# How to Calculate Mass With a Bathroom Scale

You can’t use your bathroom scale to measure the mass of the universe. But calculating mass isn’t that difficult once you understand density and the metric system.

The metric system uses units like grams and kilograms (kg), along with larger and smaller multiples of those basic units. It’s easy to understand and makes it easier for scientists around the world to work together.

## Weight

Physicists use scales and balances to find the mass of objects all the time. But what they’re really measuring is the object’s acceleration due to gravity, and this is why it’s important to make a distinction between weight and matter.

Weight is a force, and it depends on the strength of the gravitational field where the object is measured – it will be less on Mars than on Earth, more on Jupiter and very small in space, far from significant sources of gravity. In contrast, matter is the direct measure of the amount of matter present in an object, and it doesn’t depend on where it is.

The word “weight” continues to be used in some contexts, but in physics it is always referred to as matter. The metric unit of mass is the kilogram, which is defined as the mass of the International Prototype Kilogram, a platinum-iridium cylinder kept at the International Bureau of Weights and Measures in France.

## Density

Density is the ratio of an object’s mass to its volume. It’s also a measurement of how tightly packed the material is.

As a result, it’s very important to understand how density works. Density can be expressed in any combination of mass and volume units, though grams per cubic centimeter (g cc) and kilograms per cubic meter are the most common.

A brick has a much higher density than Styrofoam, which is why the brick is harder and more solid than the Styrofoam. It’s also why a brick sinks in water and an anchor floats on it.

Because it is a characteristic intensive property, density can be used to identify an unknown pure substance if you have a list of possible reference densities available. To determine bulk density, you fill a container with the material of interest and then weigh it. You can measure bulk density with a scale, balance or using a pycnometer, air comparison pycnometer, Coriolis flow meter or an immersed body method (buoyancy for liquids). Bulk density is not affected by temperature or pressure, and it’s also called specific gravity.

## Active Gravitational Mass

There are three types of mass: inertial mass to determine how much an object resists acceleration; passive gravitational mass to determine the strength of an object’s interaction with gravity, and active gravitational mass that defines how strong it is at attracting or being attracted by other objects. These three facets of mass are not the same and should not be confused.

Inertial mass is measured with balance scales, which use the principle of Hooke’s Law to read off an inertial force g (which depends on the mass M being measured). Passive gravitational mass is measured by the transverse and longitudinal velocities which a moving mass induces in test particles initially at rest near its path – it’s measured with high accuracy using laser interferometers.

The equivalence of inertial and passive gravitational masses is one of the most important experimental results in physics, originally discovered by Galileo in the Pisa experiments (see Figure 5.3). It provides the basis for Einstein’s theory of relativity and is verified to a remarkable degree of precision.

## Passive Gravitational Mass

The passive gravitational mass of an object is how it responds to a gravity field. Objects with more passive gravitational mass tend to be heavier than objects that have less. This is why the force of gravity acts on them more strongly, and it is also why they experience greater acceleration.

Gravitational force between two bodies depends on their relative mass and the distance between their centers of mass. This is why objects of different shapes fall at the same rate, assuming air resistance is negligible. This has been observed since the 17th century and is a fundamental principle of Newtonian physics and general relativity.

A new study by researchers at Leibniz University Hannover confirms this equivalence principle with 100 times greater accuracy than previous studies. If passive gravitational mass was not equal to inertial mass, then the Moon’s iron core and aluminum shell would accelerate differently. This could be detected by the Lunar Laser Ranging (LLR) experiments, but so far no such disparity has been found.

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