Isikhungo samandla adonsela phansi, noma isikhungo sobukhulu, umqondo oyisisekelo ku-physics nobunjiniyela osetshenziselwa ukunquma ibhalansi nokuzinza kwento. Isikhungo samandla adonsela phansi yindawo lapho isisindo sento sibhekwa khona njengokugxila kanye nalapho amandla adonsela phansi ethathwa khona. Ukuqonda lo mqondo kubalulekile ezinhlotsheni ezahlukene zokusebenza, kusukela ekwakhiweni kwesakhiwo kuya ekuhlaziyweni kokunyakaza kwento. Lesi sihloko sizoxoxa ngencazelo yesikhungo samandla adonsela phansi, indlela yokubala isikhungo samandla adonsela phansi ngezimo ezahlukene zento, kanye nezinkinga eziningana zezibonelo zokucacisa lo mqondo.
Incazelo Yesikhungo Sokudonsa Amandla
Isikhungo samandla adonsela phansi (isikhungo sobukhulu) yiphuzu entweni lapho isisindo sonke sento singabhekwa njengesigxilile ngenhloso yokubala amandla nezikhathi. Kuhlelo lwe-Cartesian coordinate, isikhungo samandla adonsela phansi sento enobukhulu obusatshalalisiwe singabalwa kusetshenziswa ifomula elandelayo:
\[
x_{\text{cm}} = \frac{\sum (x_i \cdot m_i)}{\sum m_i}
\]
\[
y_{\text{cm}} = \frac{\sum (y_i \cdot m_i)}{\sum m_i}
\]
\[
z_{\text{cm}} = \frac{\sum (z_i \cdot m_i)}{\sum m_i}
\]
Lapho \( (x_i, y_i, z_i) \) kuyizixhumanisi zesici esinzima \( m_i \).
Isikhungo Sokudonsa Amandla Sezinhlobo Ezihlukahlukene Zezinto
1. Isikhungo Sokudonsa Amandla Sezinto Ezifanayo
Ezintweni ezilinganayo (ezinobuningi obufanayo), isikhungo samandla adonsela phansi singanqunywa ngendlela elula. Isibonelo:
– Induku Encane: Isikhungo samandla adonsela phansi senduku encane, elinganayo enobude \(L \) sitholakala phakathi kwenduku, okungukuthi ku-\( x = \frac{L}{2} \).
– I-Slab Engunxande: Isikhungo sokudonsa phansi kwe-slab engunxande efanayo enobude \( L \) nobubanzi \( W \) sitholakala endaweni lapho kuhlangana khona ama-diagonal, okungukuthi ku-\( x = \frac{L}{2} \) kanye \( y = \frac{W}{2} \).
– Ipuleti Elingunxantathu: Isikhungo sokudonsa amandla sepuleti elingunxantathu elilinganayo sitholakala engxenyeni yesithathu yesilinganiso ngasinye sonxantathu. Kunxantathu onezixhumanisi ze-vertex \( A(x_1, y_1) \), \( B(x_2, y_2) \), kanye \( C(x_3, y_3) \):
\[
x_{\text{cm}} = \frac{x_1 + x_2 + x_3}{3}
\]
\[
y_{\text{cm}} = \frac{y_1 + y_2 + y_3}{3}
\]
2. Isikhungo Sokudonsa Amandla Sezinto Ezingafani
Ezintweni ezingalingani (ezinobuningi obungalingani), isikhungo samandla adonsela phansi kumele sibalwe ngokuhlukanisa into ibe yizinto ezincane ezinobunzima bese kubalwa isikhungo sazo samandla adonsela phansi kusetshenziswa ifomula ehlanganisiwe. Isibonelo, entweni enobukhulu obuhlukahlukene \( \rho(x, y, z) \):
\[
x_{\text{cm}} = \frac{\int x \cdot \rho(x, y, z) \, dV}{\int \rho(x, y, z) \, dV}
\]
\[
y_{\text{cm}} = \frac{\int y \cdot \rho(x, y, z) \, dV}{\int \rho(x, y, z) \, dV}
\]
\[
z_{\text{cm}} = \frac{\int z \cdot \rho(x, y, z) \, dV}{\int \rho(x, y, z) \, dV}
\]
Imibuzo Yesibonelo Sesikhungo Sokudonsa Amandla
Isibonelo Umbuzo 1: Isikhungo Sokudonsa Kwentonga Encane
Umbuzo:
Bala isikhungo sokudonsa phansi kwenduku encane, elinganayo enobude obungamamitha ayi-10.
