An yi aikin da ƙarfi
1.1 Ma'anar Aiki
Idan ka tura littafi a saman teburi har sai littafin ya koma gefe, za a ce ka yi aiki a kan littafin. Idan wani abu ya faɗi ƙasa saboda jan ƙarfin nauyi, ana cewa ƙarfin nauyi ya yi aiki a kan abin. Akasin haka, idan ka tura wani abu da dukkan ƙarfinka har sai ka yi gumi sosai, amma abin bai motsa ba kwata-kwata, ana cewa ba ka yi wani aiki a kan abin ba. A rayuwar yau da kullun, mutane za su iya cewa ka yi aiki tuƙuru ta hanyar tura abin amma a fannin kimiyyar lissafi, ba ka yin aiki a kan abin ba saboda babu wani motsi na abin.
Ana iya yin aiki akan wani abu ta hanyar amfani da ƙarfi mai ɗorewa (adadi da alkiblar da take akai) ko kuma ƙarfin da ke canzawa (adadi da alkiblar da take akai sun bambanta). Misalin ƙarfi mai ɗorewa da alkiblar da take akai shine ƙarfin nauyi, wanda ke aiki akan abu lokacin da abin yake kusa da saman ƙasa. Lokacin da abu yake cikin faɗuwa kyauta kusa da saman ƙasa, adadin da alkiblar saurin faɗuwa kyauta na abu suna dawwama saboda adadin da alkiblar ƙarfin nauyi mai ɗorewa abin suna dawwama. Misalin ƙarfi mai ɗorewa mara daidaituwa (amma tare da alkibla mara daidaituwa) shine ƙarfin bazara . Wani misali kuma shine roka da aka harba zuwa sararin samaniya ko kuma ya koma saman duniya. Lokacin da aka harba roka, adadin ƙarfin nauyi da ke aiki a kai yana canzawa a cikin juzu'i zuwa nisan murabba'i daga tsakiyar duniya.
1.1.1 Aikin da hukumar gudanarwa ta jihar (COS ) ta yi
A lissafi, aikin da ƙarfin da ke ci gaba da aiki a kan wani abu ana bayyana shi a matsayin motsi da aka ninka ta hanyar ƙarfi ko ɓangaren ƙarfi wanda ke da alkibla iri ɗaya da motsi na abin. Ka lura da wani abu a saman wani wuri mai faɗi mai tsauri tare da juyawa zuwa dama wanda ƙarfin turawa (F) ya haifar.
Hoto na 1. (Sama) Alkiblar matsar da abin yayi daidai da ƙarfi F. (Ƙasa) Alkiblar matsar da abin yayi daidai da ɓangaren ƙarfi F a cikin alkiblar kwance (F cos).
Aikin da ƙarfin turawa (F) ke yi shine:
W = (F)(s)(cos θ) = Fs (cos 0) = Fs (1)
W = Fs
Aikin da bangaren ƙarfin F ke yi a cikin alkiblar kwance (F cos θ) shine:
W = (F cos θ)(s)(cos 0) = (F cos )(s)(1)
W = Fs cos θ
Aikin da ƙarfin gogayya na motsi (f k ) ke yi shine:
W = (f k )(s)(cos 180) = (f k )(s)(-1)
W = – (f k )(s)
Aikin da ƙarfin al'ada (N) ke yi shine:
W = (N)(s)(cos 90) = (N)(s)(0) = 0
Aikin da nauyin (w) ya yi shine:
W = (w)(s)(cos 90) = (w)(s)(0) = 0
Bayani: W = aiki, s = adadin ƙaura, θ = kusurwa tsakanin ƙarfi da ƙaura.
Hoto 2.
(a) Abin yana cikin faɗuwa kyauta. Nauyin yana kan hanya ɗaya da natsuwa (b) Abin yana motsawa a tsaye sama. Alkiblar nauyin tana akasin alkiblar natsuwa.
A cikin misali na baya, aikin da nauyin (w) ya yi yana da ƙimar sifili domin alkiblar nauyin abu yana daidai da alkiblar da abin ya motsa. Ya kamata a lura cewa aikin da nauyin ya yi ba zai sami ƙimar sifili ba idan alkiblar nauyin ta yi daidai da alkiblar ko akasin alkiblar da abin ya motsa.
