Final answer:
To find the mass of the other particle, we used Newton's law of universal gravitation. The mass of the second particle is calculated as m2 = 4.556 × 10⁻²³ kg using the provided values and the gravitational constant.
Step-by-step explanation:
When calculating the mass of the other particle given a distance, the force between two particles, and the mass of one of them, we make use of Newton's law of universal gravitation, which states that the force (F) between two masses (m1 and m2) is proportional to the product of the two masses and inversely proportional to the square of the distance (r) between their centers. The formula for gravitational force is given by:
F = (G × m1 × m2) / r²
Given:
F = 6.1 × 10⁻´³ N,
m1 = 2.6 × 10⁻²⁶ kg (mass of one of the particles),
r = 3.6 × 10⁻¹ m (distance between the two particles), and
G = 6.674 × 10⁻¹¹ N·m²/kg² (gravitational constant).
Using the formula, we can solve for m2 (the mass of the other particle) as follows:
m2 = F × r² / (G × m1)
Plugging in the values, we have:
m2 = (6.1 × 10⁻´³ N × (3.6 × 10⁻¹ m)²) / (6.674 × 10⁻¹¹ N·m²/kg² × 2.6 × 10⁻²⁶ kg)
m2 = (6.1 × 10⁻´³ × 12.96 × 10⁻¹¸) / (6.674 × 10⁻¹¹ × 2.6× 10⁻²⁶)
Now simplify the expression to find m2:
m2 = (6.1 × 12.96) × 10⁻´³⁻¹¸ / (6.674 × 2.6) × 10⁻¹¹⁻²
m2 = 79.056 × 10⁻´³⁻¹¸ / 17.3524 × 10⁻¹¹⁻²⁶
m2 = 4.556 × 10⁻´¹² / 10⁻¹¹⁻²⁶
m2 = 4.556 × 10⁻²³
Therefore, m2 = 4.556 × 10⁻²³ kg.