Answer:
The result will give you the distance required from the surface of the Earth so that your weight will be 300 N.
Explanation:
To determine how far you should go from the surface of the Earth so that your weight will be 300 N, we need to consider the concept of gravitational force and the relationship between weight and distance from the center of the Earth.
1. First, let's calculate the gravitational force on Earth's surface using the weight given. Weight is the force of gravity acting on an object, and on Earth's surface, it is equal to the gravitational force acting on the object. Therefore, the weight of 600 N represents the gravitational force acting on you when you are on the Earth's surface.
2. Now, let's use the formula for gravitational force to find the distance required for your weight to be 300 N. The formula for gravitational force is F = (G * m1 * m2) / r^2, where F is the force of gravity, G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2), m1 and m2 are the masses of the two objects (in this case, your mass and the mass of the Earth), and r is the distance between the centers of the two objects.
3. Since your mass remains the same, we can consider the mass of the Earth and the distance from the Earth's center to the point where you will have a weight of 300 N as variables. Let's call the distance r2.
4. We can set up the following equation based on the above information:
(600 N) = (G * m * M) / (6.4 x 10^6 m)^2 --> Equation 1, where M is the mass of the Earth and m is your mass.
(300 N) = (G * m * M) / (r2)^2 --> Equation 2
5. We can now solve for r2 by rearranging Equation 2:
r2^2 = [(G * m * M) / (300 N)] --> Equation 3
r2 = sqrt([(G * m * M) / (300 N)]) --> Equation 4
6. Now we can substitute the values into Equation 4:
r2 = sqrt([(6.67430 × 10^-11 N m^2/kg^2) * m * M) / (300 N)])
7. The mass of the Earth, M, is approximately 5.972 × 10^24 kg. We can assume your mass, m, remains constant.
8. Finally, we can calculate the value of r2 by plugging in the values and solving for r2 using a calculator or computer:
r2 = sqrt([(6.67430 × 10^-11 N m^2/kg^2) * m * (5.972 × 10^24 kg)] / (300 N)])
The result will give you the distance required from the surface of the Earth so that your weight will be 300 N.
