Misalai 11 na Tambayoyin Motsi da Sha'awa
1. Ana jefa ƙwallon da nauyinta ya kai kilogiram 0,2 a kwance a gudun mita 10/s kuma ta bugi bango, sannan ƙwallon ta dawo da sauri iri ɗaya. Sauyin da aka samu a bugun ƙwallon shine...
Tattaunawa
2. Kwallo mai nauyin gram 10 faɗuwar rana kyauta daga wani tsayi, ya bugi ƙasa da gudun mita 15/s sannan ya yi tsalle sama da gudun mita 10/s. Ka ƙayyade motsin!
Tattaunawa
An sani :
Nauyin ƙwallon (m) = gram 10 = 0,01 kg
Saurin farko na ƙwallon (v)o) = -15 m/s
Saurin ƙarshe na ƙwallon (v)t) = 10 m/s
An tambaya : Impulse (I)
Jawab :
Tsarin Ka'idar motsin rai :
Girman motsin zuciyar shine:
I = 0,01 (10 – (-15)) = 0,01 (10 + 15)
I = 0,01 (25)
I = 0,25 kg m/s
3. Ana jefa ƙwallon gram 200 a kwance a gudun mita 4/s, sannan a buga ƙwallon a daidai lokacin da ƙwallon ta fara bugawa. Tsawon lokacin da ƙwallon ta taɓa jemage shine milise seconds 2, kuma saurin ƙwallon bayan ya bar jemage shine mita 12/s. Girman ƙarfin da jemage ke yi akan ƙwallon shine…
Tattaunawa
An sani :
Nauyin ƙwallon (m) = gram 200 = 0,2 kg
Saurin farko na ƙwallon (v)o) = 4 m/s
Saurin ƙarshe na ƙwallon (v)t) = 12 m/s
Tazarar lokacin hulɗa (t) = milis 2 = daƙiƙa (2/1000) = daƙiƙa 0,002
An tambaya : Girman ƙarfin (F)
Jawab :
Tsarin da ke haifar da sha'awa:
I = F t
Tsarin canza yanayin motsi:
mvt – mvo = m (v)t - vo)
Tsarin ka'idar Impulse-momentum :
Ƙarfin da jemage ke yi a kan ƙwallon shine Newtons 800.
4. Ana jefa ƙwallon da nauyinta ya kai gram 20 a gudun v1 = 4 ms-1 a hagu. Bayan buga bango, ƙwallon ta yi tsalle da sauri na v2 = 2 ms-1 a dama. Girman motsin da aka samar shine….
A. 0,24 Ns
B. 0,12 Ns
C. 0,08 Ns
D. 0,06 Ns
E. 0,04 Ns
Tattaunawa
An san cewa:
Nauyin ƙwallon (m) = gram 20 = 0,020 kg
Saurin ƙwallon kafin karo (v)o) = -4 m/s (zuwa hagu)
Saurin ƙwallon bayan karo (v)t) = +2 m/s (zuwa dama)
vo an ba shi alama mara kyau don bambanta alkiblarsa da vt.
An tambaya: Impulse
Amsa:
Impulse (I) = canjin motsi (Δp) = mvt – mvo
Sha'awar (I) = m (v)t - vo) = 0,02 (2 – (-4))
Sha'awar (I) = 0,02 (2 + 4) = 0,02 (6)
Impulse (I) = 0,12 Newton daƙiƙa.
Amsar da ta dace ita ce B.
5. Hoton da ke ƙasa yana nuna ƙwallo biyu A (nauyi = 2 kg) da ƙwallo B (nauyi = 5 kg) kafin da kuma bayan karo. Idan karo ya yi daidai da roba, to saurin ƙwallo A kafin karo shine….
A. 12 ms-1
B. 10 ms -1
C. 5 ms -1
D. 4 ms -1
E. 2 ms -1
Tattaunawa
An san cewa:
Nauyin ƙwallon A (m A ) = 2 kg
Nauyin ƙwallon B (m B ) = 5 kg
Gudun ƙwallon B kafin karo (v B ) = 2 m/s
Saurin ƙwallon A bayan karo (v A ') = 5 m/s
Gudun ƙwallon B bayan karo (v B ') = 4 m/s
Dukansu ƙwallo kafin da kuma bayan karo suna motsawa zuwa dama don haka ana ba da alamar tabbatacce ga gudu.
