1. Dokar Hooke ga maɓuɓɓugan ruwa
Idan aka ja maɓuɓɓugar zuwa dama, maɓuɓɓugar za ta miƙe ta ƙara tsayi (hoto na 1). Idan ƙarfin jan ba shi da girma, an gano cewa ƙaruwar tsawon bazara (Δx) ya yi daidai da girman ƙarfin jan (F). A wata ma'anar, girman ƙarfin jan, tsawon bazara ya fi girma. Kwatanta girman ƙarfin jan (F) da ƙaruwar tsawon bazara (Δx) ya kasance mai dorewa.
Ana jan maɓuɓɓugar zuwa dama don ta sami ƙaruwa a tsawon Δx. Ƙaruwar tsawon bazara ya yi daidai da ƙarfin jan.
Zana alaƙar da ke tsakanin Ƙarfi (F) da ƙaruwa a tsawon bazara (Δx), inda F yake daidai da Δx. Kwatanta F da Δx yana dawwama.
An nuna rabon ƙarfi (F) zuwa ƙaruwar tsawon bazara (Δx) ta hanyar gangaren jadawali ɗaya (hoto na 2).
F / Δ x = k
F = k Δ x
k shine ma'aunin bazara ko kuma ma'aunin elasticity na bazara. Robert Hooke (1635 - 1703) ne ya fara lura da wannan dangantaka a shekara ta 1678, saboda haka aka san ta da dokar Hooke.
Idan ƙarfin da aka yi amfani da shi a maɓuɓɓugar ya wuce iyakar ƙarfin bazara, bayan an cire ƙarfin, tsawon lokacin bazara ba zai koma ga tsawonsa na asali ba. Dokar Hooke ta shafi iyakar ƙarfin bazara ne kawai. Iyakar ƙarfin bazara ita ce matsakaicin ƙarfin da za a iya bai wa maɓuɓɓugar kafin canjin bazara ya zama na dindindin, kuma tsawon lokacin bazara ba zai iya komawa ga tsawonsa na asali ba. Idan ƙarfin ya ci gaba da ƙaruwa, maɓuɓɓugar za ta lalace.
2. Dokar Hooke game da rashin bazara
Dokar Hooke kuma ta shafi dukkan abubuwa masu ƙarfi. Idan akan abu mai ƙarfi ne, ana ba da ƙarfin waje, to abu yana fuskantar canjin siffa. Muna tattauna canje-canje a siffar waɗannan abubuwa masu ƙarfi ta amfani da manufar damuwa da matsin lamba. Damuwa tana nuna ƙarfin ƙarfin da ke sa siffar abu ta canza. Yanayin matsin lamba yana canzawa a siffar abubuwa saboda damuwa. An gano cewa ga ƙaramin damuwa da matsin lamba, matsin lamba yana daidai da matsin lamba. Rabon damuwa da matsin lamba yana dawwama, inda ake kiran wannan daidaitaccen ma'auni na elasticity.
Damuwa / Matsi = modulus mai laushi
Wannan dangantaka ana kuma kiranta da dokar Hooke, tare da yanayi damuwa tana daidai da matsin lamba kuma rabon da ke tsakanin matsin lamba da matsin lamba yana dawwama. Idan ƙarfin da ke aiki akan abu ya wuce ƙarfin abubuwa, dokar Hooke ba ta aiki. Dokar Hooke ta shafi iyakokin sassaucin abu ne kawai.
Akwai nau'ikan modulus na roba guda uku, wato Young's modulus, shear modulus, da kuma bulk modulus.
