Final answer:
To find the individual masses of two objects with a combined mass of 4.00 kg that attract each other with a force of 2.5×10⁻¹⁰ N at a distance of 0.21 m, use Newton's universal law of gravitation. Assume one mass is x and the other is 4 - x, and solve the quadratic equation derived from the gravitational force formula. The masses can then be calculated using algebra.
Step-by-step explanation:
If two objects attract each other gravitationally with a force of 2.5×10⁻¹⁰ N when they are 0.21 m apart and their total mass is 4.00 kg, to find their individual masses we can use Newton's universal law of gravitation:
F = G×(m₁×m₂)/r²
Where:
- F = gravitational force between two masses (2.5 x 10⁻¹⁰ N)
- G = gravitational constant (6.673 x 10⁻¹¹ N·m²/kg²)
- m₁ and m₂ = individual masses of the two objects
- r = distance between the centers of the two masses (0.21 m)
Given the total mass (m₁ + m₂ = 4.00 kg), let's assume m₁ = x and hence m₂ = 4 - x. Now we can set up the equation:
2.5 x 10⁻¹⁰ = (6.673 x 10⁻¹¹) × (x×(4 - x))/(0.21²)
Solving for x gives us the individual masses. This must be done using algebraic methods, more specifically, solving a quadratic equation. Once we find x, one of the masses, we can easily find the second mass by subtracting x from the total mass.