# Measurement of Mass

by Ron Kurtus (revised 18 March 2016)

The * measurement of the mass* of an object is made relative to a standard, defined mass. The

*International System of Units (SI)*standard unit of mass is the kilogram. It is represented by a prototype kilogram object.

The common way to measure the mass of an object is to compare its weight with the weight of a standard or known object on a scale.

Less common—and more difficult—ways determine the mass of an object are to see how much force is required to accelerate the object or to find the gravitational force attracting an unknown mass to a known mass.

Questions you may have include:

- What is a Standard Unit of Mass?
- How can mass be found on a lever or scale?
- What are other ways to make the measurement?

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

## Standard unit of mass

The standard unit of mass was originally defined in 1795 as the mass of one cubic centimeter of water at the melting point of water (4°C). Since a gram was too small to be used commercially, the standard was increased 1000 times to be the kilogram.

Also, to avoid problems with using water, a solid prototype kilogram made of such materials as a platinum-iridium allow is now used. Prototypes are kept in standard labs. Kilogram weights that are used are copies of the prototypes.

## Comparing on a scale

Although mass and weight are not the same thing, they are related by the equation:

W = mg

where

**W**is the weight of the object**m**is its mass**g**is the acceleration due to gravity

This means that the ratio of the masses or two objects equals the ratio of their weights:

W_{1}/W_{2}= m_{1}/m_{2}

Thus, the mass of an object is usually determined by comparing its weight with a standard weight on a scale. You can make adjustments to the Standard Weights or the position of the fulcrum to balance the scale and determine the mass of the object.

### Example

An example of finding the mass with a scale is to use a simple lever:

Using simple lever to measure mass

The equation to find the mass of the Weight to be Measured is:

m = M d_{E}/d_{L}

where

**m**is the mass of the Weight to be Measured**M**is the mass of the Standard Weights**d**is the distance to the fulcrum from the Standard Weights_{E}**d**is the distance to the fulcrum from the Weight to be Measured_{L}

By adding or subtracting weights to **M** or by moving the fulcrum, you balance the weights and determine the value for **m**.

(See Machines > Increasing Force with a Lever for more information.)

## Other measurements

You could also determine the mass of an object by measuring the force required to accelerate the object or by measuring the gravitational force between two objects. However, those methods are not straightforward or easy.

### Mass and inertia

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

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 gravitation

All matter has the property of possessing a gravitational field. Newton's *Universal Law of Gravitation* states that the force of attraction between two objects is according to the equation

F = GMm/r^{2}

where:

**F**is the force of attraction between the two objects**G**is the universal gravitational constant = 6.67*10^{-11}N-m^{2}/kg^{2}**M**is the known mass**m**is the unknown mass**r**is the square of the distance between the centers of the two objects^{2}

(

See Universal Gravitation Equation for more information.)

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. However, the problem is that the objects must be very large for the force to be measurable.

## Summary

The mass of an object can be measured relative to a standard mass. The common way to measure the mass of an object is to compare its weight with the weight of a standard or known object on a scale.

Less common—and more difficult—ways determine the mass of an object are to see how much force is required to accelerate the object or to find the gravitational force attracting an unknown mass to a known mass.

Dare to dream great thoughts

## Resources and references

### Websites

**Kilogram** - Wikipedia

### Books

## Questions and comments

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## Where are you now?

## Measurement of Mass