Respuesta :
For this problem, we use the Coulomb's Law. The working equation is written below:
F = kQ₁Q₂/d²
where
F is the electric force
k is a constant equal to 8.99 × 10⁹ N • m²/C²
Q is the charges for the two objects
d is he distance between the objects
Substituting the values,
F = (8.99 × 10⁹ N • m²/C²)(-15×10⁻⁶ C)(-11×10⁻⁶ C)/(180²)
F = 4.578×10⁻⁵ N
Next, we determine the gravitational force using the Law of Universal Gravitation:
F = Gm₁m₂/d²
where
F is the gravitational force
G is a constant equal to 6.67 × 10⁻¹¹ N • m²/kg²
m is the masses of the objects
d is the distance between the objects
F = (6.67 × 10⁻¹¹ N • m²/kg²)(58,000 kg)(52,000 kg)/(180²)
F = 6.2089×10⁻⁶ N
The sum of the two forces equal the net force:
Net force = 4.578×10⁻⁵ N + 6.2089×10⁻⁶ N = 1.079×10⁻⁵ N
F = kQ₁Q₂/d²
where
F is the electric force
k is a constant equal to 8.99 × 10⁹ N • m²/C²
Q is the charges for the two objects
d is he distance between the objects
Substituting the values,
F = (8.99 × 10⁹ N • m²/C²)(-15×10⁻⁶ C)(-11×10⁻⁶ C)/(180²)
F = 4.578×10⁻⁵ N
Next, we determine the gravitational force using the Law of Universal Gravitation:
F = Gm₁m₂/d²
where
F is the gravitational force
G is a constant equal to 6.67 × 10⁻¹¹ N • m²/kg²
m is the masses of the objects
d is the distance between the objects
F = (6.67 × 10⁻¹¹ N • m²/kg²)(58,000 kg)(52,000 kg)/(180²)
F = 6.2089×10⁻⁶ N
The sum of the two forces equal the net force:
Net force = 4.578×10⁻⁵ N + 6.2089×10⁻⁶ N = 1.079×10⁻⁵ N
Answer: The net force between the the asteroids will [tex]-3.9492\times 10^{-5} N[/tex] and the negative sign indicates that they repel each other.
Explanation:
The Coulombs forces exerted by asteroids:
Charge on asteroid-1 = [tex]Q_1=-15 \mu C=-15\times 10^{-6} C[/tex]
Charge on asteroid-2 = [tex]Q_1=-11 \mu C=-11\times 10^{-6} C[/tex]
Distance between the asteroids = 180 m
[tex]k=\frac{1}{4\pi\epsilon _o}=8.99\times 10^9 N m^2/c^2[/tex]
[tex]F_c=k\times \frac{Q_1\times Q_2}{r^2}=8.99\times 10^9 N m^2/c^2\times \frac{-15\times 10^{-6} C\times -11\times 10^{-6} C}{(180 m)^2}=4.57\times 10^{-5} N[/tex]
Since, the charges are negative they will repel each other.
The gravitational force between the asteroids:
Mass of the asteroid -1 = [tex]m_1[/tex] = 58000 kg
Mass of the asteroid -2 = [tex]m_1[/tex] = 52000 kg
G = [tex]6.67\times 10^{-11}N m^2/kg^2[/tex]
[tex]F_G=G\times \frac{m_1\times m_2}{r^2}=6.67\times 10^{-11}N m^2/kg^2\times \frac{58,000 kg\times 52000 kg}{(180 m)^2}=6.208\times 10^{-6} N[/tex]
The gravitational force is an attractive force.
Since, the charges are negatively charged they will repel each other.
The net force = [tex] F=F_G+(-F_C)=6.208\times 10^{-6} N+(-4.57\times 10^{-5} N)=-3.9492\times 10^{-5} N[/tex]
Hence, the net force between the the asteroids will [tex]-3.9492\times 10^{-5} N[/tex] and the negative sign indicates that they repel each other.