Isixazululo:
Njengoba induku ifana, isikhungo samandla adonsela phansi siphakathi kwenduku:
\[
x_{\text{cm}} = \frac{L}{2} = \frac{10 \, \text{m}}{2} = 5 \, \text{m}
\]
Ngakho-ke, isikhungo samandla adonsela phansi senduku encane singamamitha ama-5 ukusuka kolunye uhlangothi lwenduku.
Isibonelo Umbuzo 2: Isikhungo Sokudonsa Kwepuleti Eliyisikwele
Umbuzo:
Bala isikhungo sokudonsa phansi kweslabhu engunxande efanayo enobude obungamamitha ayi-8 nobubanzi obungamamitha ama-4.
Isixazululo:
Isikhungo sokudonsa amandla sepuleti elingunxande elilinganayo sisekuhlanganeni kwezinhlangothi eziphambeneyo, okungukuthi:
\[
x_{\text{cm}} = \frac{L}{2} = \frac{8 \, \text{m}}{2} = 4 \, \text{m}
\]
\[
y_{\text{cm}} = \frac{W}{2} = \frac{4 \, \text{m}}{2} = 2 \, \text{m}
\]
Ngakho-ke, isikhungo sokudonsa phansi kwepuleti elingunxande (4 m, 2 m).
Isibonelo Umbuzo 3: Isikhungo Sokudonsa Kwepuleti Elingunxantathu
Umbuzo:
Bala isikhungo sokudonsa phansi kwepuleti elingunxantathu elilinganayo ngama-vertice kuma-coordinates \( A(0, 0) \), \( B(6, 0) \), kanye \( C(3, 6) \).
Isixazululo:
Isikhungo sokudonsa amandla sepuleti elingunxantathu elilinganayo singabalwa kusetshenziswa ifomula:
\[
x_{\text{cm}} = \frac{x_1 + x_2 + x_3}{3} = \frac{0 + 6 + 3}{3} = \frac{9}{3} = 3 \, \text{m}
\]
\[
y_{\text{cm}} = \frac{y_1 + y_2 + y_3}{3} = \frac{0 + 0 + 6}{3} = \frac{6}{3} = 2 \, \text{m}
\]
Ngakho-ke, isikhungo samandla adonsela phansi sepuleti elingunxantathu (3 m, 2 m).
Isibonelo Umbuzo 4: Isikhungo Sokudonsa Amandla Sesistimu Yezinhlayiyana
Umbuzo:
Uhlelo luqukethe izinhlayiya ezintathu ezinesisindo esifanayo esingu-2 kg ngasinye, ezitholakala kuma-coordinates \( (1, 2) \), \( (3, 4) \), kanye \( (5, 6) \). Bala isikhungo sokudonsa amandla kohlelo lwezinhlayiya.
Isixazululo:
Njengoba ubuningi bezinhlayiya bufana, singasebenzisa ifomula elula ukubala isikhungo samandla adonsela phansi:
\[
x_{\text{cm}} = \frac{\sum (x_i \cdot m_i)}{\sum m_i} = \frac{(1 + 3 + 5) \cdot 2}{3 \cdot 2} = \frac{9}{3} = 3 \, \text{m}
\]
\[
y_{\text{cm}} = \frac{\sum (y_i \cdot m_i)}{\sum m_i} = \frac{(2 + 4 + 6) \cdot 2}{3 \cdot 2} = \frac{12}{3} = 4 \, \text{m}
\]
Ngakho-ke, isikhungo samandla adonsela phansi sesistimu yezinhlayiya siyi (3 m, 4 m).
Isiphetho
Isikhungo samandla adonsela phansi siwumqondo obalulekile oyisisekelo ku-physics kanye nobunjiniyela. Ukuqonda ukuthi ungabala kanjani isikhungo samandla adonsela phansi ngezimo ezahlukene zezinto kanye nezinhlelo zezinhlayiya kubalulekile ekuhlaziyeni ukulingana nokuzinza. Lesi sihloko sixoxe ngencazelo yesikhungo samandla adonsela phansi, indlela yokubala isikhungo samandla adonsela phansi sezinto ezifanayo nezingafani, futhi sinikeze izibonelo eziningana zezinkinga ukusiza ukucacisa lo mqondo.
Empilweni yansuku zonke, ukuqonda isikhungo samandla adonsela phansi kuwusizo kakhulu ezindleleni ezahlukene zokusebenza, kusukela ekwakhiweni kwesakhiwo kuya ekuthuthukisweni kobuchwepheshe. Ngokuqonda nokusebenzisa umqondo wesikhungo samandla adonsela phansi, singaklama izakhiwo ezizinzile neziphephile futhi siqonde kangcono amandla okunyakaza kwezinto.
