Ngā tinana e rua he rite te rahi o te whakaterenga – Te whakamahinga o ngā raruraru me ngā otinga o te ture nekehanga a Newton

1. E rua ngā papatipu m₁ = 2 kg me te m₂ = 5 kg kei runga i te papa whakarara, ā, e honoa ana mā te aho e whakaaturia ana i te pikitia. Ko te tauwehenga o te waku nekeneke i waenga i a m₁ ā, ko te pikinga he 0.2, ā, ko te tauwehenga o te te waku nekeneke i waenganui i te m₂ ā, ko te pikinga he 0.1.

(a) Whakatauhia ā rātou whakatere

(b) Whakatauhia te kaha kume

Mōhiotia:

Mass 1 (m₁) = 2 kirokaramu

Taumaha 2 (m₂) = 4 kirokaramu

Te tauwehenga o te waku nekeneke i waenga i te m₁ a papa whakarara (μ)_k1) = 0.2

Te tauwehenga o te waku nekeneke i waenga i te m₂ me te papa whakarara (μ)_k2) = 0.1

Whakaterenga na te kaha o te kaha (g) = 9.8 m/s²

a) Te rahi me te ahunga o te whakaterenga

w₁ = taimaha 1 = m₁ karamu = (2 kg)(9.8 m/s²) = 19.6 Niutona

w_1x =w₁ hara 30^o = (19.6 N)(0.5) = 9.8 Nīutona

w_1y =w₁ whaimana 30^o = (19.6 N)(0.87) = 17 Nīutona

N₁ = Te kaha noa i runga i te m₁ =w_1y = 17 Niutona

F_k1 = Te kaha o te waku nekeneke i runga i te m₁ = μ_k1 N₁ = (0.2)(17 N) = 3.4 Nīhana

---

w₂ = taumaha 2 = m₂ karamu = (4 kg)(9.8 m/s²) = 39.2 Niutona

w_2x =w₂ hara 60^o = (39.2 N)(0.87) = 34.1 Nīutona

w_2y =w₂ whaimana 60^o = (39.2 N)(0.5) = 19.6 Nīutona

N₂ = Te kaha noa i runga i te m₂ =w_2y = 19.6 Niutona

F_k2 = Te kaha o te waku nekeneke i runga i te m₂ = μ_k2 N₂ = (0.1)(19.6 N) = 1.96 Nīhana

---

Te rahi o te whakaterenga:

∑F_x = mā_x

w_2x > w_1x nō reira he rite tonu te ahunga o te whakaterenga ki te ahunga o w_2x.

He pai ngā kaha e tohu ana i te ahunga whakaterenga, ā, he kino ngā kaha e tohu ana i te ahunga whakahāwea ki te whakaterenga.

w_2x - F_k2 - T₂ +T₁ - w_1x - F_k1 = (m₁ +m₂) a_x

w_2x - F_k2 - w_1x - F_k1 = (m₁ +m₂ ) a_x

34.1 N – 1.96 N – 9.8 N – 3.4 N = (2 kg + 4 kg) a_x

18.94 N = (6 kg) a_x

a_x = 18.94 N : 6 kg

a_x = 3.16m/s²

Te rahi o te whakaterenga = 3.16 m/s² Te ahunga o te whakaterenga = te ahunga o T₁ = te ahunga o te w_2x

b) Te rahi o te kaha kume

Whakamahia te ture tuarua a Newton ki te mea 2:

w_2x - F_k2 - T₂ = m₂ a_x

34.1 N – 1.96 N – T₂ = (4 kg)(3.16 m/s²)

32.14 N – T₂ = 12.64 N

T₂ = 32.14 N – 12.64 N = 19.5 Ngā Newton

Te kaha kume = T = T₁ =T₂ = 19.5 Niutona

2. m₁ = 4 kg, mita₂ = 2 kg. Whakatauhia (a) te rahi me te ahunga o te whakaterenga (b) Te rahi o te kaha kume e hono ana i a m₁ me te m₂ (c) te rahi o te kaha kume e hono ana i te pūrei me te tuanui.

otinga

w₁ = m₁ karamu = (4 kg)(9.8 m/s²) = 39.2 Niutona

w₂ = m₂ karamu = (2 kg)(9.8 m/s²) = 19.6 Niutona

a) Te rahi me te ahunga o te whakaterenga

∑F_y = mā_y

w₁ > w₂ nō reira he rite tonu te ahunga o te mea ki te ahunga o te taumaha 1 (w₁)He pai ngā kaha he rite te ahunga ki te whakaterenga, ā, he kino ngā kaha he rite te ahunga ki te whakaterenga.

w₁ - T₁ +T₂ - w₂ = (m₁ +m₂) a_y

w₁ - w₂ = (m₁ +m₂) a_y

39.2 N – 19.6 N = (4 kg + 2 kg) a_y

19.6 N = (6 kg) a_y

a_y = 19.6 N : 6 kg

a_y = 3.26m/s²

Te rahi o te whakaterenga = 3.26 m/s². Te ahunga o te whakaterenga = te ahunga o w₁ .

b) Te rahi o te kaha kume e hono ana i a m₁ me te m₂

Anga Te ture tuarua a Newton i runga i te m₂ :

∑F_y = mā_y

w₁ - T₁ = m₁ a_y

39.2 N – T₁ = (4 kg)( 3.26 m/s²)

39.2 N – T₁ = 13.04 N

T₁ = 39.2 N – 13.04 N

T₁ = 26.16 Niutona

Te rahi o te kaha kume e hono ana i ngā mea = T = T₁ =T₂ = 26.16 Niutona

c) Te rahi o te kaha kume e hono ana i te pūrakau me te tuanui.

