A woman standing on the surface of the Earth, 6.38 x 106 meters from its center, has a mass of 57.0 kg. If the mass of the Earth is 5.98 x 1024 kg, what is the force of gravity on the woman?
F = GMm/r^2 = (6.67*10^-11)(5.98*10^24)(57.0)/(6.38^10^6)^2
= 558.55 N
Hmmm. 9.81 * 57 = 559.17
Must be some rounding error in the calculation, or in the values given.
the Earth is an oblate spheroid
gravitational force is not uniform over the surface
9.81 is an "average" value
To find the force of gravity on the woman, we can use Newton's law of universal gravitation, which states that the force of gravity between two objects is given by the equation:
F = G * (m1 * m2) / r^2
Where:
F is the force of gravity
G is the gravitational constant (approximately 6.67430 x 10^-11 N * (m/kg)^2)
m1 is the mass of the woman
m2 is the mass of the Earth
r is the distance between the centers of the woman and the Earth
Given:
m1 = 57.0 kg (mass of the woman)
m2 = 5.98 x 10^24 kg (mass of the Earth)
r = 6.38 x 10^6 meters (distance from the center of the Earth)
Substituting these values into the equation, we get:
F = (6.67430 x 10^-11 N * (m/kg)^2) * (57.0 kg * 5.98 x 10^24 kg) / (6.38 x 10^6 meters)^2
Calculating the expression gives:
F ≈ 5.10 x 10^2 N
Therefore, the force of gravity on the woman is approximately 5.10 x 10^2 Newtons.
To calculate the force of gravity on the woman, you can use the formula for gravitational force:
Fg = (G * m1 * m2) / r^2
Where:
Fg is the force of gravity
G is the gravitational constant, approximately 6.67 x 10^-11 Newtons per kilogram squared (N·m²/kg²)
m1 and m2 are the masses of two objects (in this case, the mass of the Earth and the mass of the woman)
r is the distance between the centers of the two objects (in this case, the distance from the woman to the center of the Earth)
Plugging in the values:
m1 (mass of the Earth) = 5.98 x 10^24 kg
m2 (mass of the woman) = 57.0 kg
r (distance from the woman to the center of the Earth) = 6.38 x 10^6 meters
Fg = (6.67 x 10^-11 N·m²/kg² * (5.98 x 10^24 kg) * (57.0 kg)) / (6.38 x 10^6 meters)^2
Now you can calculate the force of gravity on the woman.