# What is the relationship between mass and weight?

• harry_thawne
In summary, the relationship between mass and weight is constant and proportional because weight is a force that is dependent on the mass and the acceleration due to gravity, which is typically taken to be constant near Earth's surface. This is also related to the units used to measure mass and weight, which can sometimes be used interchangeably but are technically different concepts. f

#### harry_thawne

What does it mean that the relationship between mass and weight is constant and proportional?
I think I don't get it yet. The weight depends of mass, but at the same time depends of gravity, so if mass increase, the weight so does. But if we're on Earth we know that"g" has a value, therefore that "g" could be the constant in this equation that represents the relation: w=m⋅g, Is that the reason why the relationship between this two magnitudes is constant and proportional?
I hope I have explained myself well.

You may wish to read this.

Summary:: What does it mean that the relationship between mass and weight is constant and proportional?

But if we're on Earth we know that"g" has a value, therefore that "g" could be the constant in this equation that represents the relation: w=m⋅g, Is that the reason why the relationship between this two magnitudes is constant and proportional?

Yes, insofar as ##g## is constant.

There are other ways of using the term weight, but what you describe is the way it's used in science and technology.

Weight is the force of gravity on a mass (typically, a mass that is not in freefall with respect to the source of the gravity). Because most human-related measurements and discussions occur near Earth's surface, we can take the proportionality between mass and weight to be g. g is not truly constant, it changes with location and height, but it's useful enough to treat it as constant for most things. If you're launching a rocket into orbit, then you have to be more nuanced.

This is also related to the units we use to describe mass and weight. When we talk about a pound we could mean a pound of mass (454 grams) or a pound of force (~4.4 Newtons), but the distinction doesn't matter as long as we stay near Earth's surface.

• vanhees71, bhobba and sysprog
Just to try and give a short answer. Mass is an intrinsic property of an object as expressed in the definition of force F=ma. Gravity accelerates objects with a constant acceleration regardless of mass. Since F=ma that means it experiences a force from gravity - sometimes called weight. Since acceleration is constant the force and hence weight is proportional to mass. Because of that they are in some contexts used interchangeably, but really are two different things.

Thanks
Bill