6 Mīhini Māmā (Rākau Papa Hinga) – Ngā Raru me ngā Otinga
1.
Ko tēhea papa whakarara he rite te painga ā-mīhini?
A. (1) me (2)
B. (1) me (3)
C. (2) me (3)
D. (2) me (4)
otinga
Ko te papa piko tētahi o ngā mīhini māmā. He taputapu ngā mīhini māmā hei āwhina i te tangata ki te mahi i tētahi mahi. Ka whakamahia te papa piko hei whakangāwari ake i te hiki a te tangata i tētahi mea ki tētahi teitei.
Ko te painga ā-pūkaha o te papa hīkoi ko te whakatairite i te roa o te hīkoi ki te teitei o te hīkoi.
Te painga ā-pūkaha o te papa piko 1 = 50 cm / 30 cm = 5/3
Ko te painga ā-pūkaha o te papa piko 2 = 5 cm / 4 cm = 5/4
Ko te painga ā-pūkaha o te papa piko 3 = 50 cm / 40 cm = 5/4
Ko te painga ā-pūkaha o te papa piko 4 = 5 cm / 3 cm = 5/3
[irp]
2.
Tawhiti AB = BC = CD = DE, whakatauhia te kaha whakauru me hoatu ki te pūwāhi E kia taurite ai te rīwhi.
Mōhiotia:
AB = BC = CD = DE = l
Te tawhiti i waenga i te kaha whakaputa me te pūmau ( a ) = l
Te tawhiti i waenganui i te kaha whakauru me te pūmau ( b ) = 3l
Te kaha whakaputa (w) = 900 Newton
E hiahiatia ana: Te Kaha (F)
Rongoā:
Te painga ā-mīhini:
MA = b / a = 3l/l = 3
Te rahi o te kaha:
MA = w / F
F = w / MA
F = 900 Ngā Niutoni / 3
F = 300 Newton
[irp]
3.
Kia taurite ai te rīwhi, whakatauhia te rahi o tōna kaha whakauru.
otinga
Whakatauhia te tawhiti i waenga i te kaha whakauru me te pūmau ( b )
Mōhiotia:
Te tawhiti i waenga i te kaha whakaputa me te pūmau ( a ) = 25 cm
Te kaha whakaputa (w) = 480 Newton
Te kaha whakauru (F) = 160 N
E hiahiatia ana: Te tawhiti i waenga i te kaha whakauru me te pūmau (b)
Rongoā:
Te painga ā-mīhini:
MA = w / F = 480 N / 160 N = 3
Te tawhiti i waenganui i te kaha whakauru me te pūmau (b)
MA = b / a
3 = b / 25 henemita
b = (3)(25 henimita)
b = 75 henimita
Whakatauhia te rahi o te kaha (F)
Mōhiotia:
Te tawhiti i waenganui i te kaha whakaputa me te pūmau ( a ) = 25 cm – 10 cm = 15 cm
Taumaha o te mea (w) = 480 Newton
Te tawhiti i waenga i te kaha whakauru me te pūmau ( b ) = 75 cm
E hiahiatia ana: Te kaha whakauru (F)
Rongoā:
Painga ā-mīhini:
MA = b / a
MA = 75 henimita / 15 henimita
MA = 5
Te rahi o te kaha (F):
MA = w / F
F = w / MA
F = 480 Ngā Niutoni / 5
F = 96 Newton
Kia taurite ai te tūnga o te rīwhi, ka whakaitihia te kaha whakauru ki te 64 Newton (160 N – 96 N).
4. Ko te ōwehenga o te roa o a me b i te pikitia i raro nei ko a: b = 1: 2.2. Ko te uara iti rawa o te kaha F hei hiki i te mea B me te taumaha o te 330 Newtons ko…. Newton
A. 100
B. 150
C. 2200
D. 7260
Mōhiotia:
Te tawhiti i waenga i te kaha whakaputa me te pūmau ( a ) = 1
Te tawhiti i waenga i te kaha whakauru me te pūmau (b) = 2.2
Taumaha (w) = 330 Newton
E hiahiatia ana: Te kaha whakauru (F)
Rongoā:
Ngā painga ā-pūkaha o te rīwhi:
MA = w / F = b / a
MA = painga ā-pūkaha , w = taumaha, F = kaha whakauru, b = tawhiti i waenga i te kaha whakauru me te pūtahi, a = tawhiti i waenga i te kaha whakaputa me te pūtahi
w / F = b / a
330 / F = 2.2 / 1
330 / F = 2.2
330 / 2.2 = F
F = 150 Newton
Ko te whakautu tika ko B.
5. Ka panaia e tētahi tauira tētahi mea me te kaha o F mai i te pūwāhi A ki te pūwāhi B, e whakaaturia ana i te pikitia i raro nei. Mēnā ka kore e arohia te waku i waenganui i te mea me te poaka, tātaihia te painga ā-pūkaha.
A. 4
B. 5/3
C. 5/4
D. ¾
Mōhiotia:
Teitei o te papa whakarara (y) = 4 mita – 1 mita = 3 mita
Te roa o te papa whakapae (x) = 4 mita
E hiahiatia ana: Painga ā-mīhini (MA)
Rongoā:
Tātaihia te roa o te papa whakarara mā te whakamahi i te whārite a Pythagoras :
R = √3 2 +4 2 = √9+16 = √25 = 5 mita
Ngā painga ā-pūkaha o te papa piko:
KM = R / y
KM = 5 mita / 3 mita
KM = 5/3
Ko te whakautu tika ko B.
6. Ka taea te whakanui ake i te painga ā-pūkaha o te rīwhi mā te…
A. Whakapotohia te ara o te piko
B. whakanuia te koki o te piko
C. whakaitihia te koki o te piko
D. ka whakaiti i te kaha e whakamahia ana hei neke i ngā mea
Rongoā:
Ko te whārite o te painga ā-pūkaha o te papa whakarara:
Painga ā-mīhini = te roa o te papa piko/te teitei o te papa piko
– He rite tonu te painga ā-pūkaha ki te roa o te papa hianga, nō reira ka piki ake te painga ā-pūkaha mēnā ka whakanuia te roa o te papa hianga.
– He rite whakamuri te painga ā-pūkaha ki te teitei o te papa piko, nō reira, ka whakaitihia te painga ā-pūkaha mēnā ka whakanuia te teitei o te papa piko, ā, ka whakanuia te painga ā-pūkaha mēnā ka whakaitihia te teitei o te papa piko.
- Ki te whakaitihia te koki, ka whakaitihia te teitei o te papa piko. Ka piki ake te painga ā-pūkaha ki te whakaitihia te teitei o te papa piko. Nō reira, ki te whakaitihia te koki, ka nui ake te painga ā-pūkaha.
Ki te whakanuia te koki, ka whakanuia te teitei o te papa piko. Ka whakaitihia te painga ā-pūkaha ki te whakanuia te teitei o te papa piko. Nō reira, ki te whakanuia te koki, ka whakaitihia te painga ā-pūkaha.
Ko te whakautu tika ko C.
