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

I KNOW THIS MUCH----- confuesed what to plug in where. and what not to plug in. The weight is equal ‘mg”
On the Earth surface acceleration due to gravity is
mg=GmM/R²,
g=G•M•/R²,
where
the gravitational constant G =6.67•10^-11 N•m²/kg²,
Earth’s mass is M = 5.97•10^24 kg,
Earth’s radius is R = 6.378•10^6 m.
g=9.8 m/s²

Let's find “g” at the height “h” . Distance between the mas “m” (the person) and the center of the Earth is 2R =>
m•g1= G•m•M/(2R)²
g1= G•M/4R²=g/4

In the "high" building mg1= mg/4

if r = 2R then r^2 = 4 R^2

then weight = (1/4) original

okay so would it be

(6.67*10^-11)(5.97*10^24)(77.87)/4(6.378*10^6)^2?!?!?!

To solve the problem, we first need to calculate the acceleration due to gravity at the top floor of the building.

We already know that on the surface of the Earth, the acceleration due to gravity is approximately 9.8 m/s² or g = 9.8 m/s².

Now, let's find g at the height 'h' of the building. We are given that the height of the building is 6400 km or 6400 * 1000 = 6,400,000 m.

Since the building is 2 times the radius of the Earth away from the Earth's center, we can consider it at a distance of 2R from the Earth's center.

Using the formula for gravitational acceleration, g1 = G * M/(2R)², where G is the gravitational constant (6.67 * 10^-11 N*m²/kg²), M is the mass of the Earth (5.97 * 10^24 kg), and R is the radius of the Earth (6.378 * 10^6 m), we can calculate g1.

g1 = (6.67 * 10^-11 N*m²/kg² * 5.97 * 10^24 kg)/(4 * (6.378 * 10^6 m)²)

g1 = 0.000499 N/kg

Now, we know that the weight is equal to m * g, where m is the mass of the person and g is the acceleration due to gravity.

At the ground floor, the person weighs 175 lbs. We need to convert this to kilograms, which is approximately 79.38 kg (1 lb is approximately 0.45 kg).

So, at the ground floor, the weight of the person can be calculated as m * g = 79.38 kg * 9.8 m/s² = 778.44 N (rounded to two decimal places).

Now, for the top floor of the building, the weight of the person can be calculated as m * g1 = 79.38 kg * 0.000499 N/kg ≈ 0.0396 N (rounded to four decimal places).

Therefore, the person would weigh approximately 0.0396 N on the same scale if they were standing at the top floor of the building.