IMAGINE- a building 6400km. high. On the ground floor, a person weighs 175lbs when he steps on a spring scale how much would the man weigh on the same scale if he were standing at the top floor? HINT: Note that 6400km is also the radius of the earth so that the top floor is 2Re from the earths center. Think about what this means for Fgrav before you start plugging in numbers or making conversions

To determine the weight of the person on the top floor of the building, we need to consider the concept of gravity and its effect at different heights.

The weight of an object on Earth is determined by the force of gravity acting upon it. The force of gravity depends on two factors: the mass of the object and the distance between the object and the center of the Earth.

In this scenario, we are given that the building is 6400 km high, which is also the radius of the Earth (Re). Thus, the top floor of the building would be 2 times the Earth's radius away from its center, meaning the distance from the top floor to the center of the Earth is 2Re.

Considering that gravity decreases with distance, we can deduce that the force of gravity on the person standing at the top floor would be weaker compared to the person on the ground floor. This means that the weight of the person will be less.

To calculate the weight on the top floor, we can use Newton's law of universal gravitation:

Fgrav = (G * mass1 * mass2) / (distance^2)

Where:
Fgrav is the force of gravity
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2)
mass1 is the mass of the Earth
mass2 is the mass of the person
distance is the distance between the person and the center of the Earth

Since the mass of the person remains the same, we can focus on the distance factor. On the ground floor, the distance from the center of the Earth is Re, while on the top floor, it is 2Re.

Therefore, we can conclude that the force of gravity at the top floor would be (1/2)^2 = 1/4 of the force of gravity on the ground floor. In other words, the person's weight would be 1/4 of what it is on the ground floor.

To determine the weight of the person on the top floor, we can calculate 1/4 of the weight on the ground floor:

Weight on the top floor = 1/4 * Weight on the ground floor
Weight on the top floor = 1/4 * 175lbs
Weight on the top floor = 43.75lbs

Therefore, the person would weigh 43.75lbs on the spring scale if they were standing on the top floor of the 6400km high building.