Misalan Tambayoyi 9 na Ƙarfin Nauyi
1. Rabon tarin duniyoyi A da B shine 2:3 yayin da rabon radii na duniyoyi A da B shine 1:2. Idan nauyin abin da ke kan duniyar A shine w, to berate abin da ke kan duniya B shine….
A. 3/8 w
B. 3/4 w
C. 1/2 w
D. 4/3 w
E. 8/3 w
Tattaunawa
An sani :
Nauyin duniya A (m)A) = 2
Nauyin duniya B (m)B) = 3
Radius na duniya A (r)A) = 1
Radius na duniya B (r)B) = 2
Nauyin abu = m
Nauyin wani abu a duniya A = w
An tambaya : nauyin wani abu a duniya B
Jawab :
An samo dabarar nauyi daga Dokar nauyi ta Newton shine:
Bayani: w = nauyi, G = daidaitaccen nauyi na duniya, M = nauyin duniya, m = nauyin abu, r = nisan abin daga tsakiyar duniya. Idan abin yana kan saman duniya to r = radius na duniya.
Nauyin abu iri ɗaya ne, don haka maye gurbin m da w/2G
Amsar da ta dace ita ce A.
2. Ana harba roka mai nauyin w a tsaye daga saman Duniya. Idan D shine diamita na Duniya, to daidai lokacin da rokar take a tsayin 0,5 D sama da saman Duniya, nauyin rokar shine...
A. 4 w
B. 2 w
C. w
D. 0,5 w
E. 0,25 w
Tattaunawa
An san cewa:
Nauyin roka = w
Radius na duniya = nisan daga tsakiyar duniya = R
Diamita na Duniya = D = 2R
An tambaya: Nauyin rokar lokacin da rokar take a tsayin 0,5 D daga saman duniya
Amsa:
0,5 D = 0,5 (2R) = R
Nisa tsakanin rokar da tsakiyar duniya = radius na duniya + nisan da rokar ta yi daga saman duniya = R + R = 2R
Nauyi shine ƙarfin nauyi da ke aiki akan wani abu. Ƙarfin nauyi (F) yana da daidaiton juzu'i na nisan daga tsakiyar Duniya (R), don haka nauyi yana da daidaiton juzu'i na nisan.
Amsar da ta dace ita ce E.
3. Teburin bayanai na zahiri na abu A da abu B dangane da saman duniya wanda ke da radius na R. Kwatanta ƙarfin filin nauyi na abu A da abu B shine...
A. 2: 1
B. 4: 1
C. 1: 4
D. 9: 4
E. 4: 9
Tattaunawa
An sani :
Nauyin abu A (m)A) = 1
Nauyin abu B (m)B) = 2
Nisa tsakanin abu A da duniyar Duniya (r)A) = 1
Nisa tsakanin abu B da duniyar Duniya (r)B) = 2
An tambaya : kwatanta ƙarfin filin nauyi na abu A (g)A) da abu B (gB)
Jawab :
Tsarin ƙarfin filin nauyi na duniya:
Bayani: g = ƙarfin filin nauyi na duniya, G = ma'aunin nauyi na duniya, mB = taro na duniya, rB = radius na duniya
Kwatanta ƙarfin filin nauyi na abu A (g)A) da abu B (gB)
gA ku: gB
G: G/2
1: 1/2
2: 1
Amsar da ta dace ita ce A.
4. Idan matsayin abu A shine 1/2 R sama da saman duniya, yayin da matsayin abu B shine 2R sama da saman duniya (R = radius na duniya), to rabon ƙarfin filin nauyi da abubuwa A da B ke fuskanta shine...
A. 1: 8
B. 1: 4
C. 2: 3
D. 4: 1
E. 8: 1
Tattaunawa
An sani :
Nisa tsakanin abu A da tsakiyar duniya = 0,5R + R = 1,5R = 1,5
Nisa daga abu B daga tsakiyar duniya = 2R + R = 3R = 3
An tambaya : kwatanta ƙarfin filin nauyi da abubuwa A da B suka fuskanta
Jawab :
Kwatanta ƙarfin filin nauyi da abubuwa A da B suka fuskanta :
Amsar da ta dace ita ce D.
5. Wani ɗan sama jannati a saman duniya yana fuskantar filin nauyi na g, don haka lokacin da yake a tsayin R 1,5 daga saman duniya zai fuskanci filin nauyi na …. (R = radius na duniya).
A. g/0,50
B. g/2,25
C. g/6,25
D. g/7,50
Misali/6,00
Tattaunawa
Ƙarfin nauyi (F) yana daidai gwargwado kai tsaye da filin nauyi (g). Girman ƙarfin nauyi, girman filin nauyi. Ƙarfin nauyi (F) da wani abu ya fuskanta yana daidai gwargwado kai tsaye da 1/r.2, inda r = nisan abu daga tsakiyar duniya. Domin ƙarfin nauyi yana daidai gwargwado kai tsaye zuwa 1/r2 to filin nauyi (g) shi ma yana daidai gwargwado kai tsaye zuwa 1/r2.
