9 Ngā Tauira o Ngā Pātai Pakihi
1. Ka pāngia tētahi poraka e te kaha o te 20 Newtons tae noa ki te neke o te poraka ki te tawhiti o te 2 mita. Ko te mahi i mahia e te kaha F ki runga i te poraka ko…
Kōrero
E mōhiotia ana :
Te kaha (F) = 20 N
Nekehanga (s) = 2 mita
Koki = 0 (he rite te ahunga o te kaha ki te ahunga o te nekehanga, ka ōrite rānei te ahunga o te kaha ki te ahunga o te nekehanga kia kore ai te koki i hangaia e te kaha me te nekehanga)
I pātaihia Ngā Mahi (W)
Whakautu :
Tuhipoka:
Mena he rite te ahunga o te kaha ki te ahunga o te nekehanga, tatauhia te mahi mā te whakamahi i te tātai W = F s, me te kore e hiahiatia te tāpiri i te cos tit.
2. Kei te tū tonu tētahi mea i runga i tētahi mata papa maeneene. Ka pāngia te mea e te kaha F = 10 N, ka hanga he koki 30o ki te mata o te papa. Mēnā ka neke te mea mō te 1 mita, e hia te mahi ka mahia e te kaha F ki runga i te mea?
Kōrero
E mōhiotia ana :
Te Kaha (F) = 10 Newton
Te kaha i te ahunga o te nekehanga (Fx) = F cos 30o = (10)(0,5√3) = 5√3 Ngā Newton
Nekehanga (s) = 1 mita
I pātaihia : te kaha (W) ?
Whakautu :
W = Fx s = (5√3)(1) = 5√3 Joule
3. Ka taka noa tetahi mea he 1 kg te taumaha mai i te teitei o te 2 mita. Mena ko te whakaterenga nā te kaha ā-papa he 10 m/s2, tautuhia te mahi i mahia e te kaha ā-papa i runga i te mea!
Kōrero
E mōhiotia ana :
Papatipu o te mea (m) = 1 kg
Teitei (h) = 2 mita
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s2
I pātaihia Te mahi i mahia e te kaha ā-papa i runga i tētahi mea (W)
Whakautu :
Ko te ahunga o te kaha ā-papa, te taumaha rānei (w) kei raro poutū, ko te ahunga o te nekehanga (s) o te mea kei raro poutū hoki kia rite te ahunga o te kaha ā-papa ki te nekehanga o te mea.
W = F s = wh = mgh
W = (1)(10)(2) = 20 Joule
4. Kei te whakairihia he puna ki te kawenga he 1 kg te taumaha kia piki ake te roa o te puna ki te 2 cm. Mena ko te whakaterenga nā te kaha ā-papatipu he 10 m/s2, whakatau (a) te pūmau puna (b) te mahi i mahia e te puna ki runga i te kawenga
Kōrero
E mōhiotia ana :
Taumaha (m) = 1 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s2
Te pikinga o te roa o te puna (x) = 2 cm = 0,02 mita
I pātaihia : te pūmau puna me te mahi i mahia e te kaha puna
Whakautu :
(a) Pūmau puna
Te tauira ture a Hooke :
F = kx.
Whakahurihia tēnei tātai hei tatau i te pūmau puna:
k = F / x = w / x = mg / x
k = (1)(10) / 0,02 = 10 / 0,02
k = 500 Newton/mita
(b) Te mahi i mahia e te kaha o te puna
W = – ½ kx2
W = – ½ (500)(0,02)2
W = – (250)(0,0004)
W = -0,1 Joule
He kino te mahi i mahia e te kaha o te puna ki runga i te kawenga nā te mea he rerekē te ahunga o te kaha o te puna ki te ahunga o te nekehanga o te kawenga.
5. Ka whakaterea te pouaka kei runga tonu i te papa me te kaha o te 10 N kia neke ai te pouaka i te tawhiti o te 2 mita. Mena kei te ahunga ōrite te kaha pana ki te nekehanga o te pouaka, ā, ka pāngia te pouaka e te kaha waku nekeneke o te 2 Newton, ko te mahi katoa i mahia ki te pouaka ko...
Kōrero
E mōhiotia ana :
Te Kaha (F) = 10 Newton
Te kaha waku nekeneke (F)k) = 2 Niutona
Nekehanga (s) = 2 mita
I pātaihia Te whakapau kaha katoa (Wkatoa)
Whakautu :
Te mahi i mahia mā te kaha (F):
W1 = F s cos 0 = (10)(2)(1) = 20 Joule
Ko te mahi i mahia e te kaha waku nekeneke (Fk):
W2 =Fk s = (2)(2)(cos 180) = (2)(2)(-1) = -4 Joule
Ko te whakapau kaha katoa:
Wkatoa =W1 - W2
Wkatoa = 20 - 4
Wkatoa = 16 Joule
6. Kei te 10 mita te teitei o tētahi mea he 5 kg te taumaha i runga ake i te mata o te Ao. Ko te whakaterenga nā te kaha ā-papa he 10 m/s -2 . Ko te nui o te mahi e hiahiatia ana hei neke i te mea ki te teitei o te 15 mita i runga ake i te mata o te Ao ko...
