Jawab no 20 dan 21 Materi Gerak Melingkar

No. 20 
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Diket :
ketinggian satelit, h = 5,0 x 10² km = 500 km 
jari-jari Bumi, R = 6371 km 
maka jarak satelit ke poros bumi adalah,
r = h + R = 500 + 6371 = 6871 km = 6,871 x 10⁶ m
Periode satelit terhadap bumi, T = 95 menit = 95 x 60 detik = 5700 detik

Tanya :
A] Kelajuan orbit, V = __?
B] percepatan sentripetal, asp = __?

Jawab :
A]
F sp = F grav
m.V²/r = G.M.m/r²
V²/r = G.M/r² . (R²/R²)
V²/r = G.M/R² . (R²/r²)
V²/r = g . (R²/r²)
V² = g.r.(R²/r²)
V = √[g.r.(R²/r²)]
V = (R/r). √[g.r]
V = (6371/6871). √[10. 6,871 x 10⁶]
V = 0,9272 x 8,2891 x 10³
V = 7685,65352 m/s

B]
asp = V²/r
asp = 7685,65352²/6,871 x 10⁶
asp = 8,5969 m/s²

No. 21 
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Diket :
jari-jari lingkaran, r = 12 m
percepatan sentripetal max, asp = 1,96 m/s²

Tanya :
Kelajuan max yg diperbolehkan, V max = __?

Jawab :

asp = V²/r
V² = asp. r
V = √[asp. r]
V = √[1,96. 12]
V = √23,52
V max = 4,8497 m/s

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