Tambaya: Saurin ƙwallon A kafin karo (v A )
Amsa:
Lissafa saurin ƙwallon A kafin karo (v A ) ta amfani da dabarar dokar kiyaye ƙarfin motsi:
mA vA +mB vB = mA vA'+ mB vB'
2 (v A ) + (5) (2) = (2) (5) + (5) (4)
2(v A ) + 10 = 10 + 20
2(v A ) + 10 = 30
2(v A ) = 30 – 10
2(v A ) = 20
v A = 20/2
v A = 10 m/s
Amsar da ta dace ita ce B.
6. Abubuwa A da B suna motsawa kamar yadda aka nuna a hoton. Idan karo mai laushi ya faru kuma saurin abu B bayan karo ya zama 15 ms -1 , to saurin abu A bayan karo shine...
A. 2 ms-1
B. 4 ms -1
C. 8 ms -1
D. 10 ms -1
E. 12 ms -1
Tattaunawa
An san cewa:
Nauyin abu A (mA ) = 5 kg
Nauyin abu B (m B ) = 2 kg
Gudun abu A kafin karo (v A ) = 12 m/s
Gudun abu B kafin karo (v B ) = 10 m/s
Gudun abu B bayan karo (v B ') = 15 m/s
Dukansu abubuwa kafin da kuma bayan karo suna matsawa zuwa dama don haka ana ba da alamar tabbatacce ga saurin.
Tambaya: Saurin abu A bayan karo (v A ')
Amsa:
Lissafa saurin ƙwallon A kafin karo (v A ) ta amfani da dabarar dokar kiyaye ƙarfin motsi:
mA vA +mB vB = mA vA'+ mB vB'
(5) (12) + (2) (10) = (5)v A ' + (2) (15)
60 + 20 = (5)v A ' + 30
80 = (5)v A ' + 30
80 – 30 = (5)v A '
50 = (5)v A '
v A ' = 50/5
v A ' = 10 m/s
Amsar da ta dace ita ce D.
7. Kwallon ping pong mai nauyin gram 5 ya faɗi cikin sauƙi daga wani tsayi (g = 10 ms -2 ). Idan ya faɗi ƙasa, saurin ƙwallon shine 6 ms -1 kuma nan da nan bayan ya faɗi ƙasa, ƙwallon tana tsalle sama da gudun 4 ms -1 . Girman bugun da ke aiki a kan ƙwallon shine...
A. 0,50 Ns
B. 0,25 Ns
C. 0,10 Ns
D. 0,05 Ns
E. 0,01 Ns
Tattaunawa
An sani :
Nauyin ƙwallon (m) = gram 5 = 0,005 kg
Saurin ƙwallon kafin ya buga ƙasa (v)o) = -6 m/s
Saurin ƙwallon nan da nan bayan ya buga ƙasa (v)t) = 4 m/s
Gudu mai kyau da mara kyau yana nufin cewa alkiblar gudun ƙwallon ko alkiblar motsin ƙwallon kafin karo ya saba da alkiblar motsin ƙwallon bayan karo.
An tambaya : Impulse (I)
Jawab :
Ka'idar motsin motsin rai Ya ce bugun jini (Ni) kamar yadda canji a cikin ƙarfin lantarki (Δp).
I = Δp = mvt – mvo = m (v)t - vo)
I = (0,005)(4 – (-6)) = (0,005)(4 + 6) = (0,005)(10) = 0,05 Newton daƙiƙa
Amsar da ta dace ita ce D.
8. Ƙwallo mai nauyin kilogiram 0,5 ta faɗi cikin sauƙi daga tsayin h.1 = mita 7,2 a saman bene kuma yana tsalle zuwa tsayin h2 = 3,2 m. Idan saurin gudu saboda nauyi na duniya = 10 ms-2, motsin da ke aiki a kan ƙwallon shine...
A. 2,0 Ns
B. 3,0 Ns
C. 10 Ns
D. 40 Ns
E. 80 Ns
Tattaunawa
An sani :
Nauyin ƙwallon (m) = 0,5 kg
Tsawon ƙwallon faɗuwar 'free fall' (h)1) = mita 7,2
Tsawon ƙwallon da ke tsalle (h)2) = mita 3,2
Saurin nauyi na duniya (g) = 10 m/s2
An tambaya : Ƙarfin sha'awa yana aiki akan ƙwallon
Jawab :
Saurin ƙwallon kafin ya yi karo (v)o)
Lissafin saurin ƙwallon kafin bugun ta amfani da dabarar faɗuwar 'free fall'. Tsawon da aka bayar (h) = mita 7,2, hanzari saboda nauyi (g) = 10 m/s2 kuma ya nemi gudun ƙarshe kafin ya buga ƙasa, don haka yi amfani da dabarar v2 = 2 gh
vo2 = 2(10)(7,2) = 144
vo = 2(10)(7,2) = 12 m/s
Saurin ƙwallon kafin buguwa (v)o) shine -12 m/s. Alamar korau tana nuna alkibla kawai.
