Tauira o ngā pātai mō te Papa Hinga

9 Ngā Tauira o ngā Pātai Papa Hinga

Akohia ngā rauemi mō ngā ture a Newton , te kaha noa me te kaha waku kia pai ake ai tō mārama ki te matapakinga o tēnei pātai.

1. Ka tukuna he poraka 5 kg te taumaha i runga i tētahi papa whakarara maeneene e whakaaturia ana i te pikitia! (g = 10 ms ⁻² me te tg 37 ^o = 3/4). Ko te whakaterenga o te poraka ko...

A. 4,5 ms^-2

B. 6,0 ms ⁻²

C. 7,5 ms ⁻²

D. 8,0 ms ⁻²

E. 10,0 ms ⁻²

Kōrero

E mōhiotia ana:

m = 5 kg, karamu = 10 m/ ^s2

w = mg = (5)(10) = 50 N

te roa o te taha raro = 4

te roa o te taha poutū = 3

Nā te mea ko te taha raro = 4, ā, ko te taha poutū = 3, ko te hypotenuse = 5. Ka taea e koe te whakamatau mā te whakamahi i te tātai Pythagoras.

Pātai: te whakaterenga o te poraka (a)?

Whakautu:

Ko te kaha e neke ai te poraka ko w _x . He maeneene te papa whakarara, nō reira kāore he waku.

w_x = w hara θ = (w)(taha poutū / taha whakarara)

wx = (50)(3/5 ₎

wx = ₃₀ Newton

He aha te whakaterenga (a) o te poraka?

Σ F = ma

wx ₌ ma

30 = (5) he

ā = 30 / 5

a = 6 m/s ²

Ko te whakautu tika ko B.

2. Tirohia te pikitia! I te tīmatanga ka okioki tetahi poraka, kātahi ka tōia ki runga mā te kaha F e whakarara ana ki te papa whakarara. Ko te taumaha o te poraka he 8 kg, ko te tauwehenga o te waku µs ₌ 0,5 me te θ = 45 ^o . Kia tika ai te neke o te poraka ki runga, me… te kaha F.

A. 40 N

B. 60 N

C. 60√2 N

D. 80 N

E. 80√2 N

Kōrero

E mōhiotia ana :

Tauwehenga waku pumau (µs ₎ = 0,5

Koki (θ) = 45 ^o

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

Taumaha o te poraka (m) = 8 kirokaramu

Taumaha o te poraka (w) = mg = (8 kg)(10 m/s ² ) = 80 kg m/s ² = 80 Newtons

Pātai : Te rahi o te kaha F kia neke ake ai te poraka

Whakautu :

Ka neke ake te poraka mēnā ko F ≥ w _x + f _s.

Te wāhanga o te kaha ā-papa e whakarara ana ki te papa whakarara :

w _x = w hara θ = (80)(hara 45) = (80)(0,5√2) = 40√2

Te wāhanga o te kaha ā-papa e poutū ana ki te papa whakarara :

w _y = w cos θ = (80)(cos 45) = (80)(0,5√2) = 40√2

Te kaha noa :

N = w _y = 40√2

Te kaha waku pumau :

f _s = µ _s N = (0,5)(40√2) = 20√2

Te rahi o te kaha F kia neke ake ai te poraka :

F ≥ w _x + f _s

F ≥ 40√2 + 20√2

F ≥ 60√2 Newton

Ko te whakautu tika ko C.

3. Kei runga i tētahi papa whakarara te poraka, e 8 kg te taumaha, e whakaaturia ana i te pikitia e whai ake nei. Ko te kaha o waho iti rawa e hiahiatia ana hei ārai i te poraka kei paheke ki raro ko… (sin 37 ^o = 0,6, cos 37 ^o = 0,8, g = 10 ms ^-2 , µ _k = 0,1)

A. 6,4 N

B. 4,6 N

C. 48,5 N

D. 54,4 N

E. 68,8 N

Kōrero

E mōhiotia ana :

Taumaha o te poraka (m) = 8 kg

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

Taumaha o te poraka (w) = mg = (8)(10) = 80 Newton

Sin 37 ^o = 0,6

Cos 37 ^o = 0,8

Tauwehenga o te waku nekeneke (µk ₎ = 0,1

N = w _y = w cos 37 ^o = (80)(0,8) = 64 Ngā Newton

Pātai : Ko te kaha o waho iti rawa (F) e hiahiatia ana hei tautoko i te poraka kia kore ai e paheke ki raro.

