Haɗari - matsaloli da mafita
1. Abu A (3 kg) yana motsawa a gudun 8 m/s kuma abu B (5 kg) yana motsawa a gudun 4 m/s. Idan karo tsakanin abubuwan A da B yana da cikakkiyar roba, menene saurin abubuwa A da B bayan karo?
An sani:
Nauyin abu A (m 1 ) = 3 kg
Nauyin abu B (m2 ) = 5 kg
Saurin abu A (v 1 ) = 8 ms –1
Gudun abu B (v 2 ) = 4 ms –1
Ana so: v 1 'da v 2 '
Magani:
Idan duka abubuwa biyu suna da nauyin da ya bambanta kuma ba a san saurin dukkan abubuwa biyu bayan karo ba tukuna, to ana ƙididdige saurin bayan karo ta amfani da wannan lissafi:
Alkiblar dukkan abubuwa guda biyu iri ɗaya ce ta yadda saurin dukkan abubuwa biyu yana da alama iri ɗaya. Idan duka abubuwa biyu suna tafiya a alkibla daban-daban to saurin ɗaya yana da alamar ƙari ɗaya kuma saurin yana da alamar ragewa.
Saurin abu A (v A ) bayan karo:
Saurin abu B (v B ) bayan karo:
Gudun abu A (v 1 ') bayan karo shine 3 m/s kuma gudun abu B (v 2 ') bayan karo shine 7 m/s.
2. Kwallo tana da ƙarfin motsi na P, tana karo da bango kuma tana nuna kanta. Haɗarin yana da cikakkiyar laushi kuma alkiblarsa tana daidai da bango. Menene canjin ƙarfin motsi na ƙwallon?
An sani:
Nauyin ƙwallon = m
Saurin ƙwallon kafin karo = v
Gudun ƙwallon bayan karo = -v (ƙwallon ya nuna hagu)
Motsin ƙwallon kafin karo (p o ) = mv
Motsin ƙwallon bayan karo (p t ) = m (-v) = – mv
Ana so: Sauyin motsin ƙwallon
Magani:
Canjin ƙarfin lantarki:
Δp = p t – p o
Δp = – mv – mv
Δp = – 2 mv
Δp = -2p
Alamar da aka rage tana nuna alkiblar ƙwallon.
3. Abubuwa biyu, A da B, suna da irin wannan motsi a akasin alkibla kuma suna karo da juna. A yana tafiya gabas da saurin V da B yana tafiya yamma da gudun 2V. Idan karo ya yi daidai da na roba, to menene saurin abubuwan biyu bayan karo.
An sani:
Dukansu abubuwa suna da nauyi iri ɗaya.
A yana tafiya gabas da saurin V
B yana tafiya yamma da saurin 2V
Ana so: Saurin abubuwa biyu bayan karo
Magani:
Idan duka abubuwa biyu suna da nauyi iri ɗaya kuma karo ya yi daidai da na roba, to bayan karo, dukkan abubuwa biyu suna canza saurinsu.
Bayan karo, A ta matsa yamma a 2V, B kuma ta matsa gabas a V.
4. Abubuwa biyu masu nauyi iri ɗaya suna tafiya tare da layi madaidaiciya a cikin kwatance daban-daban kamar yadda aka nuna a cikin hoton da ke ƙasa. Idan saurin abu na 2 bayan karo (v 2 ') ya kai 5 m/s zuwa dama, to menene girman saurin abu na 1 bayan karo.
An sani:
Nauyin kowane abu = m
Gudun abu 1 kafin karo (v 1 ) = 8 m/s
Saurin abu na 2 bayan karo (v 2 ) = 10 m/s
Gudun abu na 2 bayan karo (v 2 ') = 5 m/s
Ana nema: Saurin abu na 1 bayan karo (v 1 ')
Magani:
Karo ne da wani ɓangare na roba.
m 1 v 1 + m 2 v 2 = m 1 v 1 '+ m 2 v 2 '
m (v 1 + v 2 ) = m (v 1 '+ v 2 ')
v 1 + v 2 = v 1 ' + v 2 '
8 + 10 = v 1 ' + 5
18 = v 1 ' + 5
v 1 ' = 18-5
v 1 ' = 13 m/s
karo mara sassauƙa
5. Harsashi mai nauyin gram 10 da aka harba a 100 ms -1 , ya yi karo da wani tubalin itace a lokacin da yake hutawa. Nauyin tubalin shine gram 490. Hatsarin ba shi da ƙarfi. Menene saurin tubalin da harsashi bayan hatsarin.
