Misalin hanzarin nauyi

Misalai 4 na Matsalolin Hanzarin Nauyi

1. Yaya girman ƙarfin nauyi yake a saman wata? Nauyin wata = 7,35 x 10²² kg, radius na wata = mita 1.740.000, ma'aunin nauyi na duniya (G) = 6,67 x 10^-11 A'a m² /kg²
Tattaunawa
Tsarin doka ta biyu ta Newton:

Bayani: G = daidaitaccen nauyi na duniya, M = nauyin ƙasa, m = nauyin abu, r = nisan daga tsakiyar duniya zuwa ga abu. Idan abu yana kan saman duniya ko kusa da saman duniya to r = radius na duniya.

Yi amfani da wannan dabarar don ƙididdige hanzarin da ke faruwa saboda nauyi (g) a saman duniya, inda M = nauyin duniya, tauraron ɗan adam, taurari da sauransu. kuma r = radius na duniya, tauraron ɗan adam, taurari da sauransu.
Menene girman saurin nauyi a saman wata?

2. Matsakaicin saurin nauyi a saman Duniya daidai yake da gA tsayin R (R = radius na duniya) daga saman duniya, girman saurin nauyi na duniya... ana bayyana shi a cikin g.
Tattaunawa
Saurin da aka samu sakamakon nauyi ya yi daidai da murabba'in nisa:

R = radius na duniya. A tsayin R daga saman duniya = a tsayin 2R daga tsakiyar duniya. Idan ana ɗaukar R a matsayin 1 to 2R = 2(1) = 2.
A tsayin R daga saman duniya, saurin da aka samu sakamakon nauyi yana da darajar ¼ g. Idan g = 9,8 m/s² Don haka a tsayin R daga saman duniya, saurin gudu saboda nauyi yana da ƙimar 2,45 m/s².

3. Matsakaicin saurin nauyi a saman Duniya shine gA tsayin 2D (D = diamita na duniya) daga saman duniya, girman saurin nauyi shine...
A. g
B. 1/2 g
C. 1/4 g
D. 1/8 g
E. 1/16 g
Tattaunawa:

Ƙarfin nauyi yana daidai da saurin nauyi. Ƙarfin nauyi yana daidai da murabba'in nisa, don haka saurin nauyi shi ma yana daidai da murabba'in nisa.
Bayani: g = hanzarin nauyi, r = nisan wuri daga tsakiyar duniya.
Saman Duniya yana da nisan R daga tsakiyar Duniya, inda R = radius na Duniya. Idan R shine 1, to saurin nauyi a saman Duniya shine:
Wannan sakamakon ya nuna cewa a saman Duniya, saurin nauyi shine g. Menene saurin nauyi a tsayin 2D?
D = 2R. 2D = 2(2R) = 4R. R shine 1 saboda haka 4R = 4
Amsar da ta dace ita ce E.

4. Idan matsayin abu A shine 2R sama da saman duniya, yayin da matsayin abu B shine 3R 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: 9
E. 9: 4
Tattaunawa:
R = radius na duniya. R yana da ƙimar 1 don haka 2R = 2 da 3R = 3.
Ƙarfin filin nauyi (g) a tsayin 2R sama da saman duniya shine:
Ƙarfin filin nauyi (g) a tsayin 3R sama da saman duniya shine:

Rabon g a tsayi 2R da 3R shine:

Saurin saurin da aka samu sakamakon nauyi a tsayin 2R ya fi sau 2,25 fiye da saurin da aka samu saboda nauyi a tsayin 3R.
Amsar da ta dace ita ce E.

Tambayoyin Hanzarin Nauyi

1. Lissafa girman saurin nauyi a saman:
(a) Rana (b) Mercury (c) Venus (d) Mars (e) Jupiter (f) Saturn (g) Uranus (h) Neptune
Bayanan da ake buƙata:
Madaidaitan nauyi na duniya (G) = 6,67 x 10^-11 A'a m² /kg²
Nauyin rana = 1,99 x 10³⁰ kg, radius na rana = 2,44 x 10⁶ m
Nauyin Mercury = 3,30 x 10²³ kg, radius na Mercury = 6,96 x 10⁸ m
Nauyin Venus = 4,87 x 10²⁴ kg, radius na Venus = 6,05 x 10⁶ m
Girman Mars = 6,42 x 10²³ kg, radius na Mars = 3,40 x 10⁶ m
Nauyin Jupiter = 1,90 x 10²⁷ kg, radius na Jupiter = 6,91 x 10⁷ m
Girman Saturn = 5,69 x 10²⁶ kg, radius na Saturn = 6,03 x 10⁷ m
Nauyin Uranus = 8,66 x 10²⁵ kg, radius na Uranus = 2,56 x 10⁷ m
Nauyin Neptune = 1,03 x 10²⁶ kg, radius na Neptune = 2,48 x 10⁷ m
Tushen bayanai kan taro da radius na rana da duniyoyi

2. Matsakaicin saurin nauyi a saman Duniya daidai yake da g. Ƙayyade hanzarin da ke faruwa saboda nauyi a tsayin …… daga saman duniya:
(a) 2R (b) 3R (c) 4R (d) 5R (e) 6R (f) 7R (g) 8R (h) 9R (i) 10 R
Ji a cikin g da lambobi!