Question

Calculate the force of gravity on a 1-Kilogram box located a point 1.3x10^7 meters from the center of Earth if the force on a 2.5-Kilogram box at the same point is 6.1 Newton’s.

Answer 1

The force of gravity on a 1-Kilogram box at the given distance from the center of Earth is calculated to be 2.44 Newtons by using the ratio of masses and the known gravitational force on a 2.5-Kilogram box.

Step-by-step explanation:

The question asks us to calculate the force of gravity on a 1-Kilogram box located at a given distance from the center of Earth using the provided force on a 2.5-Kilogram box at the same distance. This calculation is based on Newton's Universal Law of Gravitation, which can be expressed with the formula F = GmM/r2, where F is the force of gravity, G is the gravitational constant, m and M are the masses of the two objects, and r is the distance between their centers.

To find the force on the 1-Kilogram box, we recognize that the gravitational force is proportional to the mass of the object. Since we know the force on the 2.5-Kilogram box at the same distance is 6.1 Newtons, we can set up a ratio because the force scales linearly with mass. This yields F1kg = (1 kg / 2.5 kg) × 6.1 N.

F1kg = (0.4) × 6.1 N

F1kg = 2.44 N

The force of gravity on the 1-Kilogram box is therefore 2.44 Newtons.

Answer 2

The force of gravity on the 1 kg box is 2 N.

The formula for the force of gravity F on an object with mass m is

F = (GmM)/d²

Since G, M , and d are the same for both objects, (GM)/d² = a constant = k ). Then, we can write

F = km

F₂/F₁ = m₂/m₁

F₂ = F₁ × m₂/m₁

If the 2.5 kg box is object 1,

F₂= 6.1 N × (1 kg/2.5 kg) = 2 N

Note: The answer can have only one significant figure because that is all you gave for the mass of the 1 kg object.