Mass and Weight

An object's weight and its acceleration as a result of gravity are connected. The mass of a thing is the entire amount of matter that it contains. This amount is a scalar. The kilogram (kg) is the SI unit for it. The amount of iron in a 1 kilogram mass of iron is always 1 kg, regardless of where it is stored on Earth, in the International Space Station, on the Moon, on Mars, etc. Consequently, the location of an object has no bearing on its mass value. Similar to the tiniest particle, an electron possesses a specific mass. Mass has a value. It is not zero. In a similar vein, gravity acts on even the tiniest mass.

Gravity pulls everything on Earth's surface toward the center. An object's weight is the amount of gravity pulling it down. Weight has the newton (N) as its SI unit since weight is the force applied to an item. This quantity is vector-based. Because gravity is the force that pulls weight toward the center of a planet or satellite, weight is always directed there.

In accordance with Newton's second law of motion, weight, or mass'm', is subject to a force of gravity defined as W = mg, where g is the gravitational acceleration. An object's mass and gravitational acceleration determine its weight. Gravity pulls everything towards the center of the earth, so lifting anything off the surface requires exerting upward force at least equal to the force of gravity. Lifting small and large objects requires varying forces depending on the mass-to-weight relationship. Since gravity's acceleration at a given location is constant, an object's weight varies with its mass. In this instance, the object's weight (W) and mass (m) are directly proportional, or weight (W) x mass (m) [keeping the value of g constant].

In light of this, heavier objects weigh more than lighter ones. As a result, lifting an object with a larger mass requires more force than lifting one with a smaller mass. Additionally, lifting smaller stones is simpler than lifting larger ones.

Variation in Weight Due to Change of Acceleration Due to Gravity

The force of gravity determines the weight differential for a given mass. Therefore, the weight of an object and its acceleration owing to gravity are directly proportional, meaning that Weight (W) x Acceleration due to Gravity (g) [Maintaining constant mass]

The weight of the object varies because the value of 'g' varies depending on the location on Earth.

g α \(\frac1{R^2}\) is the acceleration owing to gravity, and it is inversely proportional to the square of the distance from the earth's center. Likewise, the relationship between weight and acceleration due to gravity (W) α g is straightforward. The weight of an object is less in locations far from the earth's center since there is less acceleration due to gravity there, such as on hilltops, mountains, etc. When gravity's acceleration is at its greatest on the surface of the earth, an object's weight is at its highest. The acceleration that the moon's gravity (gm) causes is six times greater than that of the earth (ge), or gm (frac 16)ge. Consequently, an object of a certain mass on Earth weighs around six times as much as the identical object on the moon. As a result, on the moon, one can jump around six times higher than on Earth. A person should be able to lift roughly six times as much weight on the moon as they can on Earth.The acceleration that the moon's gravity (gm) causes is six times greater than that of the earth (ge), or gm (frac 16)ge. Consequently, an object of a certain mass on Earth weighs around six times as much as the identical object on the moon. As a result, on the moon, one can jump around six times higher than on Earth. A person should be able to lift roughly six times as much weight on the moon as they can on Earth. As a consequence, it is possible to draw the conclusion that an object's weight on other planets or satellites differs from that of Earth when comparing the acceleration caused by gravity on those bodies. The table below provides a few instances.