tiga buah vektor masing masing adalah F1 = 8 N, F2 = 4√3 N dan F3 = 4 N, Tentukan resultan ketiga

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tiga buah vektor masing masing adalah F1 = 8 N, F2 = 4√3 N dan F3 = 4 N, Tentukan resultan ketiga vektor

Perhitungan Resultan Vektor Komponen vektor pada sumbu-x dan sumbu-y dihitung. Komponen F 1 cap F sub 1 F 1 pada sumbu-x adalah F 1 x = F 1 cos ( 0 ∘ ) = 8 N ⋅ 1 = 8 N cap F sub 1 x end-sub equals cap F sub 1 cosine open paren 0 raised to the exponent composed with end-exponent close paren equals 8 N center dot 1 equals 8 N F 1 x = F 1 c o s ( 0 ∘ ) = 8 N ⋅ 1 = 8 N . Komponen F 1 cap F sub 1 F 1 pada sumbu-y adalah F 1 y = F 1 sin ( 0 ∘ ) = 8 N ⋅ 0 = 0 N cap F sub 1 y end-sub equals cap F sub 1 sine open paren 0 raised to the exponent composed with end-exponent close paren equals 8 N center dot 0 equals 0 N F 1 y = F 1 s i n ( 0 ∘ ) = 8 N ⋅ 0 = 0 N . Komponen F 2 cap F sub 2 F 2 pada sumbu-x adalah F 2 x = F 2 cos ( 60 ∘ ) = 4 3 N ⋅ 1 2 = 2 3 N cap F sub 2 x end-sub equals cap F sub 2 cosine open paren 60 raised to the exponent composed with end-exponent close paren equals 4 the square root of 3 end-root N center dot 1 over 2 end-fraction equals 2 the square root of 3 end-root N F 2 x = F 2 c o s ( 6 0 ∘ ) = 4 3 √ N ⋅ 1 2 = 2 3 √ N . Komponen F 2 cap F sub 2 F 2 pada sumbu-y adalah F 2 y = F 2 sin ( 60 ∘ ) = 4 3 N ⋅ 1 2 3 = 6 N cap F sub 2 y end-sub equals cap F sub 2 sine open paren 60 raised to the exponent composed with end-exponent close paren equals 4 the square root of 3 end-root N center dot 1 over 2 end-fraction the square root of 3 end-root equals 6 N F 2 y = F 2 s i n ( 6 0 ∘ ) = 4 3 √ N ⋅ 1 2 3 √ = 6 N . Komponen F 3 cap F sub 3 F 3 pada sumbu-x adalah F 3 x = F 3 cos ( 240 ∘ ) = 4 N ⋅ ( − 1 2 ) = -2 N cap F sub 3 x end-sub equals cap F sub 3 cosine open paren 240 raised to the exponent composed with end-exponent close paren equals 4 N center dot open paren negative 1 over 2 end-fraction close paren equals negative 2 N F 3 x = F 3 c o s ( 2 4 0 ∘ ) = 4 N ⋅ ( − 1 2 ) = − 2 N . Komponen F 3 cap F sub 3 F 3 pada sumbu-y adalah F 3 y = F 3 sin ( 240 ∘ ) = 4 N ⋅ ( − 1 2 3 ) = -2 3 N cap F sub 3 y end-sub equals cap F sub 3 sine open paren 240 raised to the exponent composed with end-exponent close paren equals 4 N center dot open paren negative 1 over 2 end-fraction the square root of 3 end-root close paren equals negative 2 the square root of 3 end-root N F 3 y = F 3 s i n ( 2 4 0 ∘ ) = 4 N ⋅ ( − 1 2 3 √ ) = − 2 3 √ N . Jumlah komponen vektor pada sumbu-x dan sumbu-y dihitung. Jumlah komponen pada sumbu-x adalah ∑ F x = F 1 x + F 2 x + F 3 x = 8 N + 2 3 N − 2 N = ( 6 + 2 3 ) N sum cap F sub x equals cap F sub 1 x end-sub plus cap F sub 2 x end-sub plus cap F sub 3 x end-sub equals 8 N plus 2 the square root of 3 end-root N minus 2 N equals open paren 6 plus 2 the square root of 3 end-root close paren N F x = F 1 x + F 2 x + F 3 x = 8 N + 2 3 √ N − 2 N = ( 6 + 2 3 √ ) N . Jumlah komponen pada sumbu-y adalah ∑ F y = F 1 y + F 2 y + F 3 y = 0 N + 6 N − 2 3 N = ( 6 − 2 3 ) N sum cap F sub y equals cap F sub 1 y end-sub plus cap F sub 2 y end-sub plus cap F sub 3 y end-sub equals 0 N plus 6 N minus 2 the square root of 3 end-root N equals open paren 6 minus 2 the square root of 3 end-root close paren N F y = F 1 y + F 2 y + F 3 y = 0 N + 6 N − 2 3 √ N = ( 6 − 2 3 √ ) N . Resultan vektor dihitung menggunakan rumus Pythagoras. Resultan vektor adalah R = ( ∑ F x ) 2 + ( ∑ F y ) 2 cap R equals the square root of open paren sum cap F sub x close paren squared plus open paren sum cap F sub y close paren squared end-root R = ( F x ) 2 + ( F y ) 2 . R = ( 6 + 2 3 ) 2 + ( 6 − 2 3 ) 2 cap R equals the square root of open paren 6 plus 2 the square root of 3 end-root close paren squared plus open paren 6 minus 2 the square root of 3 end-root close paren squared end-root R = ( 6 + 2 3 √ ) 2 + ( 6 − 2 3 √ ) 2 . R = ( 36 + 24 3 + 12 ) + ( 36 − 24 3 + 12 ) cap R equals the square root of open paren 36 plus 24 the square root of 3 end-root plus 12 close paren plus open paren 36 minus 24 the square root of 3 end-root plus 12 close paren end-root R = ( 3 6 + 2 4 3 √ + 1 2 ) + ( 3 6 − 2 4 3 √ + 1 2 ) . R = 48 + 24 3 + 48 − 24 3 cap R equals the square root of 48 plus 24 the square root of 3 end-root plus 48 minus 24 the square root of 3 end-root end-root R = 4 8 + 2 4 3 √ + 4 8 − 2 4 3 √ . R = 96 cap R equals the square root of 96 end-root R = 9 6 √ . R = 16 ⋅ 6 = 4 6 N cap R equals the square root of 16 center dot 6 end-root equals 4 the square root of 6 end-root N R = 1 6 ⋅ 6 √ = 4 6 √ N . Jawaban Akhir Resultan ketiga vektor adalah 4 6 N 4 the square root of 6 end-root N 4 6 √ N . Link Terkait