A. . 75 Joule
B. . 250 Joule
C. . 500 Joule
D. . 750 Joule
E. 1.250 Joule
Kōrero
E mōhiotia ana:
Papatipu o te mea (m) = 5 kg
Teitei (h) = 10 mita
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Pātai: Te kaha ki te neke i tētahi mea ki te teitei o te 15 mita
Whakautu:
Ko te kaha ki te neke i tētahi mea he ōrite ki te kaha ā-papa e pā ana ki taua mea.
Ko te tātai mō te mahi i mahia e te kaha o te papatipu:
W = wh = mgh
Whakaahuatanga: W = kaha, w = kaha ā-papatipu, h = teitei, m = papatipu, g = whakaterenga ā-papatipu
Ko te tātai mō te mahi i mahia ko:
W = wh = mgh = (5 kg)(10 m/ s² )(10 m) = 500 kg m² / s² = 500 Joule
Ko te whakautu tika ko C.
7. E neke ana tētahi mea he 2 kg te taumaha i runga i tētahi mata maeneene i te tere o te 2 m/s –1 . I muri tata iho, ka neke te mea i te tere o te 5 m/s –1 . Ko te mahi i mahia ki te mea i roto i tēnei wā ko…
A. 4 Joules
B. 9 Joules
C. 15 Joule
D. 21 Joule
E. 25 Joule
Kōrero
E mōhiotia ana:
Papatipu o te mea (m) = 2 kg
Te tere tīmatanga (v o ) = 2 ms –1
Te tere whakamutunga (vt ) = 5 ms –1
Pātai: Te mahi i mahia ki te mea i roto i te wā
Whakautu:
E ai ki te ariā pūngao mahi-nekeneke, ko te katoa o te mahi i mahia ki tētahi mea he rite ki te huringa o te pūngao nekeneke o te mea. Mā te pāngarau:
W = ΔEK = EK 2 – EK 1 = 1/2 mv t 2 – 1/2 mv o 2 = 1/2 m (v t 2 – v o 2 ) = 1/2 (2)(5 2 -2 2 ) = (1)(25-4) = 21 Joules
8. He tēpu he 10 kg te taumaha e takoto ana i runga i te papa maeneene, ka panaia mō te 3 hēkona, ā, ka neke i te rārangi tika me te whakaterenga o te 2 m s −2 . Ko te nui o te mahi i mahia ko…
A. 20 Joules
B. 30 Joules
C. 60 Joule
D. 180 Joule
E. 360 Joule
Kōrero
E mōhiotia ana :
Taumaha (m) = 10 kg
Tere tīmatanga (v o ) = 0 (i te tīmatanga ka tū te tēpu)
Wā wā (t) = 3 hēkona
Whakaterenga (a) = 2 m/s 2
I pātaihia : te kaha (W)?
Whakautu :
Tuatahi, tatauhia te tawhiti i haerea mā te whakamahi i te tātai GLBB:
s = v o t + ½ i te 2 = (0)(3) + ½ (2)(3) 2
s = 0 + (1)(9) = 9
Ngā mahi i mahia i runga i te tēpu:
W = F s = (ma)(s) = (10)(2)(9) = 180 Joule
Ko te whakautu tika ko D.
9. Ka panaia ki runga tētahi poraka he 1,5 kg te taumaha e te kaha pumau F = 15 N i runga i tētahi papa piko e whakaaturia ana i te pikitia. Me kī ko te whakaterenga nā te kaha ā-papa (g) he 10 ms -2 , ā, ko te waku i waenganui i te poraka me te papa piko he kore. Ko te mahi katoa i mahia ki runga i te poraka he…
A. 15 J
B. 30 J
C. 35 J
D. 45 J
E. 50 J
Kōrero
E mōhiotia ana :
Taumaha o te poraka (m) = 1,5 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Taumaha o te poraka (w) = mg = (1,5)(10) = 15 Newton
Te kaha pana (F) = 15 Newton
Pātai : te tapeke o te mahi i mahia ki te poraka (W)?
Whakautu :
E rua ngā kaha e mahi ana i runga i te poraka; te kaha e whakarara ana ki te nekehanga o te poraka, arā, te kaha pana (F) me te taumaha o te poraka e whakarara ana ki te mata o te papa piko (wx ).
Ko te mahi i mahia e te kaha pana ko:
W1 = Fs = (15 N)(2 m) = 30 Nm = 30 Joules
Te mahi i mahia e te kaha ā-papa wx:
W 2 = w x s = (w sin 30 o )(2 m) = (15 N)(1/2)(2 m) = 15 N m = 15 Joules
Te tapeke o ngā mahi i oti i te poraka:
W katoa = W 1 – W 2 = 30 J – 15 J = 15 Joules
Ko te whakautu tika ko A.