Kei te okioki te pūrei:

∑F_y = mā_y —— he_y = 0

∑F_y = 0

He pai ngā kaha whakarunga, he kino ngā kaha whakararo:

T₃ - T₁ - T₂ = 0

T₃ =T₁ +T₂

T₁ a T₂ he rite te rahi, T₁ =T₂ = T = 26.16 N :

T₃ = 2T = 2(26.16 N) = 52.32 Ngā Niutona

3. Poraka 1 (m₁ = 10 kg) me te poraka 2 (m₂ = 15 kg) i honoa mā te taura i runga i te pūrei kore-waku. Te tauwehenga o te waku pūmau i waenga i te poraka 2 me te pikinga = 0.6. Ko te tauwehenga o te waku nekeneke i waenga i te poraka 2 me te pikinga = 0.42. Whakatauhia (a) Te rahi o te kaha iti rawa F i pā ki ngā mea kia tere ake ai ngā mea ki runga (b) Whakatauhia te rahi o te kaha kume.

otinga

w₁ = Te taumaha o te poraka 1 = m₁ karamu = (10 kg)(9.8 m/s²) = 98 Niutona

w₂ = Te taumaha o te poraka 2 = m₂ karamu = (15 kg)(9.8 m/s²) = 147 Niutona

w_2y =w₂ whaimana 30^o = (147 N)(0.87) = 127.89 Nīutona

w_2x =w₂ hara 30^o = (147 N)(0.5) = 73.5 Nīutona

N₂ = Te kaha noa i runga i te poraka 2 = w_2y = 127.89 Niutona

F_k2 = Te kaha o te waku nekeneke i runga i te poraka 2 = μ_k2 N₂ = (0.42)(127.89 N) = 53.7 Nīhana

F_s2 = Te kaha o te waku pumau i runga i te poraka 2 = μ_s2 N₂ = (0.6)(127.89 N) = 76.7 Nīhana

a) Te rahi o te kaha iti rawa F i pā ki ngā mea kia tere ake ai ngā mea ki runga

∑F_x = mā_x —— he_x = 0

∑F_x = 0

He pai ngā kaha whakarunga me ngā kaha whakarunga matau, he kino ngā kaha whakararo me ngā kaha whakarunga maui.

Wh – Wh_k2 - w_2x - w₁ - T₂ +T₁ = 0

Wh – Wh_k2 - w_2x - w₁ = 0

F = F_k2 + w_2x + w₁

F = 53.7 N + 73.5 N + 98 N

F = 225.2 Newton

b) Te rahi o te kaha kume

Whakamahia te ture nekehanga a Newton ki te poraka 1:

∑F_y = mā_y —— he_y = 0

∑F_y = 0

T₁ - w₁ = 0

T₁ =w₁ = 98 Niutona

Whakamahia te ture nekehanga a Newton ki te poraka 2:

Wh – Wh_k2 - w_2x - T₂ = 0

T₂ = F – F_k2 - w_2x

T₂ = 225.2 N – 53.7 N – 73.5 N

T₂ = 98 Niutona

Te rahi o te kaha kume = T₁ =T₂ = T = 98 Niutona

4. Poraka 1 (m₁ = 16 kg) kei runga i te mata whakapae, ā, ko te poraka 2 (m₂ = 12 kg) kei runga i tētahi papa whakarara maeneene, e honoa ana e tētahi taura e whiti ana i runga i tētahi porotiti iti, kore-waku. Poraka 3 (m₃ = 5 kg) kei runga i te poraka 2. Ko te tauwehenga o te waku nekeneke i waenga i te poraka 2 me te mata whakapae he 0,4. Ko te coefKo te uara o te waku pateko i waenga i te poraka 2 me te poraka 3 he 0,3.

(a) Ina tukuna te pūnaha mai i te okiokinga, ka paheke tahi tonu te poraka 3 me te poraka 2?

(B) Mena kei reira te poraka 3, he aha te whakaterenga o te poraka 1 me te poraka 2?

Rongoā:

a) Ina tukuna te pūnaha mai i te okiokinga, ka paheke tahi tonu te poraka 3 me te poraka 2?

w₁ = Te te taumaha o te poraka 1 = m₁ karamu = (16 kg)(9.8 m/s²) = 156.8 Niutona

w_1x =w₁ hara 60^o = (156.8 N)(0.87) = 136.4 Nīutona

w_1y =w₁ whaimana 60^o = (156.8 N)(0.5) = 78.4 Nīutona

N₁ = Te te kaha noa i pā ki te poraka 1 e te papa whakarara =w_1y = 78.4 Niutona

w₃ = Te te taumaha o te poraka 3 = m₃ karamu = (5 kg)(9.8 m/s²) = 49 Niutona

N₂₃ = Te te kaha noa i pā ki te poraka 3 e te poraka 2 =w₃ = 49 Niutona

N₃₂ = Te nte kaha noa i pā ki te poraka 2 e te poraka 3 = N₂₃ =w₃ = 49 Niutona

(N₂₃ a N₃₂ he takirua mahi-tauhohenga)

F_s23 = Te te kaha o te waku pao i pā ki te poraka 3 e te poraka 2 = μ_s N₂₃ = (0.3)(49 N) = 14.7 Newton

F_s32 = Te te kaha o te waku pumau i pā ki te poraka 2 e te poraka 3 =F_s23 = 14.7 Niutona

(F_s23 a F_s32 he takirua mahi-tauhohenga)

w₂ = Te te taumaha o te poraka 2 = m₂ karamu = (12 kg)(9.8 m/s²) = 117.6 Niutona

N₂ = Te te kaha noa i pā ki te mea 2 e te mata whakapae =w₂ +N₃₂ = 117.6 Ngā Newton + 49

Niutoni = 166.6 Niutoni

F_k2 = Te te kaha o te waku nekeneke i runga i te poraka 2 = μ_k N₂ = (0.4)(166.6 N) = 66.64 Nīhana

Whakamahia te ture nekehanga a Newton ki te poraka 3:

∑F_x = mā_x

F_s23 =m₃ a_x

—–> F_s23 = μ_s N₂₃ = μ_s w₃ = μ_s m₃ g

μ_s m₃ g = m₃ a_x

μ_s g = a_x

a_x = (0.3)(9.8 m/s²) = 2.94 m/s²

Ko te whakaterenga mōrahi o te poraka 3 kia paheke tonu ai te poraka 3 me te poraka 2 ko 2.94 m/s².

Nā, ka tatauhia e tātou te rahi o te whakaterenga o te pūnaha i muri i te tukunga mai i te okiokinga.

Ko te ahunga o te nekehanga o te poraka = te ahunga o te whakaterenga o te poraka = te ahunga o T₂ = te ahunga o w_1x.

∑F_x = mā_x

w_1x - T₁ +T₂ - F_k2 - F_s32 +F_s23 = (m₁ +m₂ +m₃) a_x

w_1x - F_k2 = (m₁ +m₂ +m₃ ) a_x

136.4 N – 66.64 N = (16 kg + 12 kg + 5 kg) a_x

69.76 N = (33 kg) a_x

a_x = 2.11m/s²

a_x he pai, ko te tikanga he rite te ahunga o te nekehanga poraka, te ahunga rānei o te whakaterenga ki te ahunga o T₂ te ahunga rānei o w_1x.

Ko te rahi o te whakaterenga ko 2.11 m / s² , lnui atu i 2.94 m / s² Nō reira, ka taea e tātou te whakatau ka paheke tahi tonu te poraka 3 me te poraka 2 i muri i te tukunga i te okiokinga.

b) Te rahi o te whakaterenga o te poraka 1 me te poraka 2

∑F_x = mā_x

w_1x - F_k2 = (m₁ +m₂) a_x

—–> F_k2 = μ_k N₂ = μ_k w₂ = μ_k m₂ karamu = (0.4)(12 kg)(9.8 m/s²) = 47.04 Niutona

136.4 N – 47.04 N = (16 kg + 12 kg) a_x

89.36 N = (28 kg) a_x

a_x = 89.36 N : 28 kg = 3.19 m/s²

[wpdm_package id='493′]

1. Papatipu me te taumaha
2. Te kaha noa
3. Te ture tuarua o te nekehanga a Newton
4. Te kaha waku
5. Te nekehanga i runga i te mata whakapae me te kore he kaha waku
6. Te nekehanga o ngā tinana e rua me te tere tere ōrite i runga i te mata whakapae taratara me te kaha waku
7. Te nekehanga i runga i te papa whakarara me te kore he kaha waku
8. Te nekehanga i runga i te papa whakarara taratara me te kaha waku
9. Te nekehanga i roto i te ararewa
10. Ka honoa te nekehanga o ngā tinana e ngā taura me ngā pūrere
11. E rua ngā tinana he rite te rahi o te whakaterenga
12. Te whakaawhiwhi i tētahi piko papatahi – ngā nekehanga porowhita
13. Te whakaawhiwhi i tētahi kōpiko peeke – ngā hihiri o te nekehanga porowhita
14. Te nekehanga ōrite i roto i te porowhita whakapae
15. Te kaha pokapū i roto i te nekehanga porowhita ōrite