Mafunso ndi Zitsanzo za Kukambirana za Chisankho cha Newton
Pendauluan
Kuyenda kwa ubale ndi lingaliro lofunika kwambiri mu fizikisi lomwe limafotokoza momwe liwiro ndi malo a chinthu zingasinthire kutengera wowonera. Sir Isaac Newton, ndi malamulo ake a kuyenda ndi mphamvu yokoka, adakhazikitsa maziko omvetsetsa kayendedwe ka ubale. Nkhaniyi ifotokoza zitsanzo zingapo ndi zokambirana za kuyenda kwa ubale kwa Newton. Tifotokoza mavutowa mwatsatanetsatane ndi njira zothetsera mavuto kuti timvetsetse mosavuta.
Lingaliro Loyamba la Newton la Kuyenda Kogwirizana
Mu fizikisi ya Newtonian, kuyenda kwa chinthu nthawi zonse kumayesedwa poyerekeza ndi chimango chofotokozera. Ngati tili ndi mafelemu awiri ofotokozera omwe akuyenda moyandikana wina ndi mnzake pa liwiro la v, ndiye kuti malo ndi liwiro la chinthu zitha kuwoneka mosiyana m'mafelemu awiriwa. Malingaliro ena oti mumvetse ndi awa:
1. Chiyerekezo cha Inertial: Chiyerekezo cha chinthu chomwe chimayenda pa liwiro losasintha ngati palibe mphamvu yomwe ikugwira ntchito pa chinthucho.
2. Liwiro Loyerekeza: Liwiro la chinthu choyesedwa poyerekeza ndi mawonekedwe ena.
3. Kusamuka Kogwirizana: Kusiyana kwa malo pakati pa zinthu ziwiri kapena chinthu chimodzi chokhala ndi mafelemu awiri osiyana a zizindikiro.
Newton anafotokoza bwino kwambiri za kayendedwe ka zinthu kudzera mu malamulo ake oyendetsera zinthu, ndipo tingagwiritse ntchito kusintha kwa zinthu ku Galileya kuti tisinthe pakati pa mafelemu awiri osagwiritsa ntchito mphamvu.
Zitsanzo za Mafunso Okambirana
Funso 1: Kusamuka kwa Chibale
Funso:
Zombo ziwiri, Sitima A ndi Sitima B, zili m'nyanja yayikulu. Sitima A ikuyenda kum'mawa pa liwiro la 20 m/s, pomwe Sitima B ikuyenda kumpoto pa liwiro la 30 m/s. Werengani liwiro la Sitima B poyerekeza ndi Sitima A.
Kukambirana:
Kuti tithetse vutoli, timagwiritsa ntchito lingaliro la liwiro loyerekeza. Liwiro loyerekeza la Ship B poyerekeza ndi Ship A likhoza kuwerengedwa pogwiritsa ntchito njira ya vector.
1. Kuyimira liwiro la Ship A (\(\vec{v_A}\)) ndi Ship B (\(\vec{v_B}\)) ngati mavekitala.
\[
\vec{v_A} = 20 \, \text{m/s kum'mawa} \amatanthauza \vec{v_A} = 20 \hat{i} \, \text{m/s}
\]
\[
\vec{v_B} = 30 \, \text{m/s kumpoto} \amatanthauza \vec{v_B} = 30 \hat{j} \, \text{m/s}
\]
2. Liwiro la Ship B kupita ku Ship A (\(\vec{v_{BA}}\)) limawerengedwa ndi:
\[
\vec{v_{BA}} = \vec{v_B} - \vec{v_A}
\]
M'malo mwa ma values a \(\vec{v_A}\) ndi \(\vec{v_B}\):
\[
\vec{v_{BA}} = 30 \hat{j} \, \text{m/s} – 20 \hat{i} \, \text{m/s}
\]
\[
\vec{v_{BA}} = -20 \hat{i} + 30 \hat{j} \, \text{m/s}
\]
3. Kuti mupeze kukula kwa liwiro loyerekeza, gwiritsani ntchito chiphunzitso cha Pythagorean:
\[
|\vec{v_{BA}}| = \sqrt{(-20)^2 + (30)^2}
\]
\[
|\vec{v_{BA}}| = \sqrt{400 + 900}
\]
\[
|\vec{v_{BA}}| = \sqrt{1300} = 10 \sqrt{13} \, \text{m/s}
\]
Kotero, liwiro la Ship B poyerekeza ndi Ship A ndi \(10 \sqrt{13}\) m/s.
Funso 2: Kuyenda Kogwirizana mu Dongosolo Logwirizanitsa
Funso:
Munthu woyenda pansi akuyenda kumpoto pa liwiro la 5 m/s kuposa sitima yoyenda kum'mawa pa liwiro la 20 m/s. Dziwani liwiro la munthu woyenda pansi poyerekeza ndi nthaka.