Whakautu :

Kāore te poraka e paheke ki raro mēnā ko F = w _x

Te wāhanga o te kaha ā-papa e whakarara ana ki te papa whakarara :

w _x = w hara θ = (80)(hara 37) = (80)(0,6) = 48

f _k = µ _k N = (0,1)(64) = 6,4

Te kaha iti rawa F kia kore ai te poraka e paheke ki raro :

F + f _k – w _x = 0

F = w _x – f _k = 48 – 6,4 = 41,6 Ngā Newton

4. Ka tōia tētahi mea he 5,0 kg te taumaha ki runga i tētahi papa whakarara taratara mā te kaha o te 71 N (g = 10 m s ^-2 , sin 37 ^o = 0,6, cos 37 ^o = 0,8). Mena ko te tauwehenga waku i waenga i te mea me te papa he 0,4, ko te whakaterenga e pā ana ki te mea ko…

A. 0,5 ms^-2

B. 2 ms ^-2

C. 2,5 ms ^-2

D. 3 ms ^-2

E. 5 ms ^-2

Kōrero

E mōhiotia ana :

Papatipu o te mea (m) = 5 kg

4. Ngā Pātai Whakamātautau Ā-Motu mō te Ahupūngao SMA 2012/2013 SA 67 Nama 5

Ka tōia tētahi mea 5,0 kg te taumaha e te taura ki runga i tētahi papa whakarara taratara mā te kaha o te 71 N (g = 10 m s ^-2 , sin 37 ^o = 0,6, cos 37 ^o = 0,8). Mena ko te tauwehenga waku i waenga i te mea me te papa he 0,4, ko te whakaterenga e pā ana ki te mea ko…

A. 0,5 ms ^-2

B. 2 ms ^-2

C. 2,5 ms ^-2

D. 3 ms ^-2

E. 5 ms ^-2

Kōrero

E mōhiotia ana :

Papatipu o te mea (m) = 5 kg

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

Taumaha o te taonga (w) = mg = (5)(10) = 50 Newton

Te Kaha F = 71 Newton

Sin 37 ^o = 0,6

Cos 37 ^o = 0,8

Tauwehenga o te waku = 0,4

Pātai : Te whakaterenga o te mea (a)

Whakautu :

Te Kaha Hua

Tuatahi, tatauhia te kaha hua e pā ana ki te mea.

Te wāhanga o te kaha ā-papa e whakarara ana ki te papa whakarara :

w _x = w hara θ = (50)(hara 37) = (50)(0,6) = 30

Te wāhanga o te kaha ā-papa e poutū ana ki te papa whakarara :

w _y = w cos θ = (50)(cos 37) = (50)(0,8) = 40

Kāhua noa :

N = w _y = 40

Te kaha waku nekeneke :

f _k = µ _k N = (0,4)(40) = 16

Te kaha hua e pā ana ki tētahi papa whakarara:

∑ F = F – w _x – f _k = 71 – 30 – 16 = 25 Ngā Newton

Te whakaterenga o tētahi mea

Ka tatauhia te whakaterenga o tētahi mea mā te whakamahi i te tātai ture tuarua a Newton:

a = ∑F / m = 25 / 5 = 5 m/s ²

Ko te whakautu tika ko E.

5.
Tirohia te pikitia! I te tīmatanga ka okioki tetahi poraka, kātahi ka tōia ki runga me te kaha F e whakarara ana ki te papa piko. Ko te taumaha o te poraka he 8 kg, ko te tauwehenga o te waku he µ._s = 0,5 me θ = 45^oKia taea ai e te poraka te neke ake, me rite te kaha F ki te….