Aikin da nauyin (w) akan abin da ke cikin faɗuwar free fall da aka nuna a cikin hoto na a shine:
W = Fs (cos θ) = wh (cos 0) = wh (1) = wh = mgh
Aikin da nauyin (w) akan abin da ke motsawa a tsaye sama wanda aka nuna a hoto na b yayi shine:
W = Fs (cos θ) = wh (cos 180) = wh (-1) = – wh = – mgh
Bayani: w = nauyi (Newton), h = tsayi (mita), m = nauyi (kg), g = hanzarin nauyi (mita a kowace daƙiƙa murabba'i).
A bisa bayanin da ya gabata, an yanke hukunci kamar haka: Na farko, idan wani abu bai fuskanci wani motsi ba, ƙarfin da aka yi wa abu ba ya yin wani aiki. Idan s = 0, W = 0; Na biyu, idan wani ƙarfi ya samar da wani kusurwa zuwa ga motsi na wani abu, ɓangaren ƙarfin ne kawai ke raba alkibla ɗaya da motsi na abin ke aiki akan abu; Na uku, ƙarfin da ke cikin alkibla daidai da alkiblar motsi na abu zai samar da kusurwar 90 o . Cos 90 = 0; Na huɗu, aiki na iya samun alama mai kyau ko mara kyau. Idan ƙarfin yana kan alkibla ɗaya da motsi na abu kuma yana samar da kusurwar 0 o , yana yin aiki mai kyau akan abu. Akasin haka, idan ƙarfin yana da alkibla akasin alkiblar motsi na abu kuma yana samar da kusurwar 180 o , yana yin aiki mara kyau akan abu.
Siffa ta 3. Ƙarfi (F) - jadawalin motsi (s). Aiki yana daidai da yankin da aka yi wa inuwa.
Aikin da ƙarfin da ke ci gaba da gudana a kan abu lokacin da abin ke fuskantar matsi daidai yake da yankin da aka yi wa inuwa a cikin jadawalin ƙarfin (F) - matsayi (s).
Ana nuna aikin a matsayin W (babban harafi), kuma ana nuna nauyi a matsayin w (ƙananan harafi). Sashin SI na aiki shine mita na Newton ∙ (N m). Yana daidai da Joule, wanda aka taƙaita shi da J.
An sanya masa suna don girmama wani likitan Ingila na ƙarni na 19 , James Prescott Joule.
Misali tambaya ta 1: Aikin da wani ƙarfi mai ɗorewa ke yi
Wani abu yana kwance a saman ƙasa mara gogayya. A kan abin, ana amfani da ƙarfin N 10, wanda ke samar da kusurwar digiri 30 a kan ƙasa. Idan abin ya motsa nisan mita 1, nawa ne ƙarfin da ke kan abin yake yi?
Magani:
Sananne: F = 10 N, s = mita 1
Ana nema: Aiki (W)
W = (F)(s)(cos 30 o ) = (10 N)(1 m)(1/2 √ 3) = 5 √ 3 N m
Misali tambaya ta 2: Aiki da ƙarfi mai ɗorewa
Kwakwa mai nauyin kilogiram 0.2 tana faɗuwa daga tsayin mita 10 daga sama da ƙasa. Idan saurin nauyi shine 10 m/s 2 , nawa ne aikin da aka yi da nauyi akan kwakwa?
Magani:
Sananne: m = 0.2 kg, h = 10 m, g = 10 m/s 2
Ana so: Aiki (W) ta nauyi (w)
W = Fs = wh = mgh = (0.2 kg)(10 m/s 2 )(10 m) = 20 kg m 2 / s 2 = 20 N m = 20 Joules
1.1.2 Aiki ta Ƙarfin Canji
Misalin ƙarfin da ke canzawa shine ƙarfin bazara. Adadin ƙarfin bazara yana canzawa koyaushe. Saboda haka, ba za a iya ƙididdige aikin da ƙarfin bazara ke yi akan wani abu ta amfani da dabarar aiki na ƙarfin da ke ci gaba ba (W = F s cos θ). Idan aka miƙe maɓuɓɓuga, gwargwadon miƙe maɓuɓɓuga, gwargwadon ƙarfin da ake buƙata don shimfiɗa maɓuɓɓuga. Kuma idan an matse maɓuɓɓuga, gwargwadon ƙarfin da ake buƙata, gwargwadon ƙarfin da ake buƙata. Lokacin da aka matse ko aka miƙe maɓuɓɓuga, ƙarfin bazara yana canzawa daga 0 (x = 0) zuwa matsakaicin ƙima (F = kx). Don haka, ana ƙididdige adadin ƙarfin bazara ta amfani da matsakaicin. Matsakaicin adadin ƙarfin bazara shine:
Aikin da spring force ke yi akan wani abu shine:
W = aiki, x = Δx = karkacewar bazara (mita), F = ƙarfin bazara (Newton).