Idan wani ɗan sama jannati yana saman duniya a nesa R (R = radius na duniya) daga tsakiyar duniya, filin nauyi da yake fuskanta shine g. Ana iya tabbatar da wannan ta hanyar lissafin da ke ƙasa:
Filin nauyi (g) yana daidai da 1/R2Idan R = 1 to 1 / R2 = 1/12 = 1 / 1 = 1. Idan nisan ɗan sama jannatin daga tsakiyar duniya = 1 to yana fuskantar filin nauyi na = (g)(1) = g.
Nisa tsakanin ɗan sama jannatin daga tsakiyar duniya shine 1,5R = 1,5(1) = 1,5 don haka yana fuskantar filin nauyi na: 1 / R2 = 1/1,52 = 1 / 2,25. Don haka idan nisan ɗan sama jannatin daga tsakiyar duniya = 1,5 to yana fuskantar filin nauyi na = (g)(1 / 2,25) = g / 2,25
Amsar da ta dace ita ce B.
6. Kwatanta ƙarfin filin nauyi na duniya ga abubuwa biyu, ɗaya a saman duniya ɗayan kuma a tsayin ½ R daga saman duniya (R = radius na duniya) shine....
A. 1: 2
B. 2: 3
C. 3: 2
D. 4: 9
E. 9: 4
Tattaunawa
An sani :
Nisa tsakanin abu A da tsakiyar duniya (r)A) = R = 1
Nisa tsakanin abu B da tsakiyar duniya (r)B) = 0,5R + R = 1,5R = 1,5
An tambaya : kwatanta ƙarfin filin nauyi da abubuwa A da B suka fuskanta
Jawab :
Kwatanta ƙarfin filin nauyi da abubuwa A da B suka fuskanta :
Amsar da ta dace ita ce E.
7. Yaya girman ƙarfin nauyi tsakanin ƙasa da wani abu da ke saman ƙasa yake? Nauyin ƙasa = 5,97 x 1024 kg, nauyin abu = 1000 kg, radius na ƙasa = 6,38 x 106 mita. Menene nauyin ko ƙarfin nauyi na duniya da ke aiki akan abu idan aka ƙididdige shi ta amfani da dabarar doka ta biyu ta Newton inda hanzarin nauyi (g) = 9,8 m/s2 ?
Tattaunawa
An san cewa:
Girman duniya (mB= 5,97 x 1024 kg
Nauyin abu (m)b) = 103 kg
Radius na duniya (r) = 6,38 x 106 mita
Madaidaitan nauyi na duniya (G) = 6,67 x 10-11 A'a m2 /kg2
Saurin gudu saboda nauyi (g) = 9,8 m/s2
An tambaya: girman ƙarfin nauyi nawa ne?
Amsa:
Girman ƙarfin nauyi tsakanin ƙasa da wani abu (ta amfani da dabarar dokar nauyi ta Newton):
Bayani w = F = ƙarfin nauyi, G = daidaitaccen nauyi na duniya, mB = taro na duniya, mb = taro na abu, r = nisa tsakanin tsakiyar duniya da tsakiyar abu. Abu yana kan saman duniya don haka r = radius na duniya.
Nauyin abu (ta amfani da dabarar doka ta biyu ta Newton):
w = mg = (1000)(9,8) = 9800 Newtons
Kwatanta wannan sakamakon lissafin da na baya. Ƙimar kusan iri ɗaya ce saboda zagaye. Za a iya kammala da cewa nauyin abu a saman Duniya shine ƙarfin nauyi na Duniya da ke aiki akan wani abu a saman Duniya.
8. Menene ƙarfin nauyi tsakanin ƙasa da wani abu a tsayin mita 10.000 sama da matakin ƙasa? Nauyin ƙasa = 5,97 x 1024 kg, nauyin abu = 1000 kg, radius na ƙasa = 6,38 x 106 Mita.
Tattaunawa:
Kwatanta da amsar lamba 1. Da nisa daga ƙasa, da kuma girman abin.
9. Rokar tana da nauyi w An harba shi tsaye daga saman duniya. Idan D shine diamita na duniya, a tantance nauyin rokar lokacin da rokar take a tsayin 2D daga saman duniya.
Tattaunawa
An san cewa:
D = diamita na duniya, R = radius na duniya, 1 D = 2 R, 2 D = 4 R
Tambaya: Menene nauyin rokar idan ta kai tsayin 2D?
Amsa:
Ƙarfin nauyi ko ƙarfin nauyi yana daidai da murabba'in nisa. A lissafi:
Tambayoyi game da ƙarfin nauyi
1. Yaya girman ƙarfin nauyi tsakanin ƙasa da wani abu da ke saman ƙasa yake? Nauyin ƙasa = 5,97 x 1024 kg, nauyin abu = 2000 kg, radius na ƙasa = 6,38 x 106 mita. Menene nauyin ko ƙarfin nauyi na duniya da ke aiki akan abu idan aka ƙididdige shi ta amfani da dabarar doka ta biyu ta Newton inda hanzarin nauyi (g) = 9,8 m/s2 ?
2. Menene ƙarfin nauyi tsakanin ƙasa da wani abu a tsayin mita 100.000 sama da matakin ƙasa? Nauyin ƙasa = 5,97 x 1024 kg, nauyin abu = 2000 kg, radius na ƙasa = 6,38 x 106 Mita.
3. Rokar tana da nauyi w An harba shi tsaye daga saman duniya. Idan D shine diamita na duniya, a tantance nauyin rokar lokacin da rokar take a tsayin 3D daga saman duniya.
