Mass

What is Mass?

Mass is a fundamental property of physical objects which measures the amount of matter within them. Unlike weight, mass is not affected by gravity. This makes it a consistent property regardless of location.

Mass Formula

In physics, mass is a fundamental property of an object and is a measure of the amount of matter it contains. The formula for mass is derived from Newton’s second law of motion, which relates mass, force, and acceleration.

Newton’s Second Law of Motion

Newton’s second law states that the force applied to an object is equal to the mass of the object multiplied by its acceleration. This relationship is expressed in the formula:

F = ma

Where:

• F is the force applied to the object (measured in newtons, N)
• m is the mass of the object (measured in kilograms, kg)
• a is the acceleration of the object (measured in meters per second squared, m/s²)

Solving for Mass

To find the mass of an object when you know the force applied to it and its acceleration, you can rearrange the formula:

m=F/a​

This equation means that the mass of an object is equal to the force applied to it divided by the acceleration it experiences.

Example Calculation

Imagine a scenario where a force of 10 newtons is applied to an object, causing it to accelerate at 2 meters per second squared. Using the mass formula, you can calculate the mass as follows:

m = 10N/(2m/s²) = 5 kg

This calculation shows that the object has a mass of 5 kilograms.

How to Find Mass?

Finding the mass of an object involves different methods depending on the context and the available tools. Here are the primary ways to determine the mass of an object:

Using a Balance Scale

The most direct method to measure mass is by using a balance scale, which compares the mass of an object to known masses.

1. Place the object on the balance scale.
2. Add known masses to the opposite side until the scale balances evenly.
3. The total of the known masses will equal the mass of the object.

This method is highly accurate and is commonly used in laboratories.

Using a Spring Scale

A spring scale measures the weight of an object, which can be converted into mass:

1. Hang the object from the spring scale.
2. Read the weight measurement.
3. Convert the weight into mass by dividing by the acceleration due to gravity (approximately 9.81 m/s² on Earth). Mass (kg)= Weight (N)​/(9.81 m/s²)

Using Water Displacement

For irregularly shaped objects, the water displacement method can determine volume, which can help find mass if the density is known:

1. Fill a graduated cylinder with water.
2. Note the initial volume of water.
3. Submerge the object completely in the water.
4. Note the new volume of water.
5. The volume of the object is the difference between the initial and new volumes.
6. If the density of the material is known, multiply it by the volume to find the mass. Mass = Density × Volume

Using Mathematical Formulas

If the object is a standard geometric shape and the density of the material is known, you can calculate its volume and then use the density to find the mass:

1. Calculate the volume of the object. (For example, the volume of a cube is s³ where s is the length of a side.)
2. Multiply the volume by the density of the material. Mass = Volume × Density

Example Calculation

If you have a cube of metal with each side measuring 2 cm, and the density of the metal is 7.87 g/cm³:

1. Calculate the volume: Volume=2 cm×2 cm×2 cm=8 cm³
2. Calculate the mass: Mass = 8 cm³ × 7.87 g/cm³ = 62.96 g

What Units are Used to Measure Mass?

Metric System (SI Units)

• Kilogram (kg): The kilogram is the base unit of mass in the International System of Units (SI) and is used globally in science and commerce. One kilogram is defined by the mass of a specific platinum-iridium alloy cylinder kept at the International Bureau of Weights and Measures.
• Gram (g): Smaller than a kilogram, the gram is often used in scientific measurements for smaller quantities. 1,000 grams make up a kilogram.
• Milligram (mg) and Microgram (µg): These are even smaller units used mainly in pharmacy, chemistry, and biology where precise small measurements are essential.

Imperial System

• Pound (lb): The pound is commonly used in the United States and other countries still utilizing the imperial system. It is primarily used in everyday activities like cooking, body weight measurement, and industrial trading.
• Ounce (oz): Smaller than a pound, the ounce is used to measure lighter weights. There are 16 ounces in a pound.

Other Units

• Tonne (metric ton): Equivalent to 1,000 kilograms, the tonne is used to measure heavier masses, especially in transportation and large-scale commerce.
• Stone: Used primarily in the UK and Ireland for body weight, one stone equals 14 pounds.
• Carat: Specifically used in the gemstone and jewelry industry, one carat is equal to 200 milligrams.

Scientific Units

• Atomic mass unit (amu or Dalton): This unit is used in chemistry and physics to express the masses of atoms and molecules. It is roughly equal to the mass of a single proton or neutron.

Example Usage

In everyday life, you might use pounds and ounces to measure ingredients in a recipe if you are in the United States. In a scientific lab, you would likely use grams or milligrams to measure chemicals. When buying jewelry, you might consider the carat weight of diamonds and other gemstones.

Difference Between Mass and Weight

Aspect	Mass	Weight
Definition	Mass is the amount of matter contained in an object.	Weight is the force exerted by gravity on an object.
Units	Measured in kilograms (kg) in the SI system.	Measured in newtons (N) in the SI system.
Constancy	Mass remains constant regardless of location.	Weight changes with the gravitational pull.
Dependency	Does not depend on gravity.	Directly depends on gravitational force.
Measurement	Measured using a balance scale.	Measured using a spring scale.
Formula	No direct formula, intrinsic property of matter.	Weight = Mass x Gravitational acceleration (W = mg)
Example	A person’s mass is the same on Earth and the Moon.	A person weighs less on the Moon than on Earth.