Odpowiedź:
Wyjaśnienie:
[tex]Dane:\\M_{P} = 1,3\cdot10^{22} \ kg\\m = 1 \ kg\\R = 1 \ 190 \ km = 1 \ 190 \ 000 \ m = 1,19\cdot10^{6} \ m\\G = 6,67\cdot10^{-11}\frac{Nm^{2}}{kg^{2}} \ - \ stala \ grawitacji[/tex]
a)
[tex]g\cdot m = G\frac{Mm}{R^{2}} \ \ \ /:\\\\g_{P} =G \frac{M_{P}}{R^{2}_{P}}\\\\g_{P} = 6,67\cdot10^{-11}\frac{Nm^{2}}{kg^{2}}\cdot\frac{1,3\cdot10^{22} \ kg}{(1,19\cdot10^{6} \ m)^{2}}\\\\g_{P} = \frac{8,671\cdot10^{11}}{1,4161\cdot10^{12}} \ \frac{N}{kg}\\\\g_{P} \approx 6,1\cdot10^{-1} \ \frac{N}{kg}\\\\\boxed{g_{P} \approx0,61\frac{N}{kg}}[/tex]
b)
[tex]g_{Z} = 9,81\frac{m}{s^{2}} = 9,81\frac{N}{kg}\\\\g_{P} = 0,61\frac{N}{kg}\\\\\frac{g_{Z}}{g_{P}} = \frac{9,81\frac{N}{kg}}{0,61\frac{N}{kg}}\\\\\boxed{\frac{g_{Z}}{g_{P}}\approx16 \ razy}[/tex]
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Odpowiedź:
a) Na ciało o masie 1 kg Pluton działa siłą ≈ 0,61 N.
b) Siła grawitacji działająca na dane ciało na Plutonie jest ≈16 razy mniejsza niż na Ziemi.
Wyjaśnienie:
[tex]Dane:\\M_{P} = 1,3\cdot10^{22} \ kg\\m = 1 \ kg\\R = 1 \ 190 \ km = 1 \ 190 \ 000 \ m = 1,19\cdot10^{6} \ m\\G = 6,67\cdot10^{-11}\frac{Nm^{2}}{kg^{2}} \ - \ stala \ grawitacji[/tex]
a)
[tex]g\cdot m = G\frac{Mm}{R^{2}} \ \ \ /:\\\\g_{P} =G \frac{M_{P}}{R^{2}_{P}}\\\\g_{P} = 6,67\cdot10^{-11}\frac{Nm^{2}}{kg^{2}}\cdot\frac{1,3\cdot10^{22} \ kg}{(1,19\cdot10^{6} \ m)^{2}}\\\\g_{P} = \frac{8,671\cdot10^{11}}{1,4161\cdot10^{12}} \ \frac{N}{kg}\\\\g_{P} \approx 6,1\cdot10^{-1} \ \frac{N}{kg}\\\\\boxed{g_{P} \approx0,61\frac{N}{kg}}[/tex]
b)
[tex]g_{Z} = 9,81\frac{m}{s^{2}} = 9,81\frac{N}{kg}\\\\g_{P} = 0,61\frac{N}{kg}\\\\\frac{g_{Z}}{g_{P}} = \frac{9,81\frac{N}{kg}}{0,61\frac{N}{kg}}\\\\\boxed{\frac{g_{Z}}{g_{P}}\approx16 \ razy}[/tex]