Motsi a tsaye - matsaloli da mafita
1. Kwallo A tana jefawa a tsaye sama da gudun mita 10/s. Bayan daƙiƙa 1, daga wannan matsayi, ana jefa Kwallo B a tsaye sama a kan hanya ɗaya, tare da gudun mita 25/s. Menene tsawon ƙwallon B idan ta haɗu da ƙwallon A.
Magani:
Wajen magance matsalar motsi a tsaye , adadin vector wanda alkiblarsa ta sama ana ba shi alama mai kyau, adadin vector wanda alkiblarsa ta ƙasa ana ba shi alama mara kyau.
An sani:
Saurin farko (v o ) na ƙwallon A = 10 m/s
Tazarar lokaci (t) na ƙwallo A = x
Saurin farko (v o ) na ƙwallon B = 25 m/s
Tazarar lokaci (t) na ƙwallon B = x - 1
Saurin gudu saboda nauyi (g) = -10 m/s 2 (an ba da alamar ragewa saboda alkiblar nauyi tana ƙasa)
Ana so: Tsawon ƙwallon B lokacin da ta haɗu da ƙwallon A (h)
h A = h B
v o t + ½ gt 2 = v o t + ½ gt 2
10x + ½ (-10) x 2 = 25 (x-1) + ½ (-10) (x-1) 2
10x – 5x 2 = 25 (x-1) – 5 (x-1) 2
10x – 5x 2 = 25x – 25 – 5 (x 2 -2x+1)
10x – 5x 2 = 25x – 25 – 5x 2 + 10x – 5
10x – 5x 2 – 25x + 25 + 5x 2 – 10x + 5 = 0
– 5x 2 + 5x 2 + 10x – 25x – 10x + 25 + 5 = 0
10x – 25x – 10x + 25 + 5 = 0
– 25x + 25 + 5 = 0
- 25x + 30 = 0
– 25x = – 30
x = -30/-25
x = daƙiƙa 1.2
Tazarar lokaci ƙwallon A a cikin iska kafin ta haɗu da ƙwallon B = daƙiƙa 1.2
Tazarar lokaci ta ƙwallon B a cikin iska kafin ta haɗu da ƙwallon A = daƙiƙa 1.2 – daƙiƙa 1 = daƙiƙa 0.2.
Tsawon ƙwallon A idan ta haɗu da ƙwallon B:
h = vo t + ½ gt 2 = (10)(1.2) + 1/2 (-10)(1.2) 2 = 12 – 5(1.44) = 12 – 7.2 = mita 4.8 a s
Tsawon ƙwallon B idan ta haɗu da ƙwallon A:
h = vo t + ½ gt 2 = (25)(0.2) + 1/2 (-10)(0.2) 2 = 5 – 5(0.04) = 5 – 0.2 = mita 4.8 a s
1. Tambaya: Me ake nufi da motsi a tsaye?
Amsa: Motsin tsaye yana nufin motsin abu sama ko ƙasa, yawanci ƙarƙashin tasirin ƙarfin nauyi.
2. Tambaya: Ta yaya hanzarin da ke faruwa sakamakon nauyi (g) yake da mahimmanci a cikin motsi a tsaye?
Amsa: Duk abubuwan da ke kusa da saman Duniya suna fuskantar saurin gudu akai-akai, , wanda yake kusan 9.81 m/s² ƙasa.
3. Tambaya: Shin abu zai iya samun saurin farko a motsi a tsaye?
Amsa: Eh, abubuwa na iya samun saurin farko na sama ko ƙasa lokacin da motsinsu na tsaye ya fara.
4. Tambaya: Me ke faruwa da saurin abin da ke faɗuwa cikin 'yanci?
Amsa: Saurin abin da ke faɗuwa cikin sauƙi yana ƙaruwa da kimanin m9.81/s a kowace daƙiƙa saboda nauyin ƙasa.
