Final answer:
To find the distance from the center of the Earth at which a 0.4 kg object has a weight of 2.0 N, we can use the equation w = mg and the relationship between weight and acceleration due to gravity. Using the values provided, the distance is approximately 4.23 × 10^6 m.
Step-by-step explanation:
To find the distance from the center of the Earth at which a 0.4 kg object has a weight of 2.0 N, we can use the equation for weight:
w = mg
Given that the weight is 2.0 N and the mass is 0.4 kg, we can calculate the acceleration due to gravity, which is the value of g. Rearranging the equation, we have:
g = w/m
Substituting the given values, we get:
g = 2.0 N / 0.4 kg = 5.0 m/s²
The acceleration due to gravity decreases as we move away from the Earth's center. We can use this information to find the distance at which a 0.4 kg object has a weight of 2.0 N. Since weight is given by:
w = mg
Rearranging the equation for distance:
r = √(GM/g)
Given that G is the gravitational constant (6.67 × 10^-11 N·m²/kg²) and M is the mass of the Earth (5.97 × 10^24 kg), we can substitute the values and calculate the distance:
r = √((6.67 × 10^-11 N·m²/kg²)(5.97 × 10^24 kg) / 5.0 m/s²)
Solving for r, we find:
r ≈ 4.23 × 10^6 m