A. 40 N
B. 60 N
C. 60√2 N
D. 80 N
E. 80√2 N

Kōrero
E mōhiotia ana :
Tauwehenga te waku pumau (µ)_s) = 0,5
Koki (θ) = 45^o
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s²
Taumaha o te poraka (m) = 8 kirokaramu
Taumaha o te poraka (w) = mg = (8 kg)(10 m/s)²) = 80 kg m/s² = 80 Niutona
I pātaihia : Te rahi o te kaha F kia neke ake ai te poraka
Whakautu :

Ka neke ake te poraka matau mēnā F ≥ w_x + f_s.
Te wāhanga o te kaha ā-papa e whakarara ana ki te papa whakarara :
w_x = w hara θ = (80)(hara 45) = (80)(0,5√2) = 40√2
Te wāhanga o te kaha ā-papa e poutū ana ki te papa whakarara :
w_y = w cos θ = (80)(cos 45) = (80)(0,5√2) = 40√2
Te kaha noa :
N = w_y = 40√2
Te kaha waku pumau :
f_s = µ_s N = (0,5)(40√2) = 20√2
Te rahi o te kaha F kia neke ake ai te poraka :
F ≥ w_x + f_s
F ≥ 40√2 + 20√2
F ≥ 60√2 Newton
Ko te whakautu tika ko C.

6.
Kei runga i tētahi papa whakarara te poraka, e 8 kg te taumaha, e whakaaturia ana i te pikitia i raro nei. Ko te kaha o waho iti rawa e hiahiatia ana hei ārai i te poraka kei paheke ki raro ko… (sin 37^o = 0,6, cos 37^o = 0,8, karamu = 10 ms^-2, µ_k = 0,1)

A. 6,4 N
B. 4,6 N
C. 48,5 N
D. 54,4 N
E. 68,8 N

Kōrero
E mōhiotia ana :
Taumaha o te poraka (m) = 8 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s²
Taumaha o te poraka (w) = mg = (8)(10) = 80 Newton
Hara 37^o = 0,6
Kohinga 37^o = 0,8
Tauwehenga o te waku nekeneke (µ)_k) = 0,1
I pātaihia : Te kaha o waho iti rawa (F) e pupuri ana i te poraka kia kore ai e paheke ki raro
Whakautu :
Kāore te poraka e paheke ki raro mēnā F = w_x
Te wāhanga o te kaha ā-papa e whakarara ana ki te papa whakarara :
w_x = w hara θ = (80)(hara 37) = (80)(0,6) = 48
f_k = µ_k N = (0,1)(64) = 6,4
Te kaha iti rawa F kia kore ai te poraka e paheke ki raro :
F + f_k - w_x = 0
F = w_x - f_k = 48 – 6,4 = 41,6 Nītona

7.
Ka kumea tētahi mea he 5,0 kg te taumaha e te taura ki runga i tētahi papa whāiti taratara mā te kaha o te 71 N (g = 10 m s ).^-2, hara 37^o = 0,6, cos 37^o = 0,8). Mena ko te tauwehenga o te waku i waenga i te mea me te papa he 0,4, ko te whakaterenga e pā ana ki te mea ko…
A. 0,5 ms^-2
B. 2 ms^-2
C. 2,5 ms^-2
D. 3 ms^-2
E. 5 ms^-2
Kōrero
E mōhiotia ana :
Papatipu o te mea (m) = 5 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s²
Taumaha o te taonga (w) = mg = (5)(10) = 50 Newton
Te Kaha F = 71 Newton
Hara 37^o = 0,6
Kohinga 37^o = 0,8
Tauwehenga o te waku = 0,4
I pātaihia Te whakaterenga o te mea (a)
Whakautu :
Te Kaha Hua
Tuatahi, tatauhia te kaha hua e pā ana ki te mea.
Te wāhanga o te kaha ā-papa e whakarara ana ki te papa whakarara :
w_x = w hara θ = (50)(hara 37) = (50)(0,6) = 30
Te wāhanga o te kaha ā-papa e poutū ana ki te papa whakarara :
w_y = w cos θ = (50)(cos 37) = (50)(0,8) = 40
Te kaha noa :
N = w_y = 40
Te kaha waku nekeneke :
f_k = µ_k N = (0,4)(40) = 16
Te kaha hua e pā ana ki tētahi papa whakarara:
∑F = F – w_x - f_k = 71 – 30 – 16 = 25 Ngā Newton
Te whakaterenga o tētahi mea
Ka tatauhia te whakaterenga o tētahi mea mā te whakamahi i te tātai ture tuarua a Newton:
a = ∑F / m = 25 / 5 = 5 m/s²
Ko te whakautu tika ko E.

