Te wā o te kaha - ngā raruraru me ngā otinga
1. Mena ko F R te kaha kupenga o F 1 , F 2 , me F 3 , he aha te rahi o te kaha F 2 me x?
Mōhiotia:
Te kaha kupenga (FR) = 40 N
Kaha 1 (F 1 ) = 10 N
Te kaha (F 3 ) = 20 N
E hiahiatia ana: Te rahi o te kaha F 2 me te tawhiti o x
Rongoā:
Kimihia te rahi o te kaha F 2 :
Ka tohu te kaha ki runga, ka tohu te kaha ki raro, he tohu te kaha ki raro.
ΣF = 0
– F R + F 1 + F 2 – F 3 = 0
– 40 + 10 + F 2 – 20 = 0
– 30 + F 2 – 20 = 0
– 50 + F 2 = 0
F 2 = 50 Ngā Newton.
Ko te tohu tāpiri e tohu ana kei runga te ahunga o te kaha.
Kimihia te x.
Kōwhiria a A hei tuaka hurihuri.
τ 1 = F 1 l 1 = (10 N)(1 m) = 10 Nm
Ka hurihia te hihi e te taipana 1 ki te taha maui o te karaka, nō reira ka hoatu e tātou he tohu pai ki te taipana 3.
τ 2 = F 2 x = (50)(x) = 50x Nm
Ka hurihia te hihi e te taipana 1 ki te taha maui o te karaka, nō reira ka hoatu e tātou he tohu pai ki te taipana 3.
τ 3 = F 3 x = (20 N)(1.75 m) = -35 Nm
Ka huri te hihi i te taipana 2 ki te taha matau, nō reira ka hoatu e tātou he tohu kino ki te taipana 2.
Te tere kupenga o te kaha :
Στ = 0
10 + 50x – 35 = 0
50x – 25 = 0
50x = 25
x = 25/50
x = 0.5 mita
2. Ka pā ngā kaha o F1 , F2 , F3 , me F4 ki te tokotoko o ABCD e whakaaturia ana i te pikitia. Mēnā ka warewarehia te papatipu o te tokotoko, he aha te rahi o te nekehanga kaha, e pā ana ki te pūwāhi A?
Ko te tuaka hurihuri = te pūwāhi A.
Mōhiotia:
Te kaha F1 = 10 N, te ringa rīwhi l1 = 0 
Te kaha F 2 = 4 N, te ringa rīwhi l 2 = 2 mita
Te kaha F 3 = 5 N, te ringa rīwhi l 3 = 3 mita
Te kaha F 4 = 10 N, te ringa rīwhi l 4 = 6 mita
E hiahiatia ana: te wā o te kaha e pā ana ki te pūwāhi A
Rongoā:
Te taima o te kaha 1 (τ 1 ) = F 1 l 1 = (10)(0) = 0
Te taima o te kaha 2 (τ 2 ) = F 2 l 2 = (4)(2) = -8 Nm
Te taima o te kaha 3 (τ 3 ) = F 3 l 3 = (5)(3) = 15 Nm
Te taima o te kaha 4 (τ 4 ) = F 4 l 4 = (10)(6) = -60 Nm
Ki te huri te taipana i te tokotoko i te taha maui o te karaka, ka tohua he tohu pai.
Ki te huri te taipana i te tokotoko ki te taha matau, ka tohua he tohu kino.
Ko te hua o te nekehanga kaha:
τ = 0 – 8 Nm + 15 Nm – 60 Nm
τ = -68 Nm + 15 Nm
τ = -53 Nm
Ko te tohu tango e tohu ana ka huri te tokotoko i te taha matau o te nekehanga kaha.
3. E toru ngā kaha e pā ana ki tētahi tokotoko, F A = F C = 10 N me F B = 20 N, e whakaaturia ana i te pikitia i raro nei. Mena ko te tawhiti o AB = BC = 20 cm, he aha te au o te kaha e pā ana ki te pūwāhi C.
Mōhiotia:
Te tuaka hurihuri i te pūwāhi C.
Te tawhiti i waenganui i a F A me te tuaka hurihuri (r AC ) = 40 cm = 0,4 mita
Te tawhiti i waenganui i a F B me te tuaka hurihuri (r BC ) = 20 cm = 0.2 mita
Te tawhiti i waenganui i a F C me te tuaka hurihuri (r CC ) = 0 cm
F A = 10 Newton
F B = 20 Newton
FC = 10 Ngā Newton
E hiahiatia ana: Ko te hua o te nekehanga kaha e pā ana ki te pūwāhi C.
Rongoā:
Te kaha o te kaha A:
Στ A = (F A )(r AC hara 90 o ) = (10 N)(0,4 m)(1) = -4 Nm
Ko te tohu tango e tohu ana ka huri te tokotoko i te taha matau o te nekehanga kaha.
Te kaha o te kaha B:
Στ B = (F B )(r BC hara 90 o ) = (20 N)(0,2 m)(1) = 4 Nm
Ko te tohu tāpiri e tohu ana ka huri te tokotoko i te taha maui o te karaka.
Te kaha o te kaha C:
Στ C = (F C )(r CC hara 90 o ) = (10 N)(0)(1) = 0
Ko te hua o te nekehanga kaha:
Στ = Στ 1 + Στ 2 + Στ 3
Στ = -4 + 4 + 0
Στ = 0 Nm
4. E 50 cm te roa o te tokotoko. E toru ngā kaha e pā ana ki te tokotoko, e whakaaturia ana i te pikitia i raro nei. Mena ko te tuaka hurihuri ko te pūwāhi C, he aha te kupenga o te nekehanga kaha.
Mōhiotia:
Te tuaka hurihuri i te pūwāhi C.
