Motsin faɗuwa kyauta - matsaloli da mafita
1. Dutse yana faɗuwa cikin sauƙi daga tsayin mita 45. Idan saurin da aka samu sakamakon nauyi ya kai 10 ms -2 , menene saurin dutsen idan ya faɗi ƙasa?
An sani:
Tsawo (h) = mita 45
Saurin gudu saboda nauyi (g) = 10 m/s 2
Ana so: Saurin ƙarshe na dutsen lokacin da ya faɗi ƙasa (v t )
Magani:
Daidaiton motsi na faɗuwa kyauta :
v t 2 = 2 gh
Saurin ƙarshe na dutsen:
v t 2 = 2 (10)(45) = 900
v t = √900 = 30 m/s 2
2. Wani abu da babu shi yana faɗuwa daga tsayi ba tare da saurin farko ba. Abu ya bugi ƙasa bayan daƙiƙa 2. Saurin da aka samu sakamakon nauyi shine 10 ms -2 . Ƙayyade tsayi
An sani:
Tazarar lokaci (t) = daƙiƙa 2
Saurin gudu saboda nauyi (g) = 10 m/s 2
Ana so: Tsawo (h)
Magani:
Daidaiton motsi na faɗuwar 'free fall':
h = ½ gt 2
Height:
h = ½ (10)(2) 2 = (5)(4) = mita 20
3. Faɗuwar abu mai nauyin kilogiram 2 daga tsayin mita 20 a sama da ƙasa. Menene tazara tsakanin lokacin da abu ke cikin iska? Saurin gudu saboda nauyi shine 10 ms -2
An sani:
Tsawo (h) = mita 20
Saurin gudu saboda nauyi (g) = 10 m/s 2
Ana so : Tazarar lokaci (t)
Magani:
Daidaiton motsi na faɗuwar 'yanci:
h = ½ gt 2
Tazarar lokaci:
20 = ½ (10)(t 2 )
20 = (5)(t 2 )
20/5 = t 2
4 = t 2
t = √4
t = daƙiƙa 2
4. Abubuwa biyu, abu na 1 da abu na 2, suna faɗuwa daga tsayin h 1 da h 2 a lokaci guda. Idan h 1 : h 2 = 2: 1, menene rabon tazara tsakanin abu na 1 da abu na 2.
An sani:
Tsayin abu 1 (h 1 ) = 2
Tsayin abu 2 (h 2 ) = 1
Saurin gudu saboda nauyi = g
Ana so : t 1 : t 2
Magani:
Abu na 1:
h 1 = 1/2 gt 1 2
2 = 1/2 = 1 2
(2)(2) = gt 1 2
4 = gt 1 2
4/g = t 1 2
t 1 = √4/g
Abu na 2:
h 2 = 1/2 gt 2 2
1 = 1/2 = 2 2
(2)(1) = gt 2 2
2 = gt 2 2
2/g = t 2 2
t 2 = √2/g
Rabon tazara tsakanin lokaci:
t 1 : t 2
√4/g: √2/g
(√4/g) 2 : (√2/g) 2
4/g: 2/g
4: 2
2: 1
5. Wani abu ya faɗi daga tsayin h a sama da ƙasa. Saurin ƙarshe lokacin da abin ya bugi ƙasa shine m10/s. Menene tazara tsakanin lokacin da za a kai ½ h a sama da ƙasa. Saurin da aka samu sakamakon nauyi shine m10/s 2.
An sani:
Saurin ƙarshe (v t ) = 10 m/s
Saurin gudu saboda nauyi (g) = 10 m/s 2
Ana so: Tazarar lokaci zuwa 1/2 awa sama da ƙasa
Magani:
Tsawon h:
v t 2 = 2 gh
10 2 = 2 (10) h
100 = awanni 20
h = 100/20
h = mita 5
Tsawon awa 1/2 = rabi (mita 5) = mita 2.5. Lokacin da ake buƙata don isa mita 2.5 sama da ƙasa:
h = 1/2 gt 2
2.5 = 1/2 (10) t 2
2.5 = 5 t 2
t 2 = 2.5 / 5 = 0.5 = (0.25)(2)
t = √(0.25)(2) = 0.5√2 = 1/2 √2 daƙiƙa
6.
Motsin faɗuwa kyauta na kwakwa ( hoto na 1 ) da kuma motsin ƙwallon da aka jefa a tsaye zuwa sama zuwa mafi girman matsayi t ta ɗalibi (hoto na 2). Kayyade nau'in motsi biyu.
Magani:
Siffa ta 1 = motsi na faɗuwa kyauta = Hanzari
Hoto na 2 = motsi a tsaye = Rage gudu
Amsar da ta dace ita ce A.
7. Dutse ya faɗi daga gini cikin sauƙi. Lokacin da dutse ke buƙata don isa ƙasa shine daƙiƙa 3 kuma saurin gudu saboda nauyi shine 10 m/s 2. A tantance tsayin ginin.
A. 15 m
B. 20 m
C. mita 30
D. 45 m
An sani:
Tazarar lokaci (t) = daƙiƙa 3
Saurin gudu saboda nauyi (g) = 10 ms -2
Ana nema: Tsawon ginin (h)
Magani:
Sananne: tazara ta lokaci (t) da hanzari saboda nauyi (g), ana so: tsayi (h) don haka yi amfani da lissafin motsi na faɗuwa kyauta: h = ½ gt 2
h = ½ (10)(3)
h = (5)(3)
h = mita 15
Amsar da ta dace ita ce A.
