Question

N asteroid of mass 58,000 kg carrying a negative charge of 15 μc is 180 m from a second asteroid of mass 52,000 kg carrying a negative charge of 11 μc. what is the magnitude of the net force the asteroids exert upon each other, assuming we can treat them as point particles? (g = 6.67 × 10-11 n • m2/kg2, k = 1/4 πε0 = 8.99 × 109 n • m2/c2)

Answer 1

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

Answer 2

Answer: The net force between the the asteroids will
`-3.9492* 10^(-5) N` and the negative sign indicates that they repel each other.

Step-by-step explanation:

The Coulombs forces exerted by asteroids:

Charge on asteroid-1 =
`Q_1=-15 \mu C=-15* 10^(-6) C`

Charge on asteroid-2 =
`Q_1=-11 \mu C=-11* 10^(-6) C`

Distance between the asteroids = 180 m

`k=(1)/(4\pi\epsilon _o)=8.99* 10^9 N m^2/c^2`

`F_c=k* (Q_1* Q_2)/(r^2)=8.99* 10^9 N m^2/c^2* (-15* 10^(-6) C* -11* 10^(-6) C)/((180 m)^2)=4.57* 10^(-5) N`

Since, the charges are negative they will repel each other.

The gravitational force between the asteroids:

Mass of the asteroid -1 =
`m_1` = 58000 kg

Mass of the asteroid -2 =
`m_1` = 52000 kg

G =
`6.67* 10^(-11)N m^2/kg^2`

`F_G=G* (m_1* m_2)/(r^2)=6.67* 10^(-11)N m^2/kg^2* (58,000 kg* 52000 kg)/((180 m)^2)=6.208* 10^(-6) N`

The gravitational force is an attractive force.

Since, the charges are negatively charged they will repel each other.

The net force =
`F=F_G+(-F_C)=6.208* 10^(-6) N+(-4.57* 10^(-5) N)=-3.9492* 10^(-5) N`

Hence, the net force between the the asteroids will
`-3.9492* 10^(-5) N` and the negative sign indicates that they repel each other.