He tuhinga mō te Tāpiri i ngā Wetere
1. Ngā rahinga o te whārite me te tauine
Haunga ngā rahinga taketake me ngā rahinga i ahu mai, ka taea tonu te wehewehe i ngā rahinga ā-tinana ki ētahi atu momo e rua, arā, ngā rahinga tauine me ngā rahinga whārite. Ko ngā rahinga pēnei i te papatipu, te tawhiti, te wā me te rōrahi, he rahinga tauine, he rahinga he rahi anake engari kāore he ahunga. Ko ngā rahinga pēnei i te nekehanga, te tere, te whakateretere, me te kaha he rahinga whārite, he rahinga he rahi, he ahunga anō hoki.
a. Te rerekētanga i waenga i te rahinga karara me te rahinga wetere
Ki te mea koe ko te taumaha o te pōro he 400 karamu, he nui tēnei kōrero hei mōhio māu ki te taumaha o te pōro. Kāore koe e hiahia ki te ahunga hei kimi i te taumaha o te pōro. Waihoki, ki te wā, ki te pāmahana, ki te rōrahi, ki te mātotoru, me ētahi atu. He maha ngā rahinga ā-tinana kāore e taea te whakaatu mā te rahi anake. Ki te mea koe he tamaiti e neke ana tae atu ki te 100 mita, kāore tēnei kōrero i te nui. Tērā pea ka pātai koe, i hea ia i neke ai? Kei te raki, kei te tonga, kei te rawhiti, kei te hauauru rānei? Waihoki, ki te mea koe ka pana koe i te tēpu me te kaha o te 200 N.
Kei hea koe e taraiwa ana? Āe, ko ēnei rahinga ka kiia he rahinga whārite, e hiahia ana kia whakamāramahia te rahi me te ahunga. Ko ngā tauira o ngā rahinga whārite ko te nekehanga, te whakaterenga, te iri, te nekehanga , me ētahi atu. Ka taea e koe te mārama ake i a koe e ako ana i ngā kaupapa e pā ana ki aua rahinga.
b. Tuhia he whārite
Ka tohua te pere ki te pere. Ka tuhia te pere kia tohu ki te ahunga o te pere. Ka whakaahuahia te roa o te pere hei te rahi o te pere. Hei tauira, i roto i te ahua o te pere o te kaha (F) me te rahi o te 2 N e anga ana te ahunga ki te raki-mā-rāwhiti, ki te 45° rānei i te tuaka-x.
c. Ngā ture mō te tuhi i ngā rahinga o te wetere
I te tuhi i tētahi whārite, ki te whakamahi koe i te tuhituhi ā-ringa, ko te tohu o tētahi whārite ka tuhia whakatītaha mā te whakamahi i ngā reta matua, ā, i runga ake me tāpiri he pere. Mō ngā pukapuka tā, ka tuhia ngā tohu whārite ki ngā reta matua me te momotuhi matotoru, hei tauira, F. Mō te rahi o te whārite, ki te whakamahi tātou i te tuhituhi ā-ringa, ka tuhia te rahi o tētahi whārite, hei tauira, |F|. Mō ngā pukapuka tā, ka tuhia te rahi o tētahi whārite ki ngā reta whakatītaha, hei tauira , F.
2. Te tāpiri i ngā whārite—ngā tikanga whakairoiro
He maha ngā huarahi hei tāpiri i ngā whārite ki te whakairoiro, tae atu ki te tikanga Hiku-ki-te-pito me te tikanga whakarara.
a. Tikanga tāpiri whārite mai i te hiku ki te pito
E mōhiotia ana ngā whārite A me B. Ko te whārite A = 3 cm e ōrite ana ki te tuaka-x (ki te rawhiti). Ko te whārite B = 2 cm e hanga ana i tētahi koki o te 30 o ki te tuaka-x (ki te raki-mā-rāwhiti). Tāpirihia a A me B mā te whakamahi i te tikanga hiku-ki-te-pito. a) R = A + B b) R = A – B
Ka inehia te rahi o te whārite hua (R) mā te whakamahi i te rūri. Ka inehia te ahunga o te whārite hua mā te whakamahi i te ine-whakarahi.
Ngā whārite e mōhiotia ana ko A, B, me C. Ka ōrite te whārite A = 3 cm ki te tuaka-x (ki te rawhiti). Ka hanga te whārite B = 2 cm i te koki 30 o ki te tuaka-x (ki te raki-mā-rāwhiti). Ka hanga te whārite C = 1 cm i te koki 60 o ki te tuaka-x (ki te raki-mā-rāwhiti). Tāpirihia a A, B, me C mā te whakamahi i te tikanga Hiku-ki-te-pito.
a) R = A + B + C
b) R = A – B – C
Ka inehia te ahunga o te whārite hua (R) mā te whakamahi i te rūrū. Ka inehia te ahunga o te whārite hua mā te whakamahi i te ine-whakarahi.
b. Tikanga whakarara
Ngā whārite e mōhiotia ana ko A, B, me C. E ōrite ana te whārite A = 3 cm ki te tuaka-x (ki te rawhiti). E hanga ana te whārite B = 2 cm i te koki 30 o ki te tuaka-x (ki te raki-mā-rāwhiti). E hanga ana te whārite C = 1 cm i te koki 60 o ki te tuaka-x (ki te raki-mā-rāwhiti). Tāpirihia a A, B, me C mā te whakamahi i tētahi whakarara.
a) R = A + B
b) R = A – B
c) R = A + B + C
d) R = A – B – C
Ka inehia te ahunga o te whārite hua (R) mā te whakamahi i te rūrū. Ka inehia te ahunga o te whārite hua mā te whakamahi i te ine-whakarahi.
