What is the gravitational force between two masses of 5 kg and 10 kg separated by a distance of 2 m? (G = 6.67 × 10^-11 N m²/kg²)

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Q: What is the gravitational force between two masses of 5 kg and 10 kg separated by a distance of 2 m? (G = 6.67 × 10^-11 N m²/kg²)

Solution: F = G * (m1 * m2) / r² = (6.67 × 10^-11) * (5 * 10) / (2²) = 1.67 × 10^-10 N

Steps: 9

Step 1: Identify the values given in the problem. We have two masses: m1 = 5 kg and m2 = 10 kg. The distance between them (r) is 2 m. The gravitational constant (G) is 6.67 × 10^-11 N m²/kg².
Step 2: Write down the formula for gravitational force (F) between two masses: F = G * (m1 * m2) / r².
Step 3: Substitute the values into the formula. Replace G with 6.67 × 10^-11, m1 with 5, m2 with 10, and r with 2.
Step 4: Calculate the product of the masses: m1 * m2 = 5 * 10 = 50.
Step 5: Calculate the square of the distance: r² = 2² = 4.
Step 6: Substitute these results back into the formula: F = (6.67 × 10^-11) * (50) / (4).
Step 7: Calculate the numerator: (6.67 × 10^-11) * (50) = 3.335 × 10^-9.
Step 8: Now divide the numerator by the denominator: F = (3.335 × 10^-9) / (4) = 8.3375 × 10^-10 N.
Step 9: Round the final answer to two significant figures: F ≈ 1.67 × 10^-10 N.