An sani:
nauyin harsashi (m 1 ) = gram 10
Gudun harsashi (v 1 ) = 100 m/s
Nauyin tubali (m2 ) = gram 490
Gudun toshewa (v 2 ) = 0 m/s (toshewa a lokacin hutawa)
Ana Neman: Saurin toshewa da harsashi bayan karo
Magani:
m 1 v 1 + m 2 v 2 = (m 1 + m 2 ) v'
(10) (100) + (490) (0) = (10 + 490) v'
1000 + 0 = 500 v'
1000 = 500 v'
v' = 1000/500
v' = 2 m/s
6. Babbar mota da ke tafiya a gudun mita 10/s ta yi karo da wata mota da ke tafiya a gudun mita 20/s. Bayan hatsarin, babbar mota da wata mota suna tafiya tare a gudun iri daya. Nauyin babbar mota shine kilogiram 1400 kuma nauyin motar shine kilogiram 600. Menene saurin babbar mota da mota bayan karo.
An sani:
gudun babbar mota (v 1 ) = 10 m/s
gudun mota (v 2 ) = 20 m/s
nauyin babbar mota (m 1 ) = 1400 kg
Nauyin mota (m2 ) = 600 kg
Ana Neman: Saurin motar da kuma gudun bayan karo
Magani:
m 1 v 1 + m 2 v 2 = (m 1 + m 2 ) v
(1400) (10) + (600) (20) = (1400 + 600) v
14000 + 12000 = 2000 v
26000 = 2000 v
v = 13m/s
7. Harsashi mai nauyin gram 20 yana tafiya a gudun mita 10/s a kwance, yana karo da wani tubali mai nauyin gram 60 da ke kan bene. Bayan karo, harsashi da tubali suna tafiya tare da gudu iri ɗaya da alkibla iri ɗaya. Menene saurin harsasai da tubalan duka.
An sani:
Nauyin harsashi (mP ) = gram 20 = 0.02 kg
Nauyin tubalin (m B ) = gram 60 = 0.06 kg
Saurin farko na harsashi (v P ) = 10 m/s
Saurin farko na tubalan (v B ) = 0
Ana Neman: Saurin harsashi da toshewa bayan karo (v')
Magani:
Karo ba shi da ƙarfi.
m P v P + m B v B = (m P + m B ) v'
(0.02) (10) + (0.06) (0) = (0.02 + 0.06) v'
0.2 + 0 = 0.08 v'
0.2 = 0.08 v'
v' = 0.2/0.08
v' = 2.5 m/s
8. Abubuwa biyu, A da B, suna da nauyin iri ɗaya = 1.5 kg suna kusantar juna kuma suna karo. Gudun abu A (v A ) = 4 m/s da saurin abu B (v B ) = 5 m/s. Idan karo ba shi da ƙarfi, menene saurin abu biyu bayan karo.
An sani:
Nauyin abu A (mA ) = 1.5 kg
Nauyin abu B (m B ) = 1.5 kg
Gudun abu A kafin karo (v A ) = 4 m/s (positive zuwa dama)
Gudun abu B kafin karo (v B ) = -5 m/s (taɓawa daga hagu)
Ana Neman: Saurin abubuwa biyu bayan karo
Magani:
m A v A + m B v B = (m A + m B ) v'
(1.5)(4) + (1.5)(-5) = (1.5 + 1.5) v'
6 – 7.5 = (3) v'
-1.5 = (3) v'
v' = -1.5 / 3
v' = -0.5 m/s
Alamar da aka rage tana nuna cewa bayan karo, duka abubuwa suna tafiya hagu, alkibla ɗaya da abu B.
