Question

Perhaps the most-common gravitational calculation is to determine the "weight" of an object of mass mo sitting on the surface of the earth (i.e., the magnitude of the gravitational attraction between the earth and the object). According to Newton's law of universal gravitation, the gravitational force on the object is Fg=G(memor2e)=(Gmer2e)mo, where me is the mass of the earth and re is the distance between the object and the center of the earth (i.e., re = radius of the earth = 6.38×103km).

Answer 1

The weight of an object of mass
`\(m_o\)` on the surface of the Earth is given by the formula
`\(W = m_o \cdot g\)`, where g is the acceleration due to gravity, approximately
`\(9.8 \, \text{m/s}^2\)`.

Step-by-step explanation:

The formula to determine the weight of an object on the surface of the Earth,
`\(W = m_o \cdot g\)`, is derived from Newton's law of universal gravitation. According to this law, the gravitational force
`(\(F_g\))` between two objects is given by
`\(F_g = (G \cdot m_e \cdot m_o)/(r_e^2)\)`, where G is the gravitational constant,
`\(m_e\)`is the mass of the Earth,
`\(m_o\)` is the mass of the object, and
`\(r_e\)`is the distance between the object and the center of the Earth.

By substituting
`\(g = (G \cdot m_e)/(r_e^2)\)` into the equation, we get
`(W = m_o \cdot g\)`) . Here, g represents the acceleration due to gravity and is approximately
`\(9.8 \, \text{m/s}^2\)\\` on the surface of the Earth. Therefore, the weight of an object is the product of its mass and the acceleration due to gravity, providing a convenient and widely used formula for gravitational calculations.

This formula simplifies the gravitational force calculation, allowing for a straightforward determination of an object's weight based solely on its mass and the gravitational acceleration at the Earth's surface.

The acceleration due to gravity is a constant near the Earth's surface, making this formula applicable for everyday scenarios and providing a practical means for calculating weights in physics and engineering contexts.