5. Tambaya: Ta yaya lokacin hawa sama yake da alaƙa da lokacin saukowa ga wani abu da aka jefa a tsaye?
Amsa: Ga wani abu da aka jefa sama sannan aka bar shi ya faɗi baya, lokacin hawa yana daidai da lokacin saukowa.
6. Tambaya: Menene saurin abu a matsakaicin tsayinsa?
Amsa: A matsakaicin tsayi, saurin abu a tsaye yana zama sifili kafin ya fara sauka.
8. Tambaya: Ta yaya juriyar iska ke shafar motsi a tsaye?
Amsa: Juriyar iska tana adawa da motsi, rage saurin gudu da saurin ƙarewa ga abubuwan da ke faɗuwa.
9. Tambaya: Menene saurin tashar?
Amsa: Saurin ƙarshe shine matsakaicin gudu da abu mai faɗuwa zai iya kaiwa idan juriyar iska ta yi daidai da ƙarfin nauyi.
10. Tambaya: Shin abu zai iya samun saurin gudu mara kyau yayin motsi sama?
Amsa: Eh, idan abu ya matsa sama da nauyi, yana da saurin gudu mara kyau daidai da -g.
12. Tambaya: Me yasa hanzarin abu ba shi da kyau ga abubuwan da aka jefa sama?
Amsa: Saboda saurin gudu saboda nauyi yana aiki ƙasa, ana ɗaukarsa mara kyau ga abubuwa da ke motsawa a akasin alkibla.
14. Tambaya: Menene faɗuwar 'yanci?
Amsa: Faɗuwa ta 'yanci ita ce motsin abu a ƙarƙashin tasirin nauyi kawai, ba tare da wani ƙarfi da ke aiki a kansa ba.
15. Tambaya: Ta yaya motsin abu ya bambanta idan aka jefa shi ƙasa idan aka jefa shi ƙasa?
Amsa: Dukansu suna fuskantar saurin gudu saboda nauyi. Duk da haka, abu da aka jefa ƙasa yana da ƙarin saurin farko, wanda hakan ke sa ya isa ƙasa da sauri fiye da wanda kawai ya faɗi.
16. Tambaya: Waɗanne abubuwa ne ke shafar saurin ƙarshen abu?
Amsa: Abubuwan da suka haɗa da nauyin abu, siffarsa, yankin samansa, da kuma matsakaicin yawansa da kuma ɗankonsa da yake faɗuwa.
17. Tambaya: Shin abu a cikin motsi a tsaye yana da kuzarin motsi da ƙarfin kuzari?
Amsa: Eh, kuzarin motsi na abu yana ƙaruwa yayin da yake faɗuwa, yayin da ƙarfinsa ke raguwa, kuma akasin haka yayin hawa.
18. Tambaya: Me yasa saurin abu yake canzawa yayin motsi a tsaye?
Amsa: Ƙarfin nauyi yana haifar da hanzari akai-akai, yana canza saurin abu har sai ya kai ga saurin ƙarshe ko ya canza alkibla.
19. Tambaya: Za a iya kwatanta motsi a tsaye a matsayin motsi mai sauri iri ɗaya?
Amsa: Eh, idan babu juriyar iska, motsi a tsaye a ƙarƙashin nauyi yana ƙaruwa daidai gwargwado tare da hanzarin .
20. Tambaya: Ta yaya ake amfani da ƙa'idar kiyaye makamashi ga motsi a tsaye?
Amsa: Jimlar kuzarin motsi da ƙarfin da ke akwai yana nan a daidai lokacin motsi a tsaye, idan aka yi la'akari da cewa babu asarar kuzari ga juriyar iska.
Fahimtar motsi a tsaye yana da mahimmanci a cikin injiniyoyi na gargajiya kuma yana da aikace-aikace masu amfani tun daga kimiyyar wasanni zuwa ƙa'idodin injiniya da aminci.
