Question
What is Earth's gravitational attraction for a rhinoceros if the rhino has a mass of 750 kg and the Earth's radius (distance) is 6.37times 10^6 meters? The Earth's mass is 5.98times 10^24kg 4.69times 10^10N 7,375 N 7400 N 4.7times 10^10N 4.69times 10^10kg 7,375 kg
Solution
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(236 Votes)
Sarah
Veteran · Tutor for 11 years
Answer
Here's how to calculate the Earth's gravitational attraction (force) on the rhinoceros:**1. Recall Newton's Law of Universal Gravitation:**The force of gravity between two objects is given by:F = G * (m1 * m2) / r^2Where:* F is the gravitational force* G is the gravitational constant (6.674 x 10^-11 N⋅m²/kg²)* m1 and m2 are the masses of the two objects* r is the distance between their centers**2. Plug in the values:*** m1 (Earth's mass) = 5.98 x 10^24 kg* m2 (rhino's mass) = 750 kg* r (Earth's radius) = 6.37 x 10^6 m* G = 6.674 x 10^-11 N⋅m²/kg²F = (6.674 x 10^-11 N⋅m²/kg²) * (5.98 x 10^24 kg * 750 kg) / (6.37 x 10^6 m)^2**3. Calculate:**F ≈ 7358.7 N**4. Round to significant figures:**Since the given values have at most three significant figures, we should round our answer accordingly:F ≈ 7360 N**Therefore, the closest answer is 7400 N.** The other options are incorrect, including those with units of kg, as force is measured in Newtons (N).