If the 50.0 kg boy were in a spacecraft 5R from the center of the earth, what would his weight be? (Use the 50.0 kg boy for significant figures)
i got 20N again not sure.. it dosnt tell me if i got them wrong or right online classes are horrible and very confusing
On the Earth
mg=GmM/R²
In the spacecraft
mg'=GmM/(5R)²= {GmM/R²}/25=mg/25
His weight is 50.0/25 =2.0 N
To calculate the weight of the 50.0 kg boy in a spacecraft 5R from the center of the earth, where R is the radius of the earth, we can use the formula for gravitational force:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2)
m1 and m2 are the masses of the two objects (in this case, the boy and the earth)
r is the distance between the centers of the two objects (in this case, 5R)
First, we need to calculate the radius of the earth (R). The approximate value of the radius of the earth is 6,371 km (or 6.371 × 10^6 meters). Therefore, R = 6.371 × 10^6 meters.
Next, we need to substitute the values into the formula:
F = (G * m1 * m2) / r^2
F = ((6.67430 × 10^-11 m^3 kg^-1 s^-2) * (50.0 kg) * (5.972 × 10^24 kg)) / (5 * R)^2
Simplifying:
F = (3.33715 × 10^15 m^3 kg^-1 s^-2 * 50.0 kg * 5.972 × 10^24 kg) / (5 * 6.371 × 10^6 meters)^2
F = (7.91512625 × 10^41) / (25 * 4.06241 × 10^13)
F ≈ 1.94 × 10^28 N
Therefore, the weight of the 50.0 kg boy in the spacecraft 5R from the center of the earth is approximately 1.94 × 10^28 N.