If the gravitational force between objects of equal mass is 2.30x10^-8 N when the objects are 10.0m apart, what is the mass of each object?
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would it be g=1.5341 × 10 to the -19?
To find the mass of each object, we can use Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
Where:
F = gravitational force between the objects
G = gravitational constant, approximately 6.67430 × 10^-11 N(m/kg)^2
m1, m2 = mass of the objects
r = distance between the objects
First, we need to rearrange the formula to solve for the mass of each object:
(m1 * m2) = (F * r^2) / G
Now we can substitute the values given in the problem:
F = 2.30 × 10^-8 N
r = 10.0 m
G = 6.67430 × 10^-11 N(m/kg)^2
(m1 * m2) = (2.30 × 10^-8 N * (10.0 m)^2) / (6.67430 × 10^-11 N(m/kg)^2)
Simplifying the equation:
(m1 * m2) = 2.30 × 10^-8 N * 100 m^2 / 6.67430 × 10^-11 N(m/kg)^2
(m1 * m2) = 2.30 × 10^-6 m^3/kg
Since the objects have the same mass, let's assume m1 = m2 = m:
m^2 = 2.30 × 10^-6 m^3/kg
Taking the square root of both sides:
m = √(2.30 × 10^-6 m^3/kg)
m ≈ 0.001516 kg
Therefore, the mass of each object is approximately 0.001516 kg.
To find the mass of each object, you can use Newton's law of universal gravitation formula:
F = (G * m₁ * m₂) / r²
where:
F is the gravitational force,
G is the universal gravitational constant (6.67 × 10^-11 N m²/kg²),
m₁ and m₂ are the masses of the two objects, and
r is the distance between the centers of the two objects.
In the given problem, we know that the gravitational force between the objects is 2.30 × 10^-8 N and the distance between them is 10.0 m. So, we can substitute these values into the formula:
2.30 × 10^-8 N = (6.67 × 10^-11 N m²/kg²) * m₁ * m₂ / (10.0 m)²
Now, we need to solve for the mass of each object. Since the problem states that the masses of the objects are equal, we can replace m₁ and m₂ with just m:
2.30 × 10^-8 N = (6.67 × 10^-11 N m²/kg²) * m² / (10.0 m)²
Simplifying further:
2.30 × 10^-8 N = (6.67 × 10^-11 N m²/kg²) * m² / 100
Next, let's isolate m² by multiplying both sides by 100:
(2.30 × 10^-8 N) * 100 = (6.67 × 10^-11 N m²/kg²) * m²
2.30 × 10^-6 N = (6.67 × 10^-11 N m²/kg²) * m²
Now we can solve for m² by dividing both sides by (6.67 × 10^-11 N m²/kg²):
m² = (2.30 × 10^-6 N) / (6.67 × 10^-11 N m²/kg²)
m² ≈ 3.448 km²/kg
Finally, take the square root of both sides to find the mass of each object:
m ≈ √(3.448 km²/kg)
m ≈ 1.858 km/kg
Therefore, the mass of each object is approximately 1.858 kilogram per kilometer.