People all over the world use metric measurements for everyday things. Paper, for example, is measured in millimetres. And doctors record our weight in kilograms.

The metric system is a decimal measuring system that uses the meter, liter and gram as units of length, capacity and weight or mass. Larger and smaller metric units relate by powers of 10.

## Gravitational Force

Gravity is a natural force that attracts all matter, from atoms to planets. This force, which is proportional to mass, is strongest between masses that are close together.

However, as the distance between masses increases, the force of gravity decreases rapidly. This is because the gravitational force is dependent on both the total mass of the two objects and the inverse square of the distance between them.

To better understand this, students may conduct an experiment that measures the force of gravity on a particular object (or hanger) and then compares it to the mass of another, known, object. Record the results of these experiments on a graph with the forces on the y-axis and the mass values on the x-axis. Facilitate a whole-class discussion of the graphs and the algebraic equation that results.

## Density

Density is a property of matter that measures how tightly particles are packed together. The formula for density is mass divided by volume; the units used are kilograms per cubic meter (kg/m3), grams per cubic centimeter (g/cm3) and litres per kilogram (l/kg).

Students can learn that the size of the atoms and their arrangement in matter determine its density. The density of a solid is greater than that of a liquid and less than that of a gas, because the particles in a solid are closely packed.

The density of an object allows scientists to predict its weight in a given environment. For example, students can determine that a brick will sink in water but a piece of Styrofoam will float. They can also use the concept of density to explain why metal anchors sink while wood and helium balloons float in air. They can also observe that the density of a battery changes when it is charged or discharged, as electricity is converted to other forms of energy.

## Force of Acceleration

Although the word “weight” is often used in a way that makes it sound as though it refers to mass, weight is really a measure of gravitational force. An object’s weight on Earth will be the same whether it is in free fall on the Moon or anywhere else on the planet, but its mass will differ depending on what type of matter it contains and the amount of energy it has.

In fact, all objects exhibit a variable force of gravity, but the size of that force is dependent on the object’s mass and the distance between its centres. This is due to Newton’s Third Law of Interactions: F = ma.

The purpose of this experiment is to illustrate the relationship between acceleration and mass. The experiment involves varying the mass of a trolley while recording corresponding changes in acceleration using a ticker-timer. These results are accumulated in a table which allows the student to manually enter the value of the force (in newtons) into the column of the table.

## Inertia

Inertia is an intrinsic property of an object, its resistance to change in motion or rest. It is determined by an object’s mass, which determines its resistance to acceleration; therefore, a body of greater mass can resist more force than a smaller one.

Similarly, if a piece of Jell-O is flung across the cafeteria table at a great speed it causes more damage than if a book falls off the shelf and lands on the same spot. Both the force and the speed that caused the impact are proportional to the object’s mass, but only the former is a direct measurement of its inertia.

It is possible to measure the mass of an object by using a balance and applying Newton’s second law, which states that m = F/a. Since a balance can accurately measure the weight of an object regardless of gravity, astronauts in space use a balance to discover their mass. Gravitational and inertial mass are identical, and Einstein’s Theory of Relativity demonstrates that energy is also equal to the product of an object’s mass and its acceleration.