Kukambirana:
Kuti tidziwe liwiro la woyenda pansi poyerekeza ndi nthaka, timagwiritsanso ntchito lingaliro la kuwonjezera vekitala.
1. Imani liwiro la munthu woyenda pansi (\(\vec{v_P}\)) ndi liwiro la sitima (\(\vec{v_K}\)) ngati mavekitala.
\[
\vec{v_P} \text{ relative to the train} = 5 \hat{j} \, \text{m/s}
\]
\[
\vec{v_K} \text{ relative to the ground} = 20 \hat{i} \, \text{m/s}
\]
2. Liwiro la munthu woyenda pansi poyerekeza ndi nthaka (\(\vec{v_{PT}}\)) ndi chiwerengero cha vekitala:
\[
\vec{v_{PT}} = \vec{v_P} + \vec{v_K}
\]
M'malo mwa ma values a \(\vec{v_P}\) ndi \(\vec{v_K}\):
\[
\vec{v_{PT}} = 5 \hat{j} \, \text{m/s} + 20 \hat{i} \, \text{m/s}
\]
3. Kuti mupeze kukula kwa liwiro loyerekeza:
\[
|\vec{v_{PT}}| = \sqrt{(20)^2 + (5)^2}
\]
\[
|\vec{v_{PT}}| = \sqrt{400 + 25}
\]
\[
|\vec{v_{PT}}| = \sqrt{425} = 5 \sqrt{17} \, \text{m/s}
\]
Motero, liwiro la woyenda pansi poyerekeza ndi pansi ndi \(5 \sqrt{17}\) m/s.
Funso 3: Kuyenda Kofanana pa Ndege Yopendekeka
Funso:
Mpira umaponyedwa ndi liwiro la \( \vec{u} = 10 \hat{i} + 10 \hat{j} \) m/s poyerekeza ndi ngolo yomwe ikuyenda pa liwiro losasintha la 15 m/s. Dziwani liwiro la mpirawo poyerekeza ndi pansi.
Kukambirana:
Gwiritsani ntchito mfundo yomweyi powonjezera ma vector.
1. Fotokozani liwiro la mpira (\(\vec{u}\)) poyerekeza ndi ngolo ndi liwiro la ngolo (\(\vec{v_K}\)) ngati mavekitala.
\[
\vec{u} = 10 \hat{i} + 10 \hat{j} \, \text{m/s}
\]
\[
\vec{v_K} = 15 \hat{i} \, \text{m/s}
\]
2. Liwiro la mpira poyerekeza ndi pansi (\(\vec{v_{BT}}\)) ndi:
\[
\vec{v_{BT}} = \vec{v_K} + \vec{u}
\]
\[
\vec{v_{BT}} = 15 \hat{i} + (10 \hat{i} + 10 \hat{j})
\]
\[
\vec{v_{BT}} = (15 + 10) \hat{i} + 10 \hat{j}
\]
\[
\vec{v_{BT}} = 25 \hat{i} + 10 \hat{j}
\]
3. Kuti mupeze kukula kwa liwiro loyerekeza:
\[
|\vec{v_{BT}}| = \sqrt{(25)^2 + (10)^2}
\]
\[
|\vec{v_{BT}}| = \sqrt{625 + 100}
\]
\[
|\vec{v_{BT}}| = \sqrt{725} = 5 \sqrt{29} \, \text{m/s}
\]
Kotero, liwiro la mpira poyerekeza ndi pansi ndi \(5 \sqrt{29}\) m/s.
Mapeto
Lingaliro la Newton la kuyenda kwachibale ndi maziko ofunikira a fizikisi yakale. Pogwiritsa ntchito mfundo zazikulu monga kuwonjezera ma vector, titha kudziwa liwiro ndi kusamuka kwa chinthu chimodzi poyerekeza ndi china kapena mafelemu osiyanasiyana ofotokozera. Zitsanzo zomwe zili pamwambapa zikuwonetsa momwe mungagwiritsire ntchito lingaliro ili m'malo osiyanasiyana, zomwe zimatithandiza kumvetsetsa bwino kuyenda kwachibale.
Mwa kumvetsetsa ndi kuchita izi, titha kumvetsetsa bwino malamulo a Newton oyendetsera zinthu komanso momwe amagwirira ntchito m'dziko lenileni. Chidziwitsochi sichimangothandiza kuthetsa mavuto a sayansi ya zakuthambo komanso chimapereka chidziwitso chakuya cha momwe chilengedwe chimagwirira ntchito.
