If you know its volume and density, you can determine the weight of a plastic object without weighing it. *Weight* is often used interchangeably with *mass* in everyday language but in fact they different. *Mass* is the amount of matter in an object and is the resistance of an object to acceleration.

Mass is constant regardless of its location, so an astronaut with a mass of 100 kg on the Earth has the same mass on the moon. *Weight*, however, is the force on a mass under the influence of gravity and is given by the relationship:

In the metric system weight has units of Newtons (N).

On the surface of the Earth the gravitational acceleration is *g*, which is 9.81 m/s^{2}. On the moon gravitational acceleration is only one-sixth that of the Earth and is 1.64 m/s^{2}.

Because weight varies with the local gravitational field, the astronaut with a mass of 100 kg has a weight of 981 N on Earth but only 164 N on the moon. In deep space, away from the gravity of any astronomical bodies, the astronaut would have a weight of 0 N, a condition popularly called *weightlessness*.

## **How to Determine Volume**

*Volume* is the amount of space an object occupies. It is possible to calculate the volume of a regular solid, like a cube, by measuring its dimensions but this method would be difficult for irregularly shaped objects. Instead, we can submerge the object in water and use the fact that the volume of displaced water is equal to the volume of the immersed object.

## **What is Density?**

The **mass density** of an object, simply called *density*, is its **mass divided by its volume**. Density is usually represented by the Greek letter *rho* (*ρ*) and is given by the equation:

Here *m* is the mass of an object and *v* is its volume. In the metric system density has units of kilograms per cubic meter (kg/m^{3}) or grams per cubic centimeter (g/cm^{3}).

If you know the density of an object, rearranging the density equation gives the expression for calculating its mass:

In turn, once you know mass you can calculate weight.

## **Determine Weight Experimentally**

1. **Obtain a piece of the plastic.** Identify the type of plastic you are testing and look up its mass density.

2. **Measure the volume of the sample.** Fill a large graduated cylinder with water to the 500 ml level. Immerse the piece of plastic completely in the water.

Many plastics are less dense than water and will float. In this case, place a heavy weight like a metal nut in the bottom of the cylinder then add water to the 500 ml level. Remove the weight and tie it to the plastic sample with a short length of thread. Drop them together into the water so the piece of plastic is completely submerged.

The volume of the weight was included when the cylinder was calibrated with water at the 500 ml level, so the weight will not affect the measurement. The difference between the new and original water levels is the volume of the object. Remember that one milliliter (ml) is equal to one cubic centimeter (cm^{3}).

3. **Calculate mass with the density equation.** The mass of the plastic is density multiplied by volume: *m* = *ρ* × *v*. Record the mass in kilograms.

4. **Calculate weight with the acceleration due to gravity.** Make sure to use the correct units in the metric system. Weight (N) = mass (kg) × acceleration due to gravity (m/s^{2}).

## **Example: Calculating the Weight of Acrylic**

If you want to determine the weight of a piece of acrylic plastic, also known as Plexiglas, Lucite or Acrylite (all trademarked names), follow the steps described in the previous section:

Step 1: **Obtain a piece of the plastic.** Cut out a sample of acrylic. The density of acrylic is 1.18 g/cm^{3}.

Step 2: **Measure the volume of the sample.** If the water level rose to 550.0 ml after the plastic was immersed in the graduated cylinder, then its volume is 550.0 ml – 500.0 ml = 50.0 ml, or 50.0 cm^{3}.

Step 3: **Calculate mass with the density equation.** The mass of the piece of plastic = density × volume = 1.18 g/cm^{3} × 50.0 cm^{3} = 59 g = 0.059 kg.

Step 4: **Calculate weight with the acceleration due to gravity**. The weight (N) = mass (kg) × acceleration due to gravity (m/s^{2}). On Earth the weight would be 0.059 kg × 9.81 m/s^{2} = 0.58 N.

References

About the Author

H. L. M. Lee is a writer, electronics engineer and owner of a small high-tech company. He also produces web content and marketing materials, and has taught physics for students taking the Medical College Admissions Test. In addition, he has written numerous scripts for engineering and physics videos for JoVE, the Journal of Visualized Experiments. H.L.M Lee earned his undergraduate engineering degree at UCLA and has two graduate degrees from the Massachusetts Institute of Technology. More information about him and his work may be found on his web site at https://www.hlmlee.com/

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