Pakati pa mphamvu yokoka, kapena pakati pa kulemera, ndi lingaliro lofunikira mu fizikisi ndi uinjiniya lomwe limagwiritsidwa ntchito kudziwa kukhazikika ndi kukhazikika kwa chinthu. Pakati pa mphamvu yokoka ndi pomwe kulemera kwa chinthu kumaonedwa kuti ndi kokhazikika komanso komwe mphamvu yokoka imaganiziridwa kuti imagwira ntchito. Kumvetsetsa lingaliro ili ndikofunikira pa ntchito zosiyanasiyana, kuyambira kapangidwe ka nyumba mpaka kusanthula kayendedwe ka chinthu. Nkhaniyi ikambirana tanthauzo la pakati pa mphamvu yokoka, momwe mungawerengere pakati pa mphamvu yokoka ya mawonekedwe osiyanasiyana a chinthu, ndi zitsanzo zingapo zamavuto kuti tifotokoze bwino lingaliro ili.
Tanthauzo la Pakati pa Mphamvu Yokoka
Pakati pa mphamvu yokoka (pakati pa kulemera) ndi mfundo yomwe ili mu chinthu chomwe kulemera konse kwa chinthucho kungaganizidwe kuti kuwerengedwe mphamvu ndi mphindi. Mu dongosolo la Cartesian coordinate, pakati pa mphamvu yokoka ya chinthu chomwe chili ndi kulemera kogawidwa chingawerengedwe pogwiritsa ntchito njira iyi:
\[
x_{\text{cm}} = \frac{\sum (x_i \cdot m_i)}{\sum m_i}
\]
\[
y_{\text{cm}} = \frac{\sum (y_i \cdot m_i)}{\sum m_i}
\]
\[
z_{\text{cm}} = \frac{\sum (z_i \cdot m_i)}{\sum m_i}
\]
Kumene \( (x_i, y_i, z_i) \) ndi ma coordinates a chinthu chachikulu \( m_i \).
Malo Okoka Mphamvu a Mitundu Yosiyanasiyana ya Zinthu
1. Malo Okokera Zinthu Zofanana
Pa zinthu zofanana (zokhala ndi kuchuluka kofanana), pakati pa mphamvu yokoka pakhoza kudziwika m'njira yosavuta. Mwachitsanzo:
– Ndodo Yopyapyala: Pakati pa mphamvu yokoka ya ndodo yopyapyala, yofanana ndi kutalika \( L \) ili pakati pa ndodo, yomwe ndi \( x = \frac{L}{2} \).
– Chidutswa cha Rectangular: Pakati pa mphamvu yokoka ya chidutswa cha rectangular chofanana chokhala ndi kutalika \( L \) ndi m'lifupi \( W \) chili pamalo olumikizirana ma diagonal, omwe ndi pa \( x = \frac{L}{2} \) ndi \( y = \frac{W}{2} \).
– Mbale Yachitatu: Pakati pa mphamvu yokoka ya mbale yachitatu yofanana ili pa gawo limodzi mwa magawo atatu a pakati pa katatu. Pa katatu yokhala ndi ma vertex coordinates \( A(x_1, y_1) \), \( B(x_2, y_2) \), ndi \( C(x_3, y_3) \):
\[
x_{\text{cm}} = \frac{x_1 + x_2 + x_3}{3}
\]
\[
y_{\text{cm}} = \frac{y_1 + y_2 + y_3}{3}
\]
2. Malo Okokera Zinthu Zosakhala Zofanana
Pa zinthu zosafanana (zopanda kuchuluka kofanana), pakati pa mphamvu yokoka payenera kuwerengedwa pogawa chinthucho m'zinthu zazing'ono ndikuwerengera pakati pa mphamvu yokoka pogwiritsa ntchito njira yolumikizirana. Mwachitsanzo, pa chinthu chokhala ndi kuchuluka kosiyanasiyana \( \rho(x, y, z) \):
\[
x_{\text{cm}} = \frac{\int x \cdot \rho(x, y, z) \, dV}{\int \rho(x, y, z) \, dV}
\]
\[
y_{\text{cm}} = \frac{\int y \cdot \rho(x, y, z) \, dV}{\int \rho(x, y, z) \, dV}
\]
\[
z_{\text{cm}} = \frac{\int z \cdot \rho(x, y, z) \, dV}{\int \rho(x, y, z) \, dV}
\]
Mafunso a Chitsanzo cha Pakati pa Mphamvu Yokoka
Chitsanzo Funso 1: Pakati pa Mphamvu ya Ndodo Yoonda
Funso:
Werengerani pakati pa mphamvu yokoka ya ndodo yopyapyala, yofanana yokhala ndi kutalika kwa mamita 10.
Yankho:
Popeza ndodoyo ndi yofanana, pakati pa mphamvu yokoka pali pakati pa ndodoyo:
\[
x_{\text{cm}} = \frac{L}{2} = \frac{10 \, \text{m}}{2} = 5 \, \text{m}
\]
Kotero, pakati pa mphamvu yokoka ya ndodo yopyapyala ili mamita 5 kuchokera kumapeto kwa ndodo.
Chitsanzo Funso 2: Pakati pa Mphamvu ya Mbale Yozungulira
Funso:
Werengerani pakati pa mphamvu yokoka ya slab yofanana yamakona anayi yokhala ndi kutalika kwa mamita 8 ndi m'lifupi mwa mamita 4.
Yankho:
Pakatikati pa mphamvu yokoka ya mbale yozungulira yofanana ili pamalo olumikizirana a diagonals, omwe ndi:
\[
x_{\text{cm}} = \frac{L}{2} = \frac{8 \, \text{m}}{2} = 4 \, \text{m}
\]
\[
y_{\text{cm}} = \frac{W}{2} = \frac{4 \, \text{m}}{2} = 2 \, \text{m}
\]
Kotero, pakati pa mphamvu yokoka ya mbale yozungulira ndi (4 m, 2 m).
Chitsanzo Funso 3: Pakati pa Mphamvu ya Mbale Yachitatu
Funso:
Werengerani pakati pa mphamvu yokoka ya mbale ya triangular yofanana ndi ma vertices pa ma coordinates \( A(0, 0) \), \( B(6, 0) \), ndi \( C(3, 6) \).
Yankho:
Pakati pa mphamvu yokoka ya mbale ya triangular yofanana ikhoza kuwerengedwa pogwiritsa ntchito njira iyi:
\[
x_{\text{cm}} = \frac{x_1 + x_2 + x_3}{3} = \frac{0 + 6 + 3}{3} = \frac{9}{3} = 3 \, \text{m}
\]
\[
y_{\text{cm}} = \frac{y_1 + y_2 + y_3}{3} = \frac{0 + 0 + 6}{3} = \frac{6}{3} = 2 \, \text{m}
\]
Kotero, pakati pa mphamvu yokoka ya mbale ya triangular ndi (3 m, 2 m).
Chitsanzo Funso 4: Pakati pa Mphamvu ya Tinthu Tating'onoting'ono
Funso:
Dongosolo limapangidwa ndi tinthu tating'onoting'ono titatu tomwe tili ndi kulemera kofanana kwa 2 kg iliyonse, yomwe ili pa ma coordinates \( (1, 2) \), \( (3, 4) \), ndi \( (5, 6) \). Werengani pakati pa mphamvu yokoka ya dongosolo la tinthu tating'onoting'ono.
Yankho:
Popeza unyinji wa tinthu tating'onoting'ono ndi wofanana, tingagwiritse ntchito njira yosavuta yowerengera pakati pa mphamvu yokoka:
\[
x_{\text{cm}} = \frac{\sum (x_i \cdot m_i)}{\sum m_i} = \frac{(1 + 3 + 5) \cdot 2}{3 \cdot 2} = \frac{9}{3} = 3 \, \text{m}
\]
\[
y_{\text{cm}} = \frac{\sum (y_i \cdot m_i)}{\sum m_i} = \frac{(2 + 4 + 6) \cdot 2}{3 \cdot 2} = \frac{12}{3} = 4 \, \text{m}
\]
Kotero, pakati pa mphamvu yokoka ya dongosolo la tinthu ndi (3 m, 4 m).
Mapeto
Pakati pa mphamvu yokoka ndi mfundo yofunika kwambiri mu sayansi ya zakuthambo ndi uinjiniya. Kumvetsetsa momwe mungawerengere pakati pa mphamvu yokoka ya mawonekedwe osiyanasiyana a zinthu ndi tinthu tating'onoting'ono ndikofunikira kwambiri pofufuza kufanana ndi kukhazikika. Nkhaniyi yafotokoza tanthauzo la pakati pa mphamvu yokoka, momwe mungawerengere pakati pa mphamvu yokoka ya zinthu zofanana komanso zosafanana, ndipo yapereka zitsanzo zingapo za mavuto kuti zithandize kumvetsetsa lingaliro ili.
M'moyo watsiku ndi tsiku, kumvetsetsa pakati pa mphamvu yokoka n'kothandiza kwambiri pa ntchito zosiyanasiyana, kuyambira pakupanga nyumba mpaka kupanga ukadaulo. Mwa kumvetsetsa ndikugwiritsa ntchito lingaliro la pakati pa mphamvu yokoka, titha kupanga nyumba zokhazikika komanso zotetezeka komanso kumvetsetsa bwino kayendedwe ka zinthu.