Ko te tawhiti i waenganui i a F 1 me te tuaka hurihuri ko (r 1 ) = 30 cm = 0,3 mita
Te tawhiti i waenganui i a F 2 me te tuaka hurihuri (r 2 ) = 10 cm = 0,1 mita
Te tawhiti i waenganui i a F 3 me te tuaka hurihuri (r 3 ) = 20 cm = 0,2 mita
F 1 = 10 Newton
F 2 = 10 Newton
F 3 = 10 Newton
E hiahiatia ana: Te hua o te nekehanga kaha e pā ana ki te pūwāhi C.
Rongoā:
Te kaha o te wā 1:
Στ 1 = (F 1 )(r 1 hara 90 o ) = (10 N)(0,3 m)(1) = -3 Nm
Ko te tohu tango e tohu ana ka huri te tokotoko i te taha matau o te nekehanga kaha.
Te kaha o te wā 2:
Στ 2 = (F 2 )(r 2 hara 90 o ) = (10 N)(0,1 m)(1) = 1 Nm
Ko te tohu tāpiri e tohu ana ka huri te tokotoko i te taha maui o te karaka.
Te kaha o te wā 3:
Στ 3 = (F 3 )(r 3 hara 30 o ) = (10 N)(0,2 m)(0,5) = -1 Nm
Ko te tohu tango e tohu ana ka huri te tokotoko i te taha matau o te nekehanga kaha.
Ko te hua o te nekehanga kaha:
Στ = Στ 1 + Στ 2 + Στ 3
Στ = -3 + 1 – 1
Στ = -3 Nm
Ko te tohu tango e tohu ana ko te hua o te au o te kaha ka huri i te tokotoko ki te taha matau.
5. E toru ngā kaha F1 , F2 , me F3 e pā ana ki tētahi tokotoko e whakaaturia ana i te pikitia i raro nei. E 4 mita te roa o te tokotoko. He aha te au o te kaha e pā ana ki te pūwāhi C?
(hara 53 o = 0.8, cos 53 o = 0.6, AB = BC = CD = DE = 1 mita)
Mōhiotia:
Te tuaka hurihuri i te pūwāhi C. 
Te Kaha 1 (F 1 ) = 5 Newton
Ko te tawhiti i waenganui i te rārangi mahi o F1 me te tuaka hurihuri (r1 ) = 2 mita
Te Kaha 2 (F 2 ) = 0.4 Newton
Ko te tawhiti i waenganui i te rārangi mahi a F 2 me te tuaka hurihuri (r 2 ) = 1 mita
Te Kaha 3 (F 3 ) = 4.8 Newton
Ko te tawhiti i waenganui i te rārangi mahi o F3 me te tuaka hurihuri (r3 ) = 2 mita
E hiahiatia ana: Te wā o te kaha e pā ana ki te pūwāhi C.
Rongoā:
Te kaha o te wā 1:
τ 1 = F 1 r hara 53 o = (5 N)(2 m)(0,8) = (10)(0,8) N = 8 N
Ko te tohu tāpiri e tohu ana ka huri te tokotoko i te taha maui o te karaka.
Te kaha o te wā 2:
τ 2 = F 2 r hara 90 o = (0,4 N)(1 m)(1) = -0,4 N
Ko te tohu tango e tohu ana ka huri te tokotoko i te taha matau o te nekehanga kaha.
Te kaha o te wā 3:
τ 3 = F 3 r hara 90 o = (4,8 N)(2 m)(1) = -9,6 N
Ko te tohu tango e tohu ana ka huri te tokotoko i te taha matau o te nekehanga kaha.
Ko te hua o te nekehanga kaha:
Στ = τ 1 – τ 2 – τ 3 = 8 – 0,4 – 9,6 = 8 – 10 = 2 Nm
Ko te tohu tāpiri e tohu ana ka huri te tokotoko i te taha maui o te karaka.
6. He aha te hua o te au o te kaha e pā ana ki te tuaka hurihuri i te pūwāhi O nā ngā kaha e pā ana ki te tokotoko, e whakaaturia ana i te pikitia i raro nei?
Mōhiotia:
Te tuaka hurihuri i te pūwāhi O. 
Te Kaha 1 (F 1 ) = 6 Newton
Ko te tawhiti i waenganui i te rārangi mahi a F 1 me te tuaka hurihuri (r 1 ) = 1 mita
Te Kaha 2 (F 2 ) = 6 Newton
Ko te tawhiti i waenganui i te rārangi mahi o F2 me te tuaka hurihuri (r2 ) = 2 mita
Te Kaha 3 (F 3 ) = 4 Newton
Ko te tawhiti i waenganui i te rārangi mahi o F3 me te tuaka hurihuri (r3 ) = 2 mita
E hiahiatia ana: Ko te hua o te nekehanga kaha e pā ana ki te pūwāhi C
Rongoā:
Te kaha o te wā 1:
τ 1 = F 1 l 1 = (6 N)(1 m) = 6 Nm
Ko te tohu tāpiri e tohu ana ka huri te tokotoko i te taha maui o te karaka.
Te kaha o te wā 2:
τ 2 = F 2 r 2 hara 30 o = (6 N)(2 m)(0,5)= 6 Nm
Ko te tohu tāpiri e tohu ana ka huri te tokotoko i te taha maui o te karaka.
Te kaha o te wā 3:
τ 3 = F 3 l 3 = (4 N)(2 m) = -8 Nm
Ko te tohu tango e tohu ana ka huri te tokotoko i te taha matau o te nekehanga kaha.
Ko te hua o te nekehanga kaha:
Στ = τ 1 + τ 2 – τ 3 = 6 + 6 – 8 = 4 Nm
Ko te tohu tāpiri e tohu ana ka huri te tokotoko i te taha maui o te karaka.
