5 Ngā Tauira o ngā Tukinga Ā-kore-whakapūmau
1. Ka pā tētahi matā he 30 karamu te taumaha e neke ana i te tere o te 30 m/s ki tētahi poraka rakau he 1 kg te taumaha e takoto kau ana. Tātaihia te tere o te poraka mēnā kua mau te matā ki roto i te poraka!
Kōrero
E mōhiotia ana :
Te taumaha o te matā (m1) = 30 karamu = 0,03 kg
Te taumaha o te poraka (m2) = 1 kirokaramu
Te tere tīmatanga o te matā (v1) = 30 m/s
Te tere tīmatanga o te poraka (v2) = 0 (poraka tūmau)
I pātaihia : te tere o te matā me te poraka i muri i te tukinga (v')
Whakautu :
Tātai te ture tiaki o te nekehanga mēnā ka piri ngā mea e rua i muri i te tukinga:
m1 v1 +m2 v2 = (m1 +m2) v'
(0,03)(30) + (1)(0) = (0,03 + 1) v'
0,9 + 0 = 1,03 v'
0,9 = 1,03 v'
v' = 0,9 / 1,03
v' = 0,87 m/s
Ko te tere o te matā me te poraka i muri i te tukinga he 0,87 m/s.
2. E 2 kg te taumaha o ia mea A me B, ā, e neke ana tetahi ki tetahi i te tere o te v.A = 6 ms-1 me te vB = 4 ms-1. Mēnā ko ngā mea e rua tukinga kore-whakapūmau tino, kātahi ko te tere o ngā mea e rua i muri i te tukinga ko...
Kōrero
E mōhiotia ana :
Papatipu o te mea A (mA) = 2 kirokaramu
Papatipu o te mea B (mB) = 2 kirokaramu
Ko te tere tīmatanga o te mea A (vA) = -6 m/s
Te tere tīmatanga o te mea B (v)B) = 4 m/s
I pātaihia : te tere o ngā mea e rua i muri i te tukinga (v')
Whakautu :
mA vA +mB vB = (mA' + mB) v'
(2)(-6) + (2)(4) = (2 + 2) v'
-12 + 8 = 4 v'
-4 = 4 v'
v' = -4 / 4
v' = -1 m/s
Ko te tere o ngā mea e rua i muri i te tukinga he 1 m/s.
3. E rua ngā mea he m te taumaha o ia mea1 = 3 kg me te m2 = 4 kg e neke ana i ngā ahunga rerekē tetahi ki tetahi i te tere v1 = 10 m/s me v2 = 12 m/s. Ka tukinga ngā mea e rua, ā, i muri i te tukinga ka piri tahi rāua. Ko te tere o ngā mea e rua i muri i te tukinga ko…
Kōrero
E mōhiotia ana :
Papatipu o te mea 1 (m1) = 3 kirokaramu
Papatipu o te mea 2 (m2) = 4 kirokaramu
Te tere o te mea 1 (v1) = -10 m/s
Te tere o te mea 2 (v2) = 12 m/s
I pātaihia : tere ngā mea e rua i muri i te tukinga (v')
Whakautu :
m1 v1 +m2 v2 = (m1' + m2) v'
(3)(-10) + (4)(12) = (3 + 4) v'
-30 + 48 = 7 v'
18 = 7 v'
v' = 18 / 7
v' = 2,6 m/s
Ko te tere o ngā mea e rua i muri i te tukinga he 2,6 m/s.
4. I pāngia tētahi waka sedan e tētahi pahi e tere ana i te tere o te 36 km/haora. I muri i te tukinga, ka tukinga te waka sedan me te pahi tetahi ki tetahi. Mena he 2000 kg te taumaha o te pahi, ā, he 1000 kg te taumaha o te waka sedan, he aha te tere o ngā waka e rua i muri i te tukinga?
A. 3,45 m/s
B. 4,67 m/s
C. 5,45 m/s
D. 6,67 m/s
E. 7,67 m/s
Kōrero:
E mōhiotia ana :
v pahi = 36 km/h = 36000 m/3600 s = 10 m/s
m pahi = 2000 kg
v sedan = 0
m sedan = 1000 kg
I pātaihia :
Te tere o te sedan me te pahi i muri i te tukinga (v')?
Whakautu :
m 1 v 1 + m 2 v 2 = (m 1 + m 2 ) v'
(2000)(10) + (1000)(0) = (2000 + 1000) v'
20.000 = 3000 v'
v' = 20.000 / 3000 = 6,67 m/s
Ko te whakautu tika ko D.
5. E tere ana tētahi matā 20 karamu i te tere o te 100 m/s ki tētahi poraka rakau tūmau, ā, ka mau ki roto. Mena he 500 karamu te taumaha o te poraka rakau, he aha te tere o te poraka rakau me te matā i muri tonu i te tukinga?
A. 1,50 m/s
B. 2,55 m/s
C. 3,85 m/s
D. 4,75 m/s
E. 5,65 m/s
Kōrero:
E mōhiotia ana :
m matā = 20 karamu = 0,02 kg
v matā = 100 m/s
poraka m = 500 karamu = 0,5 kg
poraka v = 0
I pātaihia :
Te tere o te matā me te poraka i muri tonu i te tukinga (v')?
Whakautu :
m 1 v 1 + m 2 v 2 = (m 1 + m 2 ) v'
(0,02)(100) + (0,5)(0) = (0,02 + 0,5) v'
2 + 0 = 0,52 v'
2 = 0,52 v'
v' = 2 / 0,52 = 3,85 m/s
Ko te whakautu tika ko C.
