1. Ka pāngia tētahi pito o tētahi kurupae he 2 m te roa e te kaha P. He aha te rahi o te taipana ? Ko te tuaka hurihuri i te pūwāhi A.
Mōhiotia:
Te kaha (F) = 10 N
Te roa o AB (r AB ) = 2 m
He poutū te kaha F ki te kurupae.
Ko te ringa rīwhi (l ) = r AB sin 90 o = (2 m)(1) = 2 m
E hiahiatia ana: Te taipana huri noa i te tuaka hurihuri
Rongoā:
Te taipana:
τ = F l = (10 N)(2 m) = 20 N m
Ko te tohu tāpiri nā te mea ka huri te hihi i te taha maui.
[irp]
2. Ko te roa o te kurupae AB he 2 m, ā, ko te kaha F he 10 N. He aha te kaha o te taipana? Ko te tuaka hurihuri i te pūwāhi A.
Mōhiotia:
Te kaha (F) = 10 N
Te roa o AB (r AB ) = 2 m
Ko te ringa rīwhi (l ) = r AB sin 60 o = (2 m)(0.5 √3 ) = √3 m
E hiahiatia ana: Te taipana huri noa i te tuaka hurihuri
Rongoā:
Te taipana:
τ = F l = (10 N)( √3 m) = 10 √3 N m
Ko te tohu tāpiri nā te mea ka meinga te hihi e te kaha F kia huri i te taha maui.
[irp]
3. Ko te roa o te kurupae he 2 m. Ko te rahi o F1 he 10 N, ā, ko te rahi o F2 he 15 N. Tātaihia te taipana kupenga i waenganui o te kurupae.
Te tuaka hurihuri i waenganui o te kurupae.
Mōhiotia:
Kaha 1 (F 1 ) = 10 N
Ko te tawhiti i waenganui i a F 1 me te pokapū o te kurupae (r 1 ) = 1 m
Ko te ringa rīwhi 1 (l 1 ) = r 1 sin 90 o = (1 m)(1) = 1 m
He poutū te kaha F 1 ki te kurupae.
Kaha 2 (F 2 ) = 15 N
Ko te tawhiti i waenganui i a F 2 me te pokapū o te kurupae (r 2 ) = 1 m
He poutū te kaha F 2 ki te kurupae.
Ko te ringa rīwhi 2 (l 2 ) = r 1 sin 90 o = (1 m)(1) = 1 m
E hiahiatia ana: Te taipana kupenga huri noa i te tuaka hurihuri
Rongoā:
Te taipana 1:
τ 1 = F 1 l 1 = (10 N)( 1 m) = 10 N m
Ko te tohu tāpiri nā te mea ka meinga te hihi e te kaha o F 1 kia huri ki te taha maui.
Te taipana 2:
τ 2 = F 2 l 2 = (15 N)( 1 m) = -15 N
Ko te tohu tango nā te mea ka meinga te hihi e te kaha F 2 kia huri ki te taha matau.
Te taipana kupenga:
Σ τ = τ 1 – τ 2 = 10 – 15 = – 5 N m
Ko te tohu tango nā te mea ka huri te hihi ki te taha matau.
[irp]
4. Ko te roa o te kurupae AB he 2 m, ko te rahi o F1 he 10 N, ā, ko te rahi o F2 he 10 N. Tātaihia te taipana kupenga i waenganui o te kurupae.
Te tuaka hurihuri i waenganui o te kurupae.
Mōhiotia:
Kaha 1 (F 1 ) = 10 Nn
Ko te tawhiti i waenganui i a F 1 me te pokapū o te kurupae (r 1 ) = 1 m
Ko te ringa rīwhi 1 (l 1 ) = r 1 sin 60 o = (1 m)(0.5 √3 ) = 0.5 √3 m
Kaha 2 (F 2 ) = 10 N
Ko te tawhiti i waenganui i a F 2 me te pokapū o te kurupae (r 2 ) = 1 m
He poutū te kaha F 2 ki te kurupae.
Ko te ringa rīwhi 2 (l 2 ) = r 2 sin 90 o = (1 m)(1) = 1 m
E hiahiatia ana: Te taipana kupenga huri noa i te tuaka hurihuri
Rongoā:
Te taipana 1:
τ 1 = F 1 l 1 = (10 N)( 0.5 √3 m) = 5 √3 = 8.7 Nm
Ko te tohu tāpiri nā te mea ka meinga te hihi e te kaha F 1 kia huri ki te taha matau.
Te taipana 2:
τ 2 = F 2 l 2 = (10 N)( 1 m) = -10 N m
Ko te tohu tango nā te mea ka meinga te hihi e te kaha F 2 kia huri ki te taha matau.
Te taipana kupenga:
Σ τ = τ 1 – τ 2 = 8.7 – 10 = – 1.3 N m
Ko te tohu tango nā te mea ka meinga te hihi kia huri ki te taha matau e te kaha kupenga.
