Misalai 3 na karo mai sassauƙa
1. Abu mai nauyin gram 500 yana tafiya a gudun m/s 10, abu mai nauyin gram 200 kuma yana tafiya a gudun m/s 12. Abubuwa biyu suna tafiya zuwa ga juna kuma suna karo. Idan bayan karo, gudun abu mai nauyin gram 500 ya kai m/s 6, to saurin abu mai nauyin gram 200 shine…
Tattaunawa
An sani :
Nauyin abu 1 (m1) = gram 500 = 0,5 kg
Nauyin abu 2 (m2) = gram 200 = 0,2 kg
Saurin farko na abu na 1 (v)1) = -10 m/s
Saurin farko na abu na 2 (v)2) = 12 m/s
Saurin ƙarshe na abu na 1 (v)1') = 6 m/s
v1 alamar korau da v2 yana da kyau saboda alkiblar abubuwa biyu akasin haka ne.
An tambaya : saurin ƙarshe na abu na 2 (v2')
Jawab :
A cikin karo mara kyau na roba, akasin haka karo na roba wanda ba shi da wani tasiridokar kiyaye makamashin motsi ba ta aiki kuma kawai dokar kiyaye yanayin motsi m.
m1 v1 +m2 v2 = m1 v1'+ m2 v2'
(0,5) (-10) + (0,2) (12) = (0,5) (6) + (0,2) (v)2')
-5 + 2,4 = 3 + 0,2 v2'
-2,6 = 3 + 0,2 v2'
-2,6 – 3 = 0,2 v2'
-5,6 = 0,2 v2'
v2' = -5,6 / 0,2
v2' = -28 m/s
Saurin abu 2 bayan karo (v)2') shine 28 m/s.
v1'yana da kyau kuma v2'ba shi da kyau domin bayan karo, alkiblar abubuwan biyu suna akasin haka. Alamomin da ba su da kyau da kuma na alama suna nuna cewa abubuwa biyu suna tafiya a alkiblar da ba ta dace ba.
2. Abubuwa biyu masu nauyi iri ɗaya suna motsawa zuwa ga juna a layi madaidaiciya, inda saurin abu na 1 shine 6 m/s kuma gudun abu na 2 shine 8 m/s. Idan bayan karo, abu na 2 ya koma hagu a gudun 5 m/s, to girma da alkiblar saurin abu na 1 bayan karo sune...
Tattaunawa
An sani :
Nauyin abu 1 (m1) = m
Nauyin abu 2 (m2) = m
Saurin farko na abu na 1 (v)1) = -6 m/s
Saurin farko na abu na 2 (v)2) = 8 m/s
Saurin ƙarshe na abu na 2 (v)2') = 5 m/s
An tambaya : girma da alkiblar saurin abu 1 bayan karo
Jawab :
Tsarin dokar kiyaye ƙarfin motsi :
m1 v1 +m2 v2 = m1 v1'+ m2 v2'
mv1 + mv2 = mv1'+ mv2'
m (v)1 +v2) = m (v1'+ v2')
Yawan abubuwa biyu iri ɗaya ne, don haka an cire m daga lissafin:
v1 +v2 = v1'+ v2'
-6 + 8 = v1' + 5
2 – 5 = v1'
v1' = -3 m/s
Saurin abu 1 bayan karo (v)1') shine 3 m/s. Alamar mara kyau tana nuna cewa alkiblar motsi na abu 1 yana akasin alkiblar motsi na abu 2. Idan bayan karo abu 2 ya koma dama, to abu 1 ya koma hagu. Haka nan, idan kafin karo abu 2 ya koma hagu, to abu 1 ya koma dama.
3. Kwallon 1 mai nauyin kilogiram 1 da ƙwallon 2 mai nauyin kilogiram 2 suna tafiya a hanya ɗaya kuma suna karo a cikin yanayin da ba ya sassautawa. Kafin karo, ƙwallon 1 tana motsawa a gudun mita 10/s kuma ƙwallon 2 tana motsawa a gudun mita 5/s. Kayyade saurin ƙwallon 1 bayan karo idan saurin ƙwallon 2 bayan karo ya kai mita 4/s.
Tattaunawa
An sani :
Nauyin ƙwallon 1 (m)1) = 1 kg
Nauyin ƙwallon 2 (m)2) = 2 kg
Saurin farko na ƙwallon 1 (v)1) = 10 m/s
Saurin farko na ƙwallon 2 (v)2) = 5 m/s
Saurin ƙarshe na ƙwallon 2 (v)2') = 4 m/s
Duk abubuwa biyu suna motsawa a hanya ɗaya don gudun ya sami alama iri ɗaya (wanda aka zaɓa mai kyau).
An tambaya : saurin ƙarshe na ƙwallo 1 (v1')
Jawab :
m1 v1 +m2 v2 = m1 v1'+ m2 v2'
(1)(10) + (2)(5) = (1)(v)1') + (2)(4)
10 + 10 = v1' + 8
20 – 8 = v1'
v1' = 12 m/s
Gudun ƙwallon 1 bayan karo shine 12 m/s.
