# What is the mathematical relationship between mass and weight

### BBC - GCSE Bitesize: Mass and force

3 days ago Here is a simple explanation of the difference between mass and weight, with examples and a chart comparing the two concepts. The weight of an object is the force on it due to gravity. There is a relationship between weight, mass and acceleration of free-fall (weight = mass × acceleration . Right girls and boys, it's time to dip our toes into the wonderful world of science and explore the difference between mass and weight.

Because mass and weight are separate quantities, they have different units of measure. In the International System of Units SIthe kilogram is the basic unit of mass, and the newton is the basic unit of force. The non-SI kilogram-force is also a unit of force typically used in the measure of weight. Similarly, the avoirdupois poundused in both the Imperial system and U.

Converting units of mass to equivalent forces on Earth[ edit ] Gravity anomalies covering the Southern Ocean are shown here in false-color relief. This image has been normalized to remove variation due to differences in latitude.

When an object's weight its gravitational force is expressed in "kilograms", this actually refers to the kilogram-force kgf or kg-falso known as the kilopond kpwhich is a non-SI unit of force. All objects on the Earth's surface are subject to a gravitational acceleration of approximately 9. The General Conference on Weights and Measures fixed the value of standard gravity at precisely 9. Thus the kilogram-force is defined as precisely 9.

In reality, gravitational acceleration symbol: Engineers and scientists understand the distinctions between mass, force, and weight. Engineers in disciplines involving weight loading force on a structure due to gravitysuch as structural engineeringconvert the mass of objects like concrete and automobiles expressed in kilograms to a force in newtons by multiplying by some factor around 9.

Material properties like elastic modulus are measured and published in terms of the newton and pascal a unit of pressure related to the newton. Buoyancy and weight[ edit ] Regardless of the fluid in which an object is immersed gas or liquidthe buoyant force on an object is equal to the weight of the fluid it displaces.

A hot air balloon when it has neutral buoyancy has no weight for the men to support but still retains great inertia due to its mass. Usually, the relationship between mass and weight on Earth is highly proportional; objects that are a hundred times more massive than a one-liter bottle of soda almost always weigh a hundred times more—approximately 1, newtons, which is the weight one would expect on Earth from an object with a mass slightly greater than kilograms.

A common helium-filled toy balloon is something familiar to many. When such a balloon is fully filled with helium, it has buoyancy —a force that opposes gravity. When a toy balloon becomes partially deflated, it will often become neutrally buoyant and can float about the house a meter or two off the floor.

## What Is The Difference Between Mass And Weight?

In such a state, there are moments when the balloon is neither rising nor falling and—in the sense that a scale placed under it will have no force applied to it—is, in a sense perfectly weightless actually as noted below, weight has merely been redistributed along the Earth's surface so it cannot be measured.

Though the rubber comprising the balloon has a mass of only a few grams, which might be almost unnoticeable, the rubber still retains all its mass when inflated. If one were however to weigh a small wading pool that someone then entered and began floating in, they would find that the full weight of the person was being borne by the pool and, ultimately, the scale underneath the pool. However, as noted, an object supported by a fluid is fundamentally no different from an object supported by a sling or cable—the weight has merely been transferred to another location, not made to disappear.

The mass of "weightless" neutrally buoyant balloons can be better appreciated with much larger hot air balloons. Buoyancy and the resultant reduction in the downward force of objects being weighed underlies Archimedes' principlewhich states that the buoyancy force is equal to the weight of the fluid that the object displaces.

**Relationship between weight and mass**

If this fluid is air, the force may be small. Buoyancy effects of air on measurement[ edit ] Normally, the effect of air buoyancy on objects of normal density is too small to be of any consequence in day-to-day activities. For convenience, a standard value of buoyancy relative to stainless steel was developed for metrology work and this results in the term "conventional mass".

Since objects with precisely the same mass but with different densities displace different volumes and therefore have different buoyancies and weights, any object measured on this scale compared to a stainless steel mass standard has its conventional mass measured; that is, its true mass minus an unknown degree of buoyancy. In high-accuracy work, the volume of the article can be measured to mathematically null the effect of buoyancy.

Types of scales and what they measure[ edit ] A balance-type weighing scale: Unaffected by the strength of gravity. Load-cell based bathroom scale: But do you really know the difference between weight and mass?

Have you been confusing mass with weight? It's very easy to do when you're not entirely sure of how science actually defines them. Even though they're both linked, there is a basic difference. I've put together a fairly comprehensive description for you which, importantly, is written in layman's terms and not scientific babble! Mass is a scientific measure of the amount of matter an object is made up of.

No matter where you are at given moment in time, mass is constant. So, whether you're walking to the shop to stock up on groceries or bouncing around on the moon, your mass is the same. Obviously, if you're on a diet that's not the answer you want to hear but don't panic - we'll get to the all-important definition of weight shortly.

Some other key points about mass Mass is indestructible.

### What is the mathematical relationship between mass, weight, and gravity? | Yahoo Answers

As you've seen above, no matter where you are in the universe your mass will never change Mass can never be zero. What we mean by this is that everything in the universe has mass. If it didn't it simply wouldn't exist Mass is not related to gravity, centrifugal force, etc and these forces have no effect whatsoever on your mass Mass is commonly measured in kilograms and grams. Hopefully, the descriptions above have given you a good idea of what mass really is. Don't fall into the trap of thinking that this unit of measure is not important - it is.

After all, without the huge mass that makes up planet Earth we'd have no gravity - a great way to save money on fuel as you can simply float to work, but not so great when you're trying to drink your morning espresso on your way to the office.

Weight is a form of measurement that is dependent on gravity and, unlike mass, your weight can vary depending on where you are in the universe.

Weight is a pretty important measure not only to dieters the world over but also to the scientists and egg heads who design things like space shuttles and boats - opposite end of the spectrum, but it's all about perspective. But how can weight vary whilst mass has to remain constant?

Scientists have defined weight using this equation: