Lipotso tsa Vektheri ea Fisiks bakeng sa Kereiti ea 11
Li-vector ke khopolo ea motheo fisiks e leng ea bohlokoa bakeng sa liithuti tsa sehlopha sa bo-11 ho e utloisisa. Li-vector li emela bongata eseng feela ka boholo empa hape le ka tataiso. Fisiks, bongata bo bongata bo hlahisoa e le li-vector, joalo ka lebelo, ho potlaka, matla le motsamao. Sengoloa sena se tla tšohla mehlala e 'maloa ea mathata a li-vector a atisang ho kopana le thuto ea fisiks ea sehlopha sa bo-11 le mokhoa oa ho a rarolla.
Ho Utloisisa Li-vector
Vekthara ke bongata bo nang le boholo le tataiso. Ho fapana le scalar, e nang le boholo feela, vekthara e fana ka tlhahisoleseling e eketsehileng mabapi le tataiso ea bongata. Mehlala ea li-vekthara fisiks e kenyelletsa:
– Lebelo: E hlalosa hore na ntho e tsamaya ka lebelo le lekae le hore na e lebile lehlakoreng lefe.
– Matla: E hlalosa boholo ba ho sututsa kapa ho hula le tsela eo matla a sebetsang ka yona.
– Ho potlaka: Ho hlalosa diphetoho lebelong le tataisong.
Hangata mongolo wa vektara o sebedisa ditlhaku tse nang le metsu ho tsona, jwalo ka \(\vec{A}\) kapa ditlhaku tse matla jwalo ka A.
Mesebetsi ea Motheo ea Vector
1. Ho Eketsa Vektara: Ho eketsa Vektara ho etswa ka ho eketsa dikarolo tsa yona. Haeba \(\vec{A} = (A_x, A_y)\) le \(\vec{B} = (B_x, B_y)\), jwale \(\vec{A} + \vec{B} = (A_x + B_x, A_y + B_y)\).
2. Ho Ntša Vektara: Ho ntša Vektara ho etsoa ka ho ntša likarolo tsa eona. Haeba \(\vec{A} = (A_x, A_y)\) le \(\vec{B} = (B_x, B_y)\), joale \(\vec{A} – \vec{B} = (A_x – B_x, A_y – B_y)\).
3. Katiso ea Scalar ka Vector: Katiso ena e hlahisa vector e ncha e nang le tataiso e tšoanang kapa e fapaneng le vector ea pele ho latela letšoao la scalar, empa ka boholo bo fetohileng. Haeba \(k\) e le scalar le \(\vec{A} = (A_x, A_y)\), joale \(k\vec{A} = (kA_x, kA_y)\).
4. Boholo ba Vektara: Boholo (kapa boholo) ba vektara \(\vec{A} = (A_x, A_y)\) bo ka balwa ho sebediswa foromo: \( |\vec{A}| = \sqrt{A_x^2 + A_y^2} \).
Lipotso le litharollo tsa mehlala
Mona ke mehlala e meng ea mathata a vector le litharollo tsa ona tseo hangata li kopanang le tsona lithutong tsa fisiks tsa sehlopha sa bo11.
Mohlala oa Potso ea 1: Ho eketsa vektara
Potso: Livekthara tse peli \(\vec{A}\) le \(\vec{B}\) e 'ngoe le e 'ngoe e na le likarolo \(\vec{A} = (3, 4)\) le \(\vec{B} = (1, 2)\). Bala kakaretso \(\vec{A} + \vec{B}\).
Tharollo:
\[ \vec{A} + \vec{B} = (A_x + B_x, A_y + B_y) \]
\[ \vec{A} + \vec{B} = (3 + 1, 4 + 2) \]
\[ \vec{A} + \vec{B} = (4, 6) \]
Kahoo, sephetho sa tlatsetso ea vector \(\vec{A} + \vec{B}\) ke \((4, 6)\).
Mohlala oa Potso ea 2: Ho Ntša Vector
Potso: Ha ho fanoe ka divekthara \(\vec{C} = (5, 7)\) le \(\vec{D} = (2, 3)\). Bala sephetho sa ho ntsha \(\vec{C} – \vec{D}\).
