An object with a mass of 5000kg is 6.5m away from an object with the mass of 2000kg. What is the force exerted on the smaller mass by the bigger mass?
To calculate the force exerted on the smaller mass by the bigger mass, we can use Newton's law of universal gravitation. The formula is as follows:
F = (G * m₁ * m₂) / r²
where:
F is the force between the two objects,
G is the gravitational constant (approximately 6.67430 × 10^-11 Nm²/kg²),
m₁ is the mass of the first object,
m₂ is the mass of the second object, and
r is the distance between the centers of the two objects.
In this case, the first object has a mass of 5000 kg (m₁), the second object has a mass of 2000 kg (m₂), and the distance between them is 6.5 m (r). Now we can plug these values into the formula:
F = (6.67430 × 10^-11 Nm²/kg² * 5000 kg * 2000 kg) / (6.5 m)²
First, let's calculate the denominator (6.5 m)²:
(6.5 m)² = 42.25 m²
Now, substitute this value into the formula:
F = (6.67430 × 10^-11 Nm²/kg² * 5000 kg * 2000 kg) / 42.25 m²
Next, calculate the value of the numerator (6.67430 × 10^-11 Nm²/kg² * 5000 kg * 2000 kg):
(6.67430 × 10^-11 Nm²/kg² * 5000 kg * 2000 kg) = 0.133486 Nm²
Substitute this value into the formula:
F = 0.133486 Nm² / 42.25 m²
Finally, divide the numerator by the denominator:
F ≈ 0.00316 N
Therefore, the force exerted on the smaller mass by the bigger mass is approximately 0.00316 Newtons.