yake motsawa, to aikin da ƙarfin gaba ɗaya ya yi daidai da aikin da wannan ƙarfin ya yi. Misali, idan abu yana cikin faɗuwa kyauta kuma aka yi watsi da juriyar iska, ƙarfin da ke aiki a kan abu shine nauyi.
W= Wnauyi
Idan akwai ƙarfi da yawa da ke aiki a kan wani abu yayin da abin ke motsi, to aikin da jimillar ƙarfin ya yi daidai da jimlar aikin da dukkan ƙarfin da ke aiki a kan abin suka yi.
W = W1 +W2 +W3 + … + Wn
Ana iya ƙididdige aikin da wasu ƙarfi da ke aiki a kan wani abu ke yi ta hanyar gano girman ƙarfin da aka tara sannan a ninka shi da girman gudun da aka samu.
W = (Ƙarfin sakamako)(komawa) = (sakamakon F)(s)