[irp]
5. Ko te roa o te kurupae he 10 m, ko te rahi o F1 he 10 N, ko te rahi o F2 he 10 N, ā, ko te rahi o F3 he 15 N. Ko te tawhiti i waenganui i te pūwāhi A me te pūwāhi C he 7.5 m. Kei waenganui o te kurupae te Kaha F2. Tātaihia te taipana kupenga e pā ana ki te pūwāhi C kei te 2.5 m mai i te pūwāhi B.
Kei te pūwāhi C te tuaka hurihuri
Mōhiotia:
Kaha 1 (F 1 ) = 10 N
Ko te tawhiti i waenganui i a F 1 me te pūwāhi C (r 1 ) = 2.5 m
He poutū te kaha F 1 ki te kurupae.
Ko te ringa rīwhi 1 (l 1 ) = r 1 sin 90 o = ( 2.5 m)( 1 ) = 2.5 m
Kaha 2 (F 2 ) = 10 N
Ko te tawhiti i waenganui i a F 2 me te pūwāhi C (r 2 ) = 2.5 m
He poutū te kaha F 2 ki te kurupae.
Ko te ringa rīwhi 2 (l 2 ) = r 2 sin 90 o = ( 2.5 m)(1) = 2.5 m
Kaha 3 (F 3 ) = 15 N
Ko te tawhiti i waenganui i a F 3 me te pūwāhi C (r 3 ) = 7.5 m
He poutū te kaha F 3 ki te kurupae.
Ko te ringa rīwhi 3 (l 3 ) = r 3 sin 90 o = (7.5 m)(1) = 7.5 m
E hiahiatia ana: Te taipana kupenga huri noa i te tuaka hurihuri
Rongoā:
Te taipana 1:
τ 1 = F 1 l 1 = (10 N)( 2.5 m) = 25 N m
Ko te tohu tāpiri nā te mea ka meinga te hihi e te kaha F 1 kia huri ki te taha matau.
Te taipana 2:
τ 2 = F 2 l 2 = (10 N)( 2.5 m) = 25 N m
Ko te tohu tāpiri nā te mea ka meinga te hihi e te kaha F 2 kia huri ki te taha matau.
Te taipana 3:
τ 3 = F 3 l 3 = (15 N)( 7.5 m) = -112..5 N m
Ko te tohu tango nā te mea ka meinga te hihi e te kaha F 3 kia huri ki te taha matau.
Te taipana kupenga:
Σ τ = τ 1 + τ 2 – τ 3 = 25 + 25 – 112.5 = – 62.5 N m
Ko te tohu tango nā te mea ka meinga te hihi kia huri ki te taha matau e te kaha kupenga.
[irp]
6. Ko te roa o te kurupae he 10 m, ko te rahi o F1 ko te 10 N, ko te rahi o F2 he 10 N, ā, ko te rahi o F3 ko te 10 N. Tātaihia te taipana kupenga mō te pūwāhi A, kei te 5 m mai i te pou
te whakamahinga o te kaha F1.
Te tuaka hurihuri i te pūwāhi A.
Mōhiotia:
Kaha 1 (F 1 ) = 10 N
Ko te tawhiti i waenganui i a F 1 me te pūwāhi A (r 1 ) = 5 m
Ko te ringa rīwhi 1 (l 1 ) = r 1 sin 60 o = (5 m)(0.5 √3 ) = 2.5 √3 m
Kaha 2 (F 2 ) = 10 N
Ko te tawhiti i waenganui i a F 2 me te pūwāhi A (r 2 ) = 0
He poutū te kaha F 2 ki te kurupae.
Ko te ringa rīwhi 2 (l 2 ) = r 2 sin 90 o = (0)(1) = 0
Ko te kaha 3 (F 3 ) = 10 N
Ko te tawhiti i waenganui i a F 3 me te pūwāhi A (r 3 ) = 10 m
Ko te ringa rīwhi 3 (l 3 ) = r 3 sin 30 o = (10 m)(0.5) = 5 m
E hiahiatia ana: te taipana kupenga huri noa i te tuaka hurihuri
Rongoā:
Te taipana 1:
τ 1 = F 1 l 1 = (10 N)( 2.5 √3 m ) = 25√3 = 43.3 N m
Ko te tohu tāpiri nā te mea ka meinga te hihi e te kaha F 1 kia huri ki te taha matau.
Te taipana 2:
τ 2 = F 2 l 2 = (10 N)(0) = 0
Te taipana 3:
τ 3 = F 3 l 3 = (10 N)( 5 m) = -50 N m
Ko te tohu tango nā te mea ka meinga te hihi e te kaha F 3 kia huri ki te taha matau.
Te taipana kupenga:
Σ τ = τ 1 + τ 2 – τ 3 = 43.3 + 0 – 50 = – 6.7 N m
Ko te tohu tango nā te mea ka meinga te hihi kia huri ki te taha matau e te kaha kupenga.
