Find the magnitude of the gravitational force a 65.4 kg person would experience while standing on the surface of Earth with a mass of 5.98 × 1024 kg and a radius of 6.37 × 106 m. The universal gravitational constant is 6.673 × 10−11 N · m2/kg2.
Answer in units of N
F = G*M*m/R(earth)^2
M = Earth mass
m = person's mass
Just crank out the number.
Since those are the actual earth mass and radius values, the answer must also be M*g = (65.4 kg)(9.81 m/s^2) = 642 N
Both formulas agree.
To find the magnitude of the gravitational force a person would experience while standing on the surface of the Earth, we can use Newton's law of gravitation:
F = (G * m1 * m2) / r^2
Where:
F is the magnitude of the gravitational force
G is the universal gravitational constant (6.673 × 10^−11 N · m^2/kg^2)
m1 is the mass of the person (65.4 kg)
m2 is the mass of the Earth (5.98 × 10^24 kg)
r is the radius of the Earth (6.37 × 10^6 m)
Now, let's substitute the given values into the equation:
F = (6.673 × 10^−11 N · m^2/kg^2) * (65.4 kg) * (5.98 × 10^24 kg) / (6.37 × 10^6 m)^2
First, let's do the calculation in the parentheses:
F = (6.673 × 10^−11 N · m^2/kg^2) * (65.4 kg) * (5.98 × 10^24 kg) / (4.05569 × 10^13 m^2)
Now, let's calculate the numerator:
Numerator = (6.673 × 10^−11 N · m^2/kg^2) * (65.4 kg) * (5.98 × 10^24 kg) = 0.25 N
And, let's calculate the denominator:
Denominator = (4.05569 × 10^13 m^2)
Now, let's divide the numerator by the denominator to find the magnitude of the gravitational force:
F = Numerator / Denominator = 0.25 N / (4.05569 × 10^13 m^2)
F ≈ 6.16 × 10^−9 N
Therefore, the magnitude of the gravitational force a 65.4 kg person would experience while standing on the surface of the Earth is approximately 6.16 × 10^−9 N.