Imibuzo Eyisibonelo Exoxa Ngokusetshenziswa Kwezinto Ezihlanganisiwe Ku-Physics
Ukusetshenziswa kwezinto ezihlanganisiwe ku-physics kuwumqondo obaluleke kakhulu futhi obanzi. Ukusetshenziswa kwezinto ezihlanganisiwe kuvumela ososayensi befiziksi nonjiniyela ukubala izinhlobonhlobo zezenzakalo zemvelo eziyinkimbinkimbi, kungakhathaliseki ukuthi zihlobene nokunyakaza, amandla, amandla, noma ezinye izici. Lesi sihloko sizohlola izibonelo eziningana zezinkinga futhi sixoxe ngokusetshenziswa kwezinto ezihlanganisiwe ku-physics.
1. Ukubala Umsebenzi Ngamandla Aguquguqukayo
I-Soal
Amandla ahlukahluka ngokwesikhundla \(x\) anikezwa ngu \( F(x) = 3x^2 \). Bala umsebenzi owenziwe yila mandla lapho into isuka ku-\(x = 0\) iye ku-\(x = 2 \) amamitha.
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Umsebenzi owenziwa amandla ashintshayo uwukuhlanganiswa kwamandla phezu kwebanga. Uma amandla \( F(x) \) njengomsebenzi wesikhundla \(x\) enikeziwe, singawuchaza umsebenzi kanje:
\[ W = \int_{a}^{b} F(x) \, dx \]
Esimweni esinjalo:
\[ F(x) = 3x^2 \]
\[ a = 0 \, \text{meter} \]
\[ b = 2 \, \text{meter} \]
Bese umsebenzi \(W\) uthi:
\[ W = \int_{0}^{2} 3x^2 \, dx \]
Sibala lokhu okubalulekile:
\[
W = 3 \int_{0}^{2} x^2 \, dx
= 3 \kwesobunxele[ \frac{x^3}{3} \kwesokudla]_{0}^{2}
= 3 \kwesobunxele( \frac{2^3}{3} – \frac{0^3}{3} \kwesokudla)
= 3 \kwesobunxele( \frac{8}{3} – 0 \kwesokudla)
= 8 \, \umbhalo{Joule}
\]
Ngakho-ke, umsebenzi owenziwe yibutho ungama-Joules ayi-8.
2. Ukubala Isikhungo Sesisindo Senduku Efanayo
I-Soal
Induku efanayo enobude \(L\) itholakala ku-x-axis kusukela ku-\( x = 0 \) kuya ku-\( x = L \). Bala indawo yesikhungo sobunzima benduku.
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Ngenduku efanayo, isisindo sisatshalaliswa ngokulinganayo ngobude bayo. Singacabanga ukuthi induku inesisindo esiqondile esingaguquki \(\lambda\) (isisindo ngobude beyunithi).
Isikhungo sesisindo (\(x_{cm}\)) sinikezwa ngu:
\[ x_{cm} = \frac{\int x \, dm}{\int dm} \]
Njengoba i-mass isatshalaliswa ngokulinganayo, singaveza i-\(dm = \lambda \, dx\), kanye ne-boundary integral kusukela ku-\(x = 0\) kuya ku-\(x = L\):
\[
x_{cm} = \frac{\int_{0}^{L} x \lambda \, dx}{\int_{0}^L \lambda \, dx}
\]
Ukuhlanganiswa phezu kwe-\(\lambda\) kuhlala njalo futhi kungasuswa:
\[
x_{cm} = \frac{\int_{0}^{L} x \, dx}{\int_{0}^{L} dx}
= \frac{\left[ \frac{x^2}{2} \right]_{0}^{L}}{ \left[ x \right]_{0}^{L} }
= \frac{\frac{L^2}{2} – 0}{L – 0}
= \frac{L^2 /2}{L}
= \frac{L}{2}
\]
Ngakho-ke, indawo ephakathi kwesisindo senduku iku-\( \frac{L}{2} \), noma phakathi kwenduku.
3. Ukubala Amandla E-Electrostatic Ngokusekelwe Emthethweni KaCoulomb
I-Soal
Amashaja amabili \(q_1\) kanye \(q_2\) atholakala eceleni kwe-x-axis ku-\(x = 0\) kanye \(x = L\) ngokulandelana. Bala amandla kagesi aphakathi kwamashaja amabili.
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Umthetho kaCoulomb uthi amandla aphakathi kwamacala amabili alingana ngqo nomkhiqizo wamacala futhi alingana ngokuphambene nesikwele sebanga eliphakathi kwawo:
\[ F = k_e \frac{|q_1 q_2|}{r^2} \]
Kuphi:
– \(k_e\) kuyinto engaguquki kaCoulomb \((8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2)\)
– \(r\) ibanga eliphakathi kwamacala
Kulesi simo, \(q_1\) kanye \(q_2\) zilele ku-\(x = 0\) kanye \(x = L\), bese kuba yibanga \(r = L\).
Amandla kagesi aqinile yilawa:
\[ F = k_e \frac{|q_1 q_2|}{L^2} \]
Lesi yisisombululo esivame ukusetshenziswa ekubaleni amandla kagesi phakathi kwamacala amabili abekwe ebangeni elithile.
4. Ukubala i-Magnetic Flux
I-Soal
Iluphu yentambo eyindilinga yerediyasi \(r\) ifakwa ensimini yamagnetic efanayo \(B\), eqonde ngqo endizeni yeluphu. Bala i-magnetic flux ngeluphu.
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I-magnetic flux (\(\Phi_B\)) edlula endaweni \(A\) ensimini yamagnetic \(B\) inikezwa yi:
\[ \Phi_B = \int B \cdot dA \]
Njengoba insimu kazibuthe \(B\) ifana futhi iqondile endizeni yeluphu, i-integral elula iba:
\[ \Phi_B = B \cdot A \]
Lapho indawo \(A\) yesiyingi esinerediyasi \(r\) ingu:
\[ A = \pi r^2 \]
Khona-ke i-magnetic flux edlula ku-loop yile:
\[ \Phi_B = B \cdot \pi r^2 \]
Ngakho-ke, i-magnetic flux edlula ku-loop ingu-\( B \pi r^2 \).
Isiphetho
Ukusetshenziswa kwezinto ezihlanganisiwe ku-physics akunakugwenywa uma kufanele sibale ulwazi oluhlobene nezimo zemvelo eziyinkimbinkimbi. Kusukela ekubaleni umsebenzi owenziwe amandla aguquguqukayo, ukunquma isikhungo sesisindo sento, ukubala amandla kagesi asekelwe emthethweni kaCoulomb, kuya ekubaleni ukuhamba kwamandla kagesi nge-loop yentambo ensimini yamagnetic, konke kuncike ezintweni ezihlanganisiwe ukuxazulula izinkinga. Ukuqonda okuphelele ukuthi izinto ezihlanganisiwe zisebenza kanjani ezimweni ezahlukene ze-physics akugcini nje ngokwenza lula ukuxazulula izinkinga kodwa futhi kunikeza ukuqonda okujulile mayelana nendlela esebenza ngayo indawo yonke ezingeni lama-molecule kanye nezinga le-galactic.