Tharollo:
\[ \vec{C} – \vec{D} = (C_x – D_x, C_y – D_y) \]
\[ \vec{C} – \vec{D} = (5 – 2, 7 – 3) \]
\[ \vec{C} – \vec{D} = (3, 4) \]
Kahoo, sephetho sa ho tlosa vekthara \(\vec{C} – \vec{D}\) ke \((3, 4)\).
Mohlala oa 3: Katiso ea Scalar ka Li-vector
Potso: Haeba vekthara \(\vec{E} = (6, 8)\) le scalar \(k = 3\), bala sehlahisoa sa scalar \(k\vec{E}\).
Tharollo:
\[ k\vec{E} = k (E_x, E_y) \]
\[ k\vec{E} = 3 (6, 8) \]
\[ k\vec{E} = (18, 24) \]
Kahoo, sephetho sa sehlahisoa sa scalar \(3\vec{E}\) ke \((18, 24)\).
Mohlala oa Potso ea 4: Boholo ba Vektara
Potso: Bala boholo ba vekthara \(\vec{F} = (9, 12)\).
Tharollo:
\[ |\vec{F}| = \sqrt{F_x^2 + F_y^2} \]
\[ |\vec{F}| = \sqrt{9^2 + 12^2} \]
\[ |\vec{F}| = \sqrt{81 + 144} \]
\[ |\vec{F}| = \sqrt{225} \]
\[ |\vec{F}| = 15 \]
Kahoo, boholo ba vekthara \(\vec{F}\) ke 15.
Mohlala oa Potso ea 5: Vekthara ea Liphetho
Potso: Livekthara tse peli \(\vec{G}\) le \(\vec{H}\) li na le likarolo \(\vec{G} = (7, 24)\) le \(\vec{H} = (-4, 3)\). Bala vekthara e hlahang ho tsoa ho kenyelletsong ea livekthara tse peli le boholo ba eona.
Tharollo:
Ho eketsa vektara:
\[ \vec{G} + \vec{H} = (G_x + H_x, G_y + H_y) \]
\[ \vec{G} + \vec{H} = (7 + (-4), 24 + 3) \]
\[ \vec{G} + \vec{H} = (3, 27) \]
Boholo ba vekthara e hlahang:
\[ |\vec{G} + \vec{H}| = \sqrt{(G_x + H_x)^2 + (G_y + H_y)^2} \]
\[ |\vec{G} + \vec{H}| = \ sqrt{3^2 + 27^2} \]
\[ |\vec{G} + \vec{H}| = \ sqrt{9 + 729} \]
\[ |\vec{G} + \vec{H}| = \ sqrt{738} \]
\[ |\vec{G} + \vec{H}| \hoo e ka bang 27.15 \]
Kahoo, vekthara e hlahang ea kakaretso ea \(\vec{G}\) le \(\vec{H}\) ke \((3, 27)\) ka boholo ba hoo e ka bang 27.15.
Litšebeliso tsa Li-vector ho Fisiks
Ho utloisisa li-vector ho bohlokoa hobane liketsahalo tse ngata tsa 'mele lia li ama. Mehlala e meng ea lits'ebetso tsa li-vector fisiks e kenyelletsa:
1. Matla le Motsamao: Tlhahlobong ea matla, li-vector li sebelisoa ho fumana tataiso le boholo ba matla a sebetsang nthong.
2. Masimo a Motlakase le a Makenete: Masimo a motlakase le a makenete ke bongata ba bohlokoa ba vector thutong ea electromagnetism.
3. Lebelo le Potlakiso: Lebelo le potlakiso ke li-vector tse sebelisoang ho kinematics ho hlalosa motsamao oa ntho.
4. Momentum: Momentum ke vekthara e hlalosang sehlahisoa sa boima le lebelo la ntho.
Qetello
Ho utloisisa mohopolo oa li-vector le mokhoa oa ho li sebelisa lipalo ke bokhoni ba motheo boo baithuti ba fisiks ba lokelang ho ba le bona. Mehlala ea mathata a kaholimo e bontša kamoo ts'ebetso ea motheo ea li-vector e sebelisoang kateng mathateng a fapaneng a fisiks. Ho itloaetsa ho rarolla mathata a li-vector ka mokhoa o tsitsitseng ho tla thusa ho matlafatsa kutloisiso le bokhoni ba baithuti tlhahlobong ea li-vector, e leng motheo oa bohlokoa bakeng sa lithuto tse tsoetseng pele tsa fisiks.
