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# Measurement of the Mass of Matter

by Ron Kurtus (revised 19 February 2016)

Objects are made up of called matter, which consists of molecules and atoms. Besides taking up space, a basic property of matter is its mass.

You can * measure the mass* of an object by seeing how much force is required to change its state of motion. The gravitational field of matter is another measurement of mass. Finally, there is an equivalence of mass and energy.

Questions you may have include:

- How can mass be measured by changing its motion?
- What measurements are made with gravity?
- How is mass equivalent to energy?

This lesson will answer those questions. Useful tool: Units Conversion

## Mass and motion

According to Newton's Law of Inertia, objects require a force applied to them to change their motion. The equation for that is

F = ma

where:

**F**is the force applied**m**is the mass of the object**a**is its acceleration**ma**means**m**times**a**

What this means is that if we know the amount of force pushing on an object, and we measure its acceleration or how fast it is changing its velocity, we can then calculate the mass of the object.

(*See Newton's Laws of Motion for more about his Law of Inertia.*)

## Mass and gravity

All matter has the property of possessing a gravitational field. It is uncertain whether gravity is a property of mass, but it is known that mass is affected by gravity.

### Gravitational force between objects

Newton's Universal Law of Gravity states that the force of attraction between two objects is according to the equation

F = GMm/r²

where:

**F**is the force of attraction between the two objects**G**is the universal gravitational constant = 6.67*10^{-11}N-m²/kg²**M**is the known mass**m**is the unknown mass**r**is the distance between the centers of the two objects-
**r²**is**r-**squared or**r**times**r** -
**GMm/r²**is**G**times**M**times**m**divided by**r²**

Thus, if you can measure the force between the two objects, know the mass of one, and know the distance between them, you can measure the mass of the other object.

(*See Universal Gravity Equation for more information.*)

### Weight

The mass of an object on the Earth can be measured by weighing it, according to the equation

W_{t}= mg

where:

**W**is the weight of the object on Earth_{t}**m**is its mass**g**is the gravitational constant on Earth**mg**means**m**times**g**

Since the gravitational field on Earth is so much large than the gravitational field caused by a typical object, that gravity force is considered trivial and only the force from Earth is used. Knowing the weight of an object, you can directly calculate its mass.

This equation holds on other large bodies. For example, **g** on the Moon is about 1/6 that of Earth, so that must be taken into account when measuring the mass on the Moon.

(*See Gravity Equations near Earth for more information.*)

## Mass and energy

Einstein's equation shows that a quantity of mass can be converted into "pure" energy. This is not the kinetic energy of matter in motion. Rather, it is the conversion of matter into electromagnetic radiation. This equation also is interpreted as showing the equivalence of mass and energy.

Einstein's equation is

E = mc²

where:

**E**is the total energy of a quantity of mass**m**is the mass of an object**c**is the speed of light-
**c²**is**c**-squared or**c**times**c** **mc²**is**m**times**c²**

This equation or relationship has been verified in nuclear reactions and atomic explosions.

## Summary

A basic property of matter is its mass. You can measure the mass of an object by applying Newton's Law of Inertia equation. Mass also can be measured by gravitational forces. Einstein's Equation shows the equivalence of mass and energy.

Dare to dream great thoughts

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## Measurement of the Mass of Matter