2.1 Matakan Matasa
Idan aka ja ƙarshen kebul, waya, ko igiya da ƙarfi tare da girma iri ɗaya da kuma akasin haka, kebul, waya, ko igiya yana cikin yanayin tashin hankali. Misalan rayuwar yau da kullun da suka shafi wannan sun haɗa da igiyar da ke riƙe da masu hawa dutse, wayar da ke riƙe da lif, wayoyi, ko layin kaya ko kwantena akan tsarin lodawa da sauke kaya akan jiragen ruwa, da sauransu. Kebul ɗin tashin hankali, wayoyi, ko igiyoyi suna fuskantar matsin lamba saboda matsin lamba. Mun ayyana matsin lamba a matsayin rabo na ƙarfin tayar da hankali (F) zuwa yankin giciye na abu (A). Yayin da, matsin lamba ana ayyana shi azaman rabo na ƙaruwar tsayi (Δl) zuwa tsawon farko na abu (lo). Modulus na Young shine rabo na matsin lamba da matsin lamba.
Matsi mai ƙarfi / matsin lamba mai ƙarfi = Matakan Young
F/A : Δl/lo = Y
Idan matsin lamba na tensile ya yi ƙanƙanta, tsawon abin zai koma daidai bayan an cire ƙarfin. Idan matsin lamba na tensile ya wuce ƙarfin abin, tsawon abin ba zai koma daidai ba bayan an cire ƙarfin. Idan matsin lamba na tensile ya ci gaba da ƙaruwa, abin zai karye.
2.2 Tsarin Shear
Sanya littafi mai kauri a saman teburin. Sanya hannunka a saman littafin ka tura saman littafin gaba. Turawarka tana aiki a saman littafin da kuma alkiblarsa gaba, daidai da saman littafin. Ƙasan littafin yana nan a kwance ta hanyar gogayya mai tsauri a akasin alkiblar turawa. Da farko, siffar littafin murabba'i ne ko murabba'i, bayan an tura ta, siffar littafin ta koma parallelogram. Canje-canje a siffar littafin misali ne na faruwar matsi na yanke saboda kasancewar matsi na yankewa.
Ana bayyana matsin lamba na yankewa a matsayin rabon ƙarfi (F) zuwa yankin saman (A) da aka canza. Ana bayyana matsin lamba na yankewa a matsayin rabon Δx zuwa tsayin abu (h). Ana kiran rabon matsin lamba na yankewa da matsin lamba na yankewa.
Matsi/Matsalar yanke = Modulus ɗin yanke
F/A : Δx/h = Rage modulus
2.3 Babban Modulus
A cikin wani fim na gaskiya game da Yaƙin Duniya na Biyu, akwai wuraren yaƙi a cikin teku ta amfani da jiragen ruwa masu saukar ungulu. Domin suna son ɓoyewa daga jiragen ruwa na abokan gaba, jirgin ruwa na wata ƙasa ya yi zurfi ya nutse har ya kai kusan ƙasan teku. Abin mamaki, bangon jirgin ruwa ya fashe har ruwan teku ya shiga cikin jirgin ruwa. Bangon jirgin ruwa ya fashe saboda matsin lambar da ruwan teku ya yi a saman jirgin ruwa. Matsin ruwan teku ya yi daidai da zurfin ruwan teku. Da zurfin nutsewa, haka nan matsin lambar ruwan teku da yake fuskanta ya fi girma. Idan ginin bangon jirgin ruwa bai yi ƙarfi ba, bangon jirgin ruwa zai fashe.
Labarin wani jirgin ruwa mai ƙarƙashin ruwa da ya fashe sakamakon matsin ruwan teku a samansa gaba ɗaya misali ne na wani abu da ke fuskantar matsin lamba saboda matsin lamba. Ana bayyana matsin lamba a matsayin rabon jimlar ƙarfin (F) da ke aiki a kan saman abu gaba ɗaya zuwa yankin saman (A) na abu. Ana bayyana matsin lamba a matsayin rabon raguwar girma (-ΔV) zuwa girman farko (Vo) na abu. Ana kiran rabon matsin lamba na girma zuwa matsin lamba mai girma.
Matsi mai ƙarfi / matsin lamba = babban modulus
– ΔF/A : ΔV/V o = babban modulus
Abubuwa masu ƙarfi da ruwa suna da babban tsarin, amma abubuwa masu ƙarfi ne kawai ke da tsarin Young da tsarin shear.