8. 'Ya'yan itace suna faɗuwa daga bishiyarsu a tsayin mita 12 sama da ƙasa. Idan saurin gudu saboda nauyi shine g = 10 m/s 2 kuma an yi watsi da gogayya ta iska, to a tantance tsayin 'ya'yan itacen a sama da ƙasa bayan daƙiƙa 1.
A. 7 m
B. 6 m
C. mita 5
D. 4 m
An sani:
Tsawon itace (h) = mita 12
Saurin gudu saboda nauyi (g) = 10 m/s 2
Tazarar lokaci (t) = daƙiƙa 1
Ana so: Tsawon 'ya'yan itacen da ke sama da ƙasa
Magani:
Bayan daƙiƙa 1, 'ya'yan itacen ba su faɗi ba har zuwa:
h = ½ gt 2 = ½ (10)(1) 2 = (5)(1) = mita 5
Tsawon 'ya'yan itacen sama da ƙasa bayan daƙiƙa 1:
Mita 12 – mita 5 = mita 7
Amsar da ta dace ita ce A.
- Menene motsi na faɗuwa kyauta?
Amsa : Motsin faɗuwa kyauta yana nufin motsin wani abu a ƙarƙashin rinjayar ƙarfin nauyi kawai, ba tare da wani ƙarfi (kamar juriyar iska) da ke aiki a kai ba.
- Ta yaya hanzarin da ake samu saboda nauyi, wanda galibi ake wakilta a matsayin , yana shafar abu mai faɗuwa cikin 'yanci?
Amsa : Duk abubuwan da ke cikin faɗuwar 'yanci kusa da saman Duniya suna fuskantar saurin gudu akai-akai saboda nauyi, , wanda yake kimanin Wannan yana nufin cewa saurin abu yana ƙaruwa da wannan adadin a kowace daƙiƙa ta faɗuwar 'yanci.
- Idan juriyar iska ba ta da yawa, ta yaya nauyin abu ke tasiri ga saurin faɗuwar sa kyauta?
Amsa : Idan babu juriyar iska, nauyin abu ba ya tasiri ga saurin faɗuwarsa kyauta. Duk abubuwa, ba tare da la'akari da nauyinsu ba, za su faɗi da sauri iri ɗaya saboda nauyi, .
- Me yasa 'yan sama jannati ke shawagi a cikin Tashar Sararin Samaniya ta Duniya (ISS) idan har yanzu akwai ƙarfin nauyi a can?
Amsa : 'Yan sama jannati a cikin ISS sun bayyana suna shawagi ba wai saboda babu nauyi ba, amma saboda 'yan sama jannati da ISS suna cikin yanayin faɗuwa kyauta a duniya. A zahiri suna faɗuwa daidai da ISS, suna haifar da jin rashin nauyi.
- Menene bambanci tsakanin nauyi da nauyi a cikin mahallin faɗuwar 'yanci?
Amsa : Tsawa shine ma'aunin adadin abu a cikin abu kuma yana kasancewa daidai ba tare da la'akari da wurin da yake ba. Nauyi, a gefe guda, shine ƙarfin da ake amfani da shi akan abu saboda nauyi. Yana bambanta dangane da filin nauyi. A lokacin faɗuwar 'free fall, abu yana jin rashin nauyi saboda babu wani ƙarfi na yau da kullun da ke aiki a kansa, amma nauyinsa bai canza ba.
- Idan aka jefa abu sama, me zai faru da saurinsa yayin da yake tashi? Kuma me zai faru idan ya fara faɗuwa ƙasa?
Amsa : Idan aka jefa abu sama, yana raguwa a ƙarƙashin tasirin nauyi. Saurinsa yana raguwa har sai ya zama sifili a mafi girman matsayi. Yayin da yake fara faɗuwa ƙasa, yana ƙaruwa saboda nauyi, yana ƙara saurinsa zuwa ƙasa.
- Menene saurin ƙarshe a cikin mahallin faɗuwar 'free fall'?
Amsa : Saurin ƙarshe shine matsakaicin gudu da abu mai faɗuwa zai iya kaiwa lokacin da ƙarfin ƙasa na nauyi ya daidaita ta hanyar ƙarfin juriyar iska zuwa sama. A wannan lokacin, abu ba ya ƙara sauri kuma yana ci gaba da faɗuwa a saurin da ba ya canzawa.
- Ta yaya tsayin da abu ya faɗo daga sama yake tasiri ga lokacin da ake ɗauka kafin a isa ƙasa?
Amsa : Lokacin da abu zai ɗauka kafin ya isa ƙasa daidai yake da tushen murabba'in tsayin da ya faɗo daga ciki (idan ba shi da juriyar iska). Abu da ya faɗi daga wani tsayi mafi girma zai ɗauki lokaci mai tsawo kafin ya isa ƙasa fiye da wanda ya faɗi daga wani tsayi mai guntu.
- Me zai faru da ƙarfin da abu zai iya samu yayin da yake faɗawa ƙarƙashin nauyi?
Amsa : Yayin da abu ke faɗuwa cikin sauƙi a ƙarƙashin nauyi, ƙarfinsa (idan aka kwatanta da ƙasa) yana raguwa. Wannan raguwar ƙarfinsa yana canzawa zuwa kuzarin motsi, wanda ke sa saurin abu ya ƙaru.
- Idan aka jefar da abubuwa biyu masu siffofi daban-daban amma nauyi ɗaya daga tsayi ɗaya a cikin wani wuri mai tsabta, wa zai fara faɗowa ƙasa?
Amsa : A cikin wani wuri mai duhu, inda babu juriyar iska, dukkan abubuwa biyu za su faɗi ƙasa a lokaci guda. Siffarsu ba za ta yi tasiri ba domin nauyi ne kawai ke aiki a kansu, kuma nauyinsu iri ɗaya ne.
