Te wā o te kaha (taipana)

Rauemi o te Mana (Taipana)

Ngā Ringa Kāhua
Whakaarohia tētahi mea e hurihuri ana, pērā i te tatau. Ina whakatuwheratia, ina kati rānei te tatau, ka hurihuri. Ko te hononga e hono ana i te tatau ki te pakitara te tuaka hurihuri.
He ahua o te tatau e kitea ana i runga. Whakaarohia tētahi tauira e panaia ana tētahi tatau e ngā kaha e rua, he rite te rahi me te ahunga o ngā kaha e rua; ko te ahunga o te kaha he poutū ki te tatau.
I te tīmatanga ka panaia te tatau ki te kaha F₁ kei te tawhiti r₁ mai i te tuaka hurihuri. Whai muri i tēnā ka panaia te tatau ki te kaha F₂ kei te tawhiti r₂ mai i te tuaka hurihuri. Ahakoa he rite te rahi me te ahunga o te kaha F1 ki te F₂, kaha F₂ ka tere ake te hurihuri o te tatau i te kaha F₁. Arā, ko te kaha F₂ ka nui ake te whakaterenga koki i te kaha F₁Ka taea e koe te whakaatu i tēnei.
Ko te kaha te mea e pāngia ana e te kaha, engari ko te tawhiti i waenganui i te pūwāhi mahi a te kaha me te tuaka hurihanga (r). Mena he poutū te ahunga o te kaha ki te mata o te mea pērā i te tauira i runga ake nei, ko te ringa o te kaha (l) he ōrite ki te tawhiti i waenganui i te pūwāhi mahi a te kaha me te tuaka hurihanga (r). He aha mēnā kāore te ahunga o te kaha e poutū ki te mata o te mea?
Arotakehia ētahi atu tauira e rua e whakaaturia ana i te ahua i runga ake nei. Ahakoa he rite te rahi o ngā kaha F2 me F3, he rerekē ngā ahunga o ngā kaha e rua, nō reira he rerekē ngā ringa o te kaha (l). I runga whakaahua c, ka ōrite te ahunga o te rārangi mahi o te kaha ki te tuaka hurihuri kia kore ai te ringa o te kaha. Ka mōhiotia te ringa kaha mā te tuhi i tētahi rārangi mai i te tuaka hurihuri ki te rārangi mahi o te kaha, me poutū te rārangi mai i te tuaka hurihuri, me hanga rānei i tētahi koki o te 90^o me te rārangi mahi a te kaha.
Mātakitaki whakaahua b kia mārama ake ai koe ki te pūtake o te tātai ringa kaha e whai ake nei.
Ngā Mōhiohio:
l = te ringa o te kaha, r = te tawhiti o te pūwāhi mahi a te kaha mai i te tuaka hurihuri
Ka whakamahia te whārite 1 hei tatau i te ringa kaha.
Mena he poutū a F ki a r, ko te koki i hangaia he 90^o.
l = r sin 90^o = (r)(1)
l = r
Mena ka ōrite a F ki a r, ko te koki i hangaia he 0^o.
l = r sin 0^o = (r)(0)
l = 0

Te Wā o te Kaha, o te Taipana rānei
Te kaha nui o te wā
I roto i te pāngarau, ko te rahi o te au o te kaha te hua o te whakarea i te rahi o te kaha (F) ki te ringa o te kaha (l).
Ka whakamahia te whārite 2 hei tatau i te rahi o te au o te kaha.
Ko te ine ā-ao mō te taipana ko te mita Newton, e whakarāpopototia ana ko N.m. He rite tonu te ine ā-ao mō te taipana ki te ine mahi me te pūngao, engari ehara te taipana i te pūngao, nō reira kāore e hiahiatia kia whakakapia tōna ine ki te ine Joule. He maha ngā wā ka whakamahia e ngā tohunga ahupūngao te kupu Taipana, ko ngā kaihangarau ia he maha ngā wā ka whakamahia e rātou te kupu Moment of Force.

Te ahunga o te nekehanga kaha
He rahinga whārite te kaha o te wā, nō reira, hei tāpiri atu ki tōna rahi, he ahunga anō tōna. He ngāwari te whakatau i te ahunga o te kaha o te wā mā te whakamahi i te ture ringa-matau. Hurihia ngā maihao e whā o tō ringa matau, me te pupuri tonu i tō koromatua matau kia tū tika. Ko te ahunga hurihanga o ngā maihao e whā ko te ahunga hurihanga, ko te ahunga e tohua ana e te koromatua ko te ahunga o te kaha o te wā.
Mena kei runga te ahunga o te nekehanga kaha (i te tuaka-y pai) kei te taha matau rānei (i te tuaka-x pai), ka pai te nekehanga kaha, te taipana rānei. I tetahi atu taha, ki te mea kei raro te ahunga o te nekehanga kaha (i te tuaka-y) kei te taha maui rānei (i te tuaka-x), ka kino te nekehanga kaha.
Arā, ki te huri te mea i te taha matau ki te taha matau, ka kino te au o te kaha. I tetahi atu taha, ki te huri te mea i te taha maui ki te taha matau, ka pai te au o te kaha.

Tauira raruraru

1. E rima ngā kaha e pā ana ki tētahi tapawhā he 10 cm te roa o ōna taha, e whakaaturia ana i te pikitia e whai ake nei. Ko te tere hua o ngā kaha ki te tuaka i te pūwāhi e whakawhiti ana i ngā hauroki o te tapawhā ko…

Kōrero

E mōhiotia ana:

Te roa o te whakarara = 5√2 cm = (5)(1,4) cm = 7 cm = 0,07 m

Hara 45 ^o = 0,5√2 = (0,5)(1,4) = 0,7

I pātaihia: Te taipana hua

Whakautu:

Taipana 1:

τ ₁ = (10 N)(0,07 m)(hara 45 ^o ) = (10 N)(0,07 m)(0,7) = 0,49 Nm

Mā te taipana 1 ka huri te tapawhā ki te taha maui, nō reira ka hoatu he tohu pai.

Taipana 2:

τ ₂ = (4 N)(0,07 m)(hara 45 ^o ) = (4 N)(0,07 m)(0,7) = 0,196 Nm

Mā te taipana 2 ka huri te tapawhā ki te taha maui, nō reira ka hoatu he tohu pai.

Taipana 3:

τ ₃ = (10 N)(0,07 m)(hara 45 ^o ) = (10 N)(0,07 m)(0,7) = 0,49 Nm

Mā te taipana 3 ka huri te tapawhā ki te taha maui, nō reira ka hoatu he tohu pai.

Taipana 4:

τ ₄ = (5√2 N)(0,07 m)(hara 90 ^o ) = (7 N)(0,07 m)(1) = 0,49 Nm

Mā te taipana 4 ka huri te tapawhā ki te taha maui, nō reira ka hoatu he tohu pai.

Taipana 5:

τ ₅ = (9 N)(0,07 m)(hara 45 ^o ) = (9 N)(0,07 m)(0,7) = -0,44 Nm

Mā te taipana 5 ka huri te tapawhā ki te taha matau, nō reira ka hoatu he tohu kino ki a ia.

Te taipana hua:

τ = 0,49 + 0,196 + 0,49 + 0,49 – 0,44 = 1,47 + 0,196 – 0,44 = 1,666 – 0,44 = 1,226 Nm