8. Tirohia te pikitia! I te tīmatanga ka okioki tetahi poraka, kātahi ka tōia ki runga mā te kaha F e whakarara ana ki te papa piko. Ko te taumaha o te poraka he 2 kg, ko te tauwehenga o te waku pateko = 0,3, ā, ko te koki = 45 ^o . Kia tika ai te neke o te poraka ki runga, ko te kaha F me… g = 10 m/s ²

Kōrero
E mōhiotia ana:
m = 2 kg, karamu = 10 m/s², = 45^o, μ_s = 0,3
Pātai: Kia tika ai te neke o te poraka ki runga, e hia te rahi o te kaha F?
Whakautu:

Ngā Mōhiotanga: F = te kaha kume, w = te kaha ā-papa, w_x = te wāhanga o te taumaha o te poraka e whakarara ana ki te mata o te papa whakarara, w_y = te wāhanga o te taumaha o te poraka e poutū ana ki te mata o te papa whakarara, N = te kaha noa, f_s = te kaha waku pumau.

I roto i te pātai, e mōhiotia ana te tauwehenga o te waku pateko, ko te tikanga he taratara te mata o te papa piko, nō reira he kaha waku e aukati ana i te nekehanga o te poraka.
Kia taea ai e te poraka te neke ake, me ōrite te kaha F ki te w._x +f_sKa neke ake te mea ina nui ake a F i a w_x +f_s.

w = mg = (2)(10) = 20 Ngā Niutona
w_x = w sin 45^o = (20)(½ √2) = 10√2 Ngā Newton
w_y = w cos 45^o = (20)(½√2) = 10√2 Ngā Newton
N = w_y = 10√2
f_s = μ_s N = (0,3)(10√2) = 3√2 Ngā Newton

Kia neke ake ai te poraka:
F = w_x +f_s = 10√2 + 3√2= 13√2 Ngā Newton
Ko te whakautu tika ko C.

9. Kei runga i tētahi papa whakarara te taumaha o tētahi mea, e 2 kg te taumaha, e whakaaturia ana i te pikitia i raro nei. Mēnā ko te tauwehenga o te waku pūmau i waenga i te poraka me te papa whakarara he 0,2√3, ā, ko te g = 10 ms ^–2 , ko te kaha hua e neke ai te mea ko…

Kōrero
E mōhiotia ana:
m = 2 kg, karamu = 10 m/s², = 30^o, μ_s = 0,2√3
I pātaihia: Ko te kaha hua e neke ai tētahi mea?

Whakautu:

Ka ārai tonu te waku i te nekehanga o tētahi mea, nō reira ka whakaaturia te ahunga o te kaha waku he rerekē ki te ahunga o te nekehanga o te mea. E whakaarohia ana kei te neke te mea ki raro, nō reira ka whakaaturia te kaha waku ki runga. E whakaarohia ana kei te neke te mea ki raro nā te mea kāore he kaha e kukume ana i a ia ki runga.
w = mg = (2)(10) = 20 Ngā Niutona
w_x = w sin 30^o = (20)( ½ ) = 10 Newton
w_y = w cos 30^o = (20)( ½ √3) = 10√3 Ngā Newton
N = w_y = 10√3 Nūtene
f_s = μ_s N = (0,2√3)(10√3) = (2)(3) = 6 Ngā Niutoni
Ko te kaha hua e neke ai tētahi mea ko:
F = w_x - f_s = 10 – 6 = 4 Nītona
w_x nui atu i te f_s nō reira ka neke te mea ki raro, i te ahunga o w_x.
Ko te whakautu tika ko A.

Pūtake pātai:

Ngā Pātai Ahupūngao Whakamātautau ā-Motu mō te Kura Tuarua/Kura Tuarua Mahi-ā-ringa