1. Ka heke te tere o tētahi pouaka 2-kg mai i te 10 m/s ki te okioki. Ko te tauwehenga o te waku nekeneke ko te 0.2. Ko te whakaterenga nā te kaha ā-papatipu ko te 10 m/s2 . He aha te rahi o te nekehanga?
Mōhiotia;
Taumaha (m) = 2 kg
Te tere tīmatanga (v o ) = 10 m/s
Te tere whakamutunga (vt ) = 0 m/s
Ko te tauwehenga o te waku nekeneke ( μk ) = 0.2
Taumaha (w) = mg = (1 kg)(10 m/s² ) = 10 kg m/s² = 10 N
E hiahiatia ana: Te rahi o te nekehanga (d)
Rongoā:
Te mātāpono mahi-pūngao mīhini :
W nc = ΔEM
W nc = ΔEK + ΔEP
W nc = ½ m (v t 2 – v o 2 ) + mgh
W nc = te mahi i mahia e te kaha kore-pūmau e pā ana ki te mea
ΔEK = te huringa o te pūngao nekeneke
ΔEP = te huringa o te pūngao pūmanawa
m = papatipu
v = te tere
g = te whakaterenga nā te kaha ā-papa
h = te huringa o te teitei
Ko te panonitanga o te teitei h = 0, nō reira ko ΔEP = 0
W nc = ΔEK
Ngā mahi i mahia e te kaha kore-pūmau:
W nc = -F c d = – μ k N d = – μ k wd = – μ k mgd
W nc = -(0.2)(2)(10)(s)
W nc = – (4)(2)
Ko te tohu tango e tohu ana ko te ahunga o te kaha waku nekeneke he ritenga ke ki te ahunga o te nekehanga.
Te huringa o te pūngao nekeneke:
ΔEK = ½ m (v t 2 – v o 2 ) = ½ (2)(0 – 10 2 ) = 0 – 100 = -100
Te rahi o te nekehanga:
W nc = ΔEK
– 4 hēkona = – 100
s = -100/-4
s = 25 m
[irp]
2. Ka paheke iho tētahi poraka i runga i tētahi papa whakarara. Ko te tauwehenga o te waku nekeneke ko te 0.4. Ko te whakaterenga nā te kaha ā-papa ko te g = 10 ms -2 . Tātaihia te tere whakamutunga ina pā te poraka ki te whenua.
Mōhiotia:
Teitei tīmatanga (h o ) = 6 m
Teitei whakamutunga ( t ) = 0 m
Te tere tīmatanga (v o ) = 0
Ko te tauwehenga o te waku nekeneke ( μk ) = 0.4
Te whakaterenga nā te kaha ā-papa (g) = 10 ms -2
cos θ = 8/10
Ko te wāhanga poutū o te taumaha = w y = w cos θ = mg cos θ = m (10) (8/10) = m (10)(4/5) = m (40/5) = 8 m
Te kaha noa = N = w y = 8 m
Te kaha o te waku nekeneke = f k = μ k N = μ k w y = (0.4)(8 m) = 3.2 m
E hiahiatia ana: Te tere whakamutunga ( vt )
Rongoā:
Te mātāpono mahi-pūngao mīhini:
W nc = Δ EM
W nc = Δ EK + Δ EP
Te huringa o te pūngao nekeneke:
ΔEK = 1/2 m (vt2 -vo2) = 1/2 m (vt2 - 0) = 1/2 mvt2
Te huringa o te pūngao pūmanawa:
Δ EP = mg (h t – h o ) = m (10)(0-6) = m (10)(-6) = – 60 m
Te mahi i mahia e te kaha o te waku nekeneke:
W nc = – f k s = – ( 3.2 m)(10) = – 32 m
Ko te tohu tango e tohu ana ko te ahunga o te kaha o te waku nekeneke he ritenga ke ki te ahunga o te nekehanga.
Ko te tere whakamutunga (vt ) :
W nc = Δ EK + Δ EP
– 32 m = 1/2 mv t 2 – 60 m
– 32 m = m (1/2 v t 2 – 60)
– 32 = 1/2 v t 2 – 60
– 32 + 60 = 1/2 v t 2
28 = 1/2 v t 2
2 (28) = v t 2
56 = v t 2
vt = √4.14
v t = 2 √14 ms -1
[irp]
3. Ka paheke iho tētahi poraka i runga i tētahi papa whakarara. Ko te tere tīmatanga he 0 m/s, ā, ko te tere whakamutunga he 10 ms -1 . Mena ko te kaha o te waku nekeneke he 2 N, ā, ko te whakaterenga nā te kaha ā-papatipu g = 10 ms -2 , he aha te teitei (h)?
Mōhiotia:
Taumaha (m) = 1 kg
Te tere tīmatanga (v o ) = 0 (te okiokinga poraka)
Te tere whakamutunga (vt ) = 10 ms -1
Teitei tīmatanga (h o ) = h
Teitei whakamutunga ( t ) = 0
Te kaha o te waku nekeneke (f k ) = 2 N
Te whakaterenga nā te kaha ā-papa (g) = 10 ms -2
Teitei e hiahiatia ana: Teitei (h)
Rongoā:
Te mahi i mahia e te kaha o te waku nekeneke:
W nc = – f k s = – (2 )(15) = – 30
Ko te tohu tango e tohu ana ko te ahunga o te kaha o te waku nekeneke he ritenga ke ki te ahunga o te nekehanga.
Te huringa o te pūngao nekeneke:
ΔEK = 1/2 m (vt2 -vo2) = 1/2 (1)(102 - 0) = 1/2 (102) = 1/2 (100) = 50
Te huringa o te pūngao pūmanawa:
Δ EP = mg (h t – h o ) = (1)(10)(0-h) = (10)(-h) = -10 h
Te mātāpono mahi-pūngao mīhini:
W nc = Δ EK + Δ EP
– 30 = 50 – 10 hāora
10 hāora = 50 + 30
10 hāora = 80
h = 80/10
h = 8 mita
4. Ki te neke iho tētahi poraka i tētahi papa whāiti, kāti….
A. He nui ake te mahi i mahia e te kaha ā-papa i runga i te poraka i te huringa o te pūngao pūmanawa o te poraka
B. Ka piki ake te pūngao miihini
C. Ka whakaitihia te nui o te pūngao nekeneke me tōna pūngao pūmanawa
D. Ka oti te mahi mā te kaha waku e rite ana ki te huringa o te pūngao nekeneke o te poraka
otinga
He hē a A
Ko te mahi i mahia e te kaha o te papatipu i runga i te poraka he rite ki te huringa o te pūngao pūmanawa papatipu o tētahi poraka.
He hē a B
Mena he maeneene te papa whakarara- c , he pumau tonu te pūngao ā-pūmanawa o te poraka. Ina kei te tihi o te papa whakarara, ā, kāore anō kia neke, he ōrite te pūngao ā-pūmanawa o te poraka ki te pūngao pūmanawa ā-papa. Kei te okioki tonu te poraka, nō reira he kore tōna pūngao nekeneke. Ina neke iho i te papa whakarara, ka whakaitihia te teitei o te poraka, nō reira ka whakaitihia hoki te pūngao pūmanawa ā-papa. Ka heke te pūngao pūmanawa ā-papa nā te mea ka huri ki te pūngao nekeneke. Ahakoa ka huri te pūngao pūmanawa ā-papa ki te pūngao nekeneke, he pumau tonu te pūngao ā-pūmanawa.
Mena he taratara te papa piko, ka heke te pūngao ā-pūkaha o te poraka nā te mahi kino a te kaha waku. He kaha kore-pūmau te kaha waku. Ka heke te pūngao ā-pūkaha o te mea nā te mahi a te kaha kore-pūmau ki runga i tētahi mea.
He tika a C
He taratara te papa piko, nō reira he kaha waku e wero ana i te nekehanga o te poraka. He kaha kore-pūmau te kaha waku. E kī ana te ariā mahi-pūngao mīhini ko te mahi i mahia e te kaha kore-pūmau (hei tauira, te kaha waku) he ōrite ki te huringa o te pūngao mīhini. I tēnei whai, kei te heke te pūngao mīhini.
Ko te pūngao ā-pūkaha o te poraka = te pūngao pūmanawa ā-papa + te pūngao nekeneke.
He hē a D.
Ko te mahi i mahia e te kaha waku i runga i te poraka he rite ki te huringa o te pūngao miihini o te poraka, ehara i te huringa o te pūngao nekeneke o te poraka. He pono kei te wero te kaha waku i te nekehanga o te poraka, ā, ka whakaitihia te tere o te poraka, ka whakaitihia hoki te pūngao nekeneke o te poraka. Engari kia mōhio koe ko te pūngao nekeneke o te poraka i ahu mai i te pūngao pūmanawa ā-papa. Nō reira, he pono te kī ko te mahi i mahia e te kaha waku he rite ki te huringa o te pūngao miihini (ka heke te pūngao miihini).
Ko te whakautu tika ko C.
5. Ka pāngia tētahi mea i runga i te papa taratara, ā, ka neke mō te 3 hēkona, kātahi ka tū. Mena ko te taumaha e mōhiotia ana o te mea he 10 karamu, ko te kaha waku i waenganui i te mea me te papa he 2 kirodina. Tātaihia te mahi i mahia e te kaha waku.
A. 0.18 J
B. -0.18 J
C. 0.36 J
D. -0.36 J
Mōhiotia:
Wā wā (t) = 3 hēkona
Tere whakamutunga (vt ) = 0 m/s (e okioki ana te mea)
Taumaha o te mea (m) = 10 karamu = 10/1000 kg = 1/100 kg = 0.01 kg
Te kaha waku (F) = 2 kirotini = 2 x 10 3 dynes
E hiahiatia ana: Mahi (W) i mahia e te kaha waku
Rongoā:
Te hurihanga o ngā waeine kaha:
1 Newton = 1 x 10 5 dyne
1 tāne = 1 / 10 5 Ngā Newton = 1 x 10 -5 Ngā Newton = 10 -5 Ngā Newton
Te kaha waku (F) = 2 x 10 3 dyne = 2 x 10 3 x 10 -5 Newton = 2 x 10 -2 Newton = 2/100 Newton = 0.02 Newton
E ai ki te ariā mahi-pūngao mīhini, ka mahia te mahi e tētahi kaha kore-pūmau i runga i tētahi mea e ōrite ana ki te huringa o te pūngao mīhini o taua mea.
Ki te neke tetahi mea i runga i te papa whakarara, ko te pūngao ā-pūmanawa (ME) = te pūngao pūmanawa ā-papa (PE) + te pūngao nekeneke (KE). Engari ki te neke noa te mea i runga i te papa whakapae, ā, kāore he huringa teitei, ko te pūngao ā-pūmanawa = te pūngao nekeneke. I runga i te papa whakapae, he kore te pūngao pūmanawa ā-papa nā te mea kāore he huringa teitei.
He kaha kore-pūmau te kaha waku. Ko te tikanga ka whakaitihia e te kaha waku te tere o te mea me te pūngao nekeneke o te mea. Ka taea te whakatau ko te mahi i mahia e te kaha waku ki runga i te mea he rite ki te hekenga o te pūngao miihini.
Pāngarau:
Mahi (W) = Te huringa o te pūngao ā-ringa (ΔEM)
Fs = ΔEP + ΔEK
Fs = mg Δh + ½ m ( vt 2 – vo 2 )
Fs = mg (0) + ½ m (0 2 – v o 2 )
Fs = 0 + ½ m (– (v o 2 ))
F s = – ½ mv o 2 ———— Whārite 1
Whakaahuatanga: F = te kaha waku, d = te nekehanga, m = te papatipu, v = te tere tīmatanga
Kāore anō kia mōhiotia te nekehanga (d) me te tere tīmatanga (v o ) nā te mea ka tatauhia tuatahitia te v o te d rānei. Ko te mahi i mahia e te kaha waku ka tatauhia mā te whakamahi i tētahi o ngā whārite i muri i te mōhiotia o te v o te d rānei.
Ko te whārite o te nekehanga (d) i runga i te nekehanga rārangi kore-taurite:
v t 2 = v o 2 + 2 (-a) s
Ko te tere whakamutunga (vt ) = 0, ā, ko te whakaterenga (a) he tohu kino nā te mea kua whakaroahia te tere o te mea (kua whakaitihia te tere o te mea).
0 = vo2 – 2 ngā pānuitanga
vo2 = 2 pānuitanga
d = v o 2 / 2 a ———— Whārite 2
Hurihia a d i te whārite 2 ki a d i te whārite 1:
F d = – ½ mv o 2
F (v o 2 /2a) = – ½ mv o 2
(F/2a) v o 2 = – ½ mv o 2
F/2a = – ½ m
F = (2)(a)(-1/2)(m)
F = – (a)(m)
a = – (F / m)
a = – 0.02 Ngā Newton / 0.01 kirokaramu
a = – 2 Newton/kirokaramu
a = – 2 m/s 2
Whārite hei tatau i te tere tīmatanga (v o ) i roto i te nekehanga rārangi kore-taurite:
vt = v o + i —–> Tere whakamutunga (v t ) = 0, Whakaterenga (a) = 2 m/s 2 , wā (t) = 3 hēkona
0 = v o + (-2)(3)
0 = v o – 6
v o = 6 mita/hekona
Te mahi (W) i mahia e te kaha waku:
W = – ½ mv o 2 = -1/2 (0.01)(6 2 ) = -1/2 (0.01)(36)
W = -1/2 (0.36)
W = – 0.18 Joule
Ko te mahi i mahia e te kaha waku he tohu kino, arā, ka whakaitihia te pūngao miihini o te mea e te mahi.
Mena e mōhiotia ana ko d, ka taea te tatau i te mahi mā te whakamahi i te whārite o W = F d.
Ko te whakautu tika ko B.
[wpdm_package id='1178′]
- Ngā raruraru me ngā otinga mō te mahi i mahia mā te kaha
- Ngā raruraru me ngā otinga mō te pūngao mahi-nekeneke
- Ngā raruraru me ngā otinga o ngā mātāpono mahi-pūngao miihini
- Ngā raruraru me ngā otinga o te pūngao pūmanawa ā-papa
- Te pūngao pūmanawa o ngā raruraru me ngā otinga o te puna rapa
- Ngā raruraru hiko me ngā otinga
- Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga hinga noa
- Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga ki runga, ki raro hoki i te nekehanga hinga noa.
- Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga i runga i te mata piko
- Te whakamahinga o te tiakitanga o te pūngao miihini mō te nekehanga i runga i te paparangi piko
- Te whakamahinga o te tiaki i te pūngao miihini mō te nekehanga pere