Misali tambaya ta 3: Aiki da ƙarfin da ba ya canzawa
A kan maɓuɓɓugar ruwa, ana ɗaukar nauyin da aka dakatar da shi da nauyin kilogiram 1, don haka maɓuɓɓugar ruwan ta miƙe da cm 2. Idan saurin nauyi ya kai m 10/s 2 , a ƙayyade (a) ma'aunin maɓuɓɓugar ruwa (b) aikin da ƙarfin maɓuɓɓugar ruwa ya yi akan nauyin.
Magani:
An san: m = 1 kg, g = 10 m/s 2 , x = Δx = 2 cm = 0.02 m.
(a) ma'aunin bazara
(b) an yi aikin ne ta hanyar ƙarfin bazara akan nauyi
W = -1/2 kx 2 = -1/2 (500)(0.02) 2 = – (250)(0.0004) = -0.1 Joule
Aikin da ƙarfin bazara ke yi akan nauyin yana da ƙima mara kyau saboda alkiblar ƙarfin bazara tana akasin alkiblar motsi na nauyin (ƙarfin bazara yana kan alkiblar sama, nauyi yana kan alkiblar ƙasa).
1.2 Aiki Mai Tsafta ko Aiki Mai Tsafta ta Ƙarfin Sadarwa
Idan akwai ƙarfi ɗaya kawai da ke aiki a kan abu lokacin da abin ke fuskantar matsi, aikin da ƙarfin yanar gizo ke yi daidai yake da aikin da ƙarfin ya yi. Misali, idan abu yana cikin faɗuwa kyauta kuma an yi watsi da ƙuntatawar iska, ƙarfin da ke aiki a kan abu shine ƙarfin nauyi. A wannan yanayin, ƙarfin yanar gizo da ke aiki a kan abu shine ƙarfin nauyi (duba hoto na 2).
W net = W nauyi
Idan wasu ƙarfi suna aiki akan wani abu lokacin da abin ke fuskantar matsi, aikin da ƙarfin yanar gizo ke yi daidai yake da aikin yanar gizo da duk ƙarfin da ke aiki akan abin ke yi (duba hoto na 1).
W net = W 1 + W 2 + W 3 + W 4
Ana iya ƙididdige aikin da ƙarfin yanar gizo ke yi akan wani abu ta hanyar gano ƙarfin yanar gizo da farko sannan a ninka shi da adadin motsi.
W = ΣF s
Misali tambaya ta 4: Cibiyar sadarwa
Ana tura akwati mai tsayawa a saman bene da ƙarfin N20 har sai akwatin ya yi nisa da mita 1. Idan ƙarfin turawa yana daidai da alkiblar da akwatin ya motsa kuma a kan akwatin yana aiki da ƙarfin gogayya na 2 N, a ƙayyade adadin aikin raga da ƙarfin raga da ke kan akwatin ya yi.
Magani:
Sananne: F = 20 N, f k = 2 N, s = 1 m
W 1 = F s = (20 N)(1 m) = 20 Nm = Joules 20
W 2 = f k s = – (2 N)(1 m) = – 2 Nm = – Joules 2
Aikin yanar gizo ko aikin da rundunar tsaro ta yanar gizo ke yi
W net = W 1 - W 2 = 20 J - 2 J = 18 J
Misali tambaya ta 4) Ƙarfin turawa (F) yana aiki mai kyau, ƙarfin gogayya na motsi (f k ) yana aiki mara kyau