3. Te tāpiri i ngā whārite – atātaritanga tikanga
Ko te whakatau i te rahi me te ahunga o te whārite hua mā te tikanga whakairoiro tētahi huarahi. Ko te tika o ngā hua ka whakawhirinaki ki tō tika me tō tika ki te tuhi me te pānui i te tauine. Ko te rahi me te ahunga o te whārite hua ka tino tika ake mā roto i ngā tātaitanga pāngarau.
a. Te tatau i te tapeke o ngā pūwero e 2 mā te whakamahi i te ture cosine
Ko te tātai mō te whakatau i te rahi o te whārite hua:
Ko te tātai mō te whakatau i te ahunga o te whārite hua:
C = te hua o te wetere
A = te whārite 1
B = te whārite 2
cos ∠(A, B) = koki i hangaia e ngā whārite A me B
Tauira raruraru 1:
Ka hanga e F 1 = 2 N he koki 30 i te tuaka-x, ka hanga e F 2 = 3 N he koki 60 o i te tuaka-x, θ = 30 o.
Tauira raruraru 2:
Ka ōrite a F 1 = 2 N ki te tuaka-x, ka hanga a F 2 = 3 N i tētahi koki o te 90 o huri noa i te tuaka-x, θ = 90 o.
b. Te tāpiri i ngā whārite mā ngā wāhanga
Arotakehia tētahi whārite F e hanga ana i tētahi koki e pā ana ki te tuaka-x, e whakaaturia ana i te pikitia i raro nei. Ko F x me F y ngā whārite wāhanga o te whārite F.
Ka whakatauhia te rahi o te whārite wāhanga mā te whakamahi i te tātai:
F x = F cos θ
F y = F sin θ
Arotakehia ngā whārite e rua F1 me F2 e hanga ana i tētahi koki e pā ana ki te tuaka-x, e whakaaturia ana i te pikitia i raro nei. F1x me F1y he wāhanga o te whārite F1, nō reira ko F2x me F2y he wāhanga o te whārite F2.
Ka whakatauhia te whārite wāhanga mā te whakamahi i te tātai:
F1x =F1 cos θ
F 1y = F 1 sin θ
F 2x = F 2 cos θ
F 1y = F 1 sin θ
Te tāpiri i ngā whārite wāhanga:
Fx = F1x + F2x
F y = F 1y + F 2y
Ka whakatauhia te hua o te whārite mā te whakamahi i te tātai:
Ka whakatauhia te ahunga o te whārite hua mā te whakamahi i te tātai:
Tauira raruraru 1:
Tāutuhia ngā wāhanga o te whārite F, ko tōna rahi he 20 N, ā, ka hanga he koki 30 ° huri noa i te tuaka-x.
F x = (20 N)(cos 30 o ) = 17 N
F y = (20 N)(hara 30 o ) = 10 N
Tauira raruraru 2:
Ka hanga e F 1 = 20 N he koki 30 o te taha ki te tuaka-x, ā, ka hanga e F 2 = 15 N he koki 180o te taha ki te tuaka-x. Tātaihia te rahi me te ahunga o te whārite hua.
F 1x = (20 N)(cos 30 o ) = 17 N
F 2x = F 1 = – 15 N
F 1y = (20 N)(hara 30 o ) = 10 N
F 2y = 0
Te tāpiri i ngā whārite wāhanga:
F x = F 1x – F 2x = 17 N – 15 N = 2 N
F y = 10 N
Ko te hua o te wetere:
F 2 = F x 2 + F y 2 = 2 2 + 10 2 = 4 + 100 = 104
F = 10.2N
Te ahunga o te whārite hua:
θ = tan −15 = 78.7 o mō te tuaka-x
Tauira raruraru 3:
F1, F2, me F3 ko 20 N, 30 N me te 40 N. F1 ka hanga he koki o te 60o mō te tuaka-x, F2 ka hanga he koki o te 150o mō te tuaka-x, me te F3 ka hanga he koki o te 315o mō te tuaka-x. Whakatauhia te rahi me te ahunga o te whārite hua.
F 1x = (20 N)(cos 60 o ) = 10 N
F 1y = (20 N)(hara 60 o ) = 17 N
F 2x = (30 N)(cos 30 o ) = -26 N
F 2y = (30 N)(hara 30 o ) = 15 N
F 3x = (40 N)(cos 45 o ) = 28 N
F 3y = (40 N)(hara 45 o ) = -28 N
Te tāpiri i te whārite wāhanga:
F x = F 1x – F 2x + F 3x = 10 N – 26 N + 28 N = 12 N
F y = F 1y + F 2y – F 3y = 17 N + 15 N – 28 N = 4 N
Te hua o te wetere:
F 2 = F x 2 + F y 2 = 12 2 + 4 2 = 144 + 16 = 160
F = 13N
Te ahunga o te whārite hua:
θ = tan −1 0.3 = 17 o mō te tuaka-x
