How do I calculate finding the weight of someone, on the earth's surface with a radius of 3900 miles, and their weight 625ft above the surface?
To calculate the weight of someone on Earth's surface, you need to take into account two factors: the gravitational force and the altitude above the Earth's surface. Here's how you can calculate it:
Step 1: Determine the formula for gravitational force:
The formula for gravitational force is F = (G * m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two objects.
Step 2: Identify the known values:
In this case, we know the following:
- Gravitational constant (G) is approximately 6.67430 × 10^-11 N(m/kg)^2.
- The mass of the person (m1) is required. Assuming an average weight, we can use the value of 625 pounds.
- The radius of the Earth (r) is 3900 miles.
Step 3: Convert units:
To ensure the units are consistent, convert the values to the appropriate unit. In this case, convert the weight from pounds to kilograms. 1 pound is approximately equal to 0.453592 kg.
Step 4: Calculate the weight:
Plug the values into the formula for gravitational force:
F = (G * m1 * m2) / r^2
F = (6.67430 × 10^-11 N(m/kg)^2 * (625 * 0.453592 kg) * m2) / (3900 miles * 1.60934 km/mile)^2
The 1.60934 factor is used to convert miles to kilometers.
Step 5: Simplify and calculate:
Now you can simplify and calculate the weight.
Please note that in order to completely solve the problem, we need to know the value of "m2." This value represents the mass of the Earth or any other object attracting the person. If we assume the mass of the Earth (m2) as 5.972 × 10^24 kg, then we can proceed with calculations using this value.
F = (6.67430 × 10^-11 N(m/kg)^2 * (625 * 0.453592 kg) * (5.972 × 10^24 kg)) / (3900 miles * 1.60934 km/mile)^2
By evaluating this expression, you will find the weight of the person on Earth's surface at a height of 625 ft above it.