g HW 5.6.The Moon and the Earth both orbit the center of mass of the Earth-Moon system.Earth is 81 times more massive than the M
1 answer:
Answer:
= 4.688 106 m
Explanation:
The expression for the center of mass is
R cm = 1 / M ∑
Where M is the total mass of the system, ri and m1 are the distance and mass of each particle from a defined origin
Let's look for the total mass, the mass of the moon is m and that of the earth Me
M = + m
M = 81m + m
M = 82 m
The distance from the earth to the moon is R = 384.4 106 m
= 1 / M (M R1 + m R)
= 1 / 82m (0 + m R)
= R / 82
= 384.4 106/82
= 4.688 106 m
The radius of the earth is
= 6371 103 m
= 6.371 106 m
We can see that the center of mass of the system is within the beating radius
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Answer:
a) the magnitude of the force is
F= Q() and where k = 1/4πε₀
F = Qqs/4πε₀r³
b) the magnitude of the torque on the dipole
τ = Qqs/4πε₀r²
Explanation:
from coulomb's law
E =
where k = 1/4πε₀
the expression of the electric field due to dipole at a distance r is
E(r) = , where p = q × s
E(r) = where r>>s
a) find the magnitude of force due to the dipole
F=QE
F= Q()
where k = 1/4πε₀
F = Qqs/4πε₀r³
b) b) magnitude of the torque(τ) on the dipole is dependent on the perpendicular forces
τ = F sinθ × s
θ = 90°
note: sin90° = 1
τ = F × r
recall F = Qqs/4πε₀r³
∴ τ = (Qqs/4πε₀r³) × r
τ = Qqs/4πε₀r²