Saurin ƙwallon nan da nan bayan karo (v)t)
Lissafin saurin ƙwallon nan da nan bayan an yi tasiri ta amfani da dabarar motsi a tsaye sama. Tsawon da aka bayar (h) = mita 3,2, hanzari saboda nauyi (g) = -10 m/s2, saurin ƙarshe a matsakaicin tsayi (vt2) = 0 kuma ana tambayar saurin farko nan da nan bayan an buga ƙasa, don haka yi amfani da dabarar vt2 = vo2 + 2 gh
vt2 = vo2 + 2 gh
0 = kuo2 + 2 (-10)(3,2)
vo2 = 64
vo = √64 = 8 m/s
Saurin ƙwallon bayan karo (v)t(8 m/s)
Sha'awar motsa jiki a kan ƙwallon (I)
Ana ƙididdige impulse ta amfani da dabarar theorem na impulse-momentum.
Impulse (I) = canjin motsi (Δp)
Ni = m (v)t - vo) = (0,5)(8-(-12)) = (0,5)(8 + 12) = 0,5(20) = 10 daƙiƙa na Newton
Amsar da ta dace ita ce C.
9. Ana jefa ƙwallon gram 100 a kwance a gudun mita 5/s. Sannan ana bugun ƙwallon a daidai da alkiblar da aka saba. Idan ƙwallon ta ci gaba da hulɗa da jemage na tsawon ms 2 kuma gudun ƙwallon bayan ya bar jemage ya kai mita 10/s, girman ƙarfin da jemage ke bayarwa shine...
A. 200 N
B. 250 N
C. 300 N
D. 350 N
E. 400 N
Tattaunawa:
An sani :
m = gram 100 = 0,1 kg
vo = +5 m/s
t = milis 2 = 2 x 10-3 daƙiƙa
vt = +10 m/s
An tambaya :
Ƙarfin da batter ɗin ya yi a kan ƙwallon (F)?
Jawab :
Tsarin da ke haifar da bugun zuciya :
I = F t
Tsarin canza yanayin aiki :
Ka'idar motsin motsin rai :
Impulse = canjin motsi
Amsar da ta dace ita ce B.
10. Ana jefa ƙwallon da nauyinta ya kai kilogiram 0,1 a kwance zuwa dama da gudun mita 20/s. Bayan an buge ta, ƙwallon ta koma hagu da gudun mita 30/s. Ƙarfin da jemage ya ba wa ƙwallon shine….
A. 4 N s
B. –4 N s
C. 5 N s
D. –5 N s
E. 10 N s
Tattaunawa:
An sani :
m = 0,1 kg, vo = +20 m/s, vt = -30 m/s
An tambaya :
Sha'awa (I)?
Jawab :
Impulse = canjin motsi
Ni = m (v)t - vo) = (0,1)(-30 – 20) = (0,1)(-50) = -5 N s
Amsar da ta dace ita ce D.
11. Wasan ƙwallon baseball mai nauyin kilogiram 0,5 da farko yana motsawa zuwa hagu da gudun mita 2/s. Sannan ana buga ƙwallon da ƙarfi F akasin motsin ƙwallon, don haka saurin ƙwallon yana canzawa zuwa mita 5/s. Idan ƙwallon ta taɓa jemage na tsawon daƙiƙa 0,01, canjin motsi shine...
A. 8,0 kg m/s
B. 6,5 kg m/s
C. 5,5 kg m/s
D. 3,5 kg m/s
E. 2,5 kg m/s
Tattaunawa:
An sani :
m = 0,5 kg, vo = -2 m/s, vt = 5 m/s, t = 0,01 daƙiƙa
An tambaya :
Sauyin yanayin aiki?
Jawab :
Canji a cikin ƙarfin motsi = m (v)t - vo) = (0,5) (5 - (-2)) = (0,5) (7) = 3,5 kg m/s = 3,5 N s
Amsar da ta dace ita ce D.
