91Ó°ÊÓ

Weight is the force exerted by gravity on an object. To determine the weight of an object, we use the formula:

• \( W = mg \)

Here, \( W \) represents weight, \( m \) is the object's mass, and \( g \) is the acceleration due to gravity. Remember, weight is different from mass. It depends on both the mass of the object and the local gravitational field strength.When solving problems, it's essential to keep units consistent:

• Mass is often measured in kilograms (kg).
• Acceleration due to gravity is typically measured in meters per second squared (\( m/s^2 \)).
• Weight will then be in newtons (N).

Remember that weight changes depending on the gravitational force of the body it is on. Hence, weight can vary while the mass remains constant.

Mass and gravity interact in an interesting way. An object's mass is a measure of the amount of matter it contains, staying constant regardless of location. Gravity, on the other hand, is a force that the Earth (or any celestial body) exerts on objects due to its mass.Gravity depends on:

• The mass of the celestial body (e.g., Earth).
• The distance between the object and the center of the celestial body.

If the Earth's mass were doubled while keeping the same density, its gravitational force would increase. The formula for gravity includes the mass of the Earth \( M \) and the radius \( R \):

• \[ g = \frac{GM}{R^2} \]

Since gravity is contingent on mass, doubling Earth’s mass (while keeping the same size) directly doubles the gravitational pull on objects at its surface.

The acceleration due to gravity, denoted \( g \), is a crucial factor when calculating weight. It represents how quickly an object accelerates toward the surface due to Earth’s gravity. On average, on Earth, \( g \) is approximately \( 9.81 \, m/s^2 \).Factors influencing acceleration due to gravity include:

• The mass of Earth or the other celestial body of interest.
• Distance from the center of the mass to the point where \( g \) is being measured.

In our exercise, doubling Earth's mass results in doubling \( g \). Because \( g \) is directly tied to the Earth’s mass, if the mass is modified, \( g \) adjusts proportionally. Consequently, this doubled \( g \) leads to a doubled weight for any object on Earth's surface. Understanding \( g \) is essential in grasping how weight and gravitational forces interplay in gravitational calculations.