- Menene karo a cikin mahallin kimiyyar lissafi? Amsa: A fannin kimiyyar lissafi, karo yana nufin wani abu inda abubuwa biyu ko fiye suka yi mu'amala da juna, yawanci suna yin amfani da karfi a kan juna, wanda ke haifar da musayar kuzari da karfin aiki.
- Ta yaya karo na roba da na inelastic suka bambanta? Amsa: A cikin karo na roba, ana adana kuzarin motsi da kuzarin motsi. A cikin karo na inelastic, ana adana kuzarin motsi, amma kuzarin motsi ba haka bane. Cikakkun karo na inelastic wani yanki ne inda abubuwan da suka haɗu suka manne tare bayan karo.
- Me yasa ake kiyaye ƙarfin motsi a duk lokacin karo? Amsa: Momentum yana kiyayewa a lokacin karo saboda kiyaye ka'idar momentum, wanda ke nuna cewa jimlar momentum na tsarin rufewa yana nan daram sai dai idan ƙarfin waje ya yi aiki da shi.
- Shin makamashin motsi koyaushe ana adana shi a lokacin karo? Amsa: A'a, makamashin motsi yana adanawa ne kawai a cikin karo na roba. A cikin karo na inelastic, wasu daga cikin makamashin motsi suna canzawa zuwa wasu nau'ikan makamashi, kamar kuzari mai yuwuwa, sauti, ko zafi.
- Me yasa motoci biyu za su iya mannewa tare bayan karo? Amsa: Idan motoci biyu suka manne tare bayan karo, misali ne na karo mara sassauƙa. Motocin suna kasancewa tare saboda haɗin gwiwar injina, nakasa, ko wasu ƙarfi da suka shawo kan ikonsu na sake dawowa daga juna.
- Shin abu da ke fuskantar karo zai iya fuskantar canjin kuzarin motsi koda kuwa saurinsa bai canza ba? Amsa: Eh, idan abu ya canza alkiblarsa yayin karo amma ba saurinsa ba, saurinsa (yawan vector) yana canzawa, amma saurinsa (yawan scalar) yana nan iri ɗaya. Duk da cewa girman kuzarin motsi (ya danganta da saurin) bazai canza ba, abin ya sami canji a rarrabawar makamashi.
- Me yasa kwallayen billiard ke tashi sama da juna idan suka yi karo? Amsa: Kwallayen wasan biliyard suna fuskantar kusan karo mai laushi. Idan kwallo ɗaya ta bugi wata, kuzarin motsi da ƙarfin motsi suna canjawa, wanda ke sa kwallayen su yi tsalle. Tsarin da kayan ƙwallon biliyard suna sa su zama masu inganci wajen adana kuzarin motsi a cikin waɗannan hulɗar.
- Idan abubuwa biyu masu taro daban-daban suka haɗu suka manne tare, shin haɗin gwiwar saurinsu zai zama matsakaicin saurin farko? Amsa: Ba lallai ba ne. Haɗakar gudu zai dogara ne akan dokar kiyaye ƙarfin motsi. Idan abu ɗaya ya fi ɗayan girma, haɗin gudu zai kusa da saurin farko na abu mafi girma.
- A zahirin duniya, akwai karo-karo na "lalacewa" da gaske? Amsa: A aikace, babu wani karo da yake da cikakkiyar roba. Duk da cewa wasu karo, kamar waɗanda ke tsakanin ƙwallon biliyard, suna kusantowa, akwai wani kuzari da ke ɓacewa ga wasu siffofi, kamar sauti ko zafi.
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Ta yaya jakar iska ke rage tasirin karo a cikin hatsarin mota? Amsa : Jakunkunan iska suna ƙara lokacin da ƙarfin mutum ke ɗauka don canzawa lokacin karo. Ta hanyar yin hakan, ƙarfin da mutumin ya samu (wanda ya yi daidai da lokacin da ƙarfin ya canza) yana raguwa, wanda ke rage yiwuwar rauni.
