Mass

In this mini-lesson, we will explore the concept of mass. We will learn what is mass, how to calculate mass, and examples of mass while discovering interesting facts about it.

Everything you see around you has mass.

For example, a table, a chair, your bed, a football, a glass, and even air has mass.

That being said, all objects are light or heavy because of their mass.

a boy standing on a weighing scale

Lesson Plan

 

What Is Mass?

In the subject of physics, mass is the most basic property of matter and it is one of the fundamental quantities.

Mass is defined as the amount of matter present in a body. 

The SI unit of mass is the kilogram (kg). 

The formula of mass can be written as: 

\[ \text Mass = \dfrac {\text Density}{\text Volume}\]

Note: The mass of a body is constant; it doesn’t change at any time. Only in certain extreme cases when a huge amount of energy is given or taken from a body, the mass may be impacted. For example, in a nuclear reaction, a tiny amount of matter is converted into a huge amount of energy, this reduces the mass of the substance.


What Is the Unit of Mass?

The SI unit of mass is "kilograms" or kg.

Note: 1kg is equal to 2.20462 pounds.

Try your hand in the following simulation to know more about the mass of various objects.


Differences Between Mass and Weight

The differences between mass and weight are shown in the table here.

  Mass Weight
Definition •Mass is defined as the amount of matter in a substance •Weight is defined as the amount of force acting on the mass of an object because of acceleration due to gravity.
Denotation •Mass is represented by “M.”

•Weight is represented by “W."

Formula •Mass is always constant for a body.
•One way to calculate mass: Mass = volume × density.
•Weight is the measure of the gravitational force acting on a mass.
•Formula of weight: Weight = mass × acceleration due to gravity
Unit of Measurement •The SI unit of mass is  "kilogram".  •The SI unit of weight is Newton (N).
Quantity Type •Mass is a base quantity.
•Mass only has magnitude and hence, it is a scalar quantity
•Weight is a derived quantity.
•Weight has both magnitude and direction (toward the center of gravity) and hence, it is a vector quantity.
Measuring Instrument •Mass can be easily measured using any ordinary balance.
For example beam balance, lever balance, pan balance, etc.
•Weight can be measured by a spring balance or by using its formula given above.

Did you know that we have different weights on the earth, the moon, and in space?

However, our mass is the same everywhere.

mass and weight on the earth, the moon, and in space

 
important notes to remember
Important Notes
  1. Mass only has magnitude and hence, it is a scalar quantity.
  2. Weight has both magnitude and direction; it is a vector quantity.
  3. Mass can also be defined as "stored energy in particles."
  4. Mass represents the total atoms or particles that it contains. 

Solved Examples

Example 1

 

 

Damian has a book that has a mass of 2.2 kg.

What is the weight of the book on the Earth?

Solution

Mass of text book = 2.2 kg

Acceleration due to gravity = 9.8 m/s2

Weight formula = \(\text {mass} \times \text{acceleration due to gravity}\)

Weight of text book \(= 2.2 kg \times 9.8 m/s^2 \)

Weight of textbook = 21.56 N

\(\therefore\)The weight of a textbook on Earth is 21.56 N
Example 2

 

 

Sam assumes the acceleration due to gravity on the moon is 1.6 m/s2.

If he has an object that has a weight of 50 N on Earth, what is its mass on the moon?

Solution

Weight of object = 50 N

Acceleration due to gravity on moos = 1.6 m/s2

Weight formula = \(\text {mass} \times \text{acceleration due to gravity} \)

\(50 = \text {mass} \times {1.6 m/s^2} \)

\(mass = \dfrac{50}{1.6}\)

\(\therefore\) Mass of the object on the moon is 31.25 kg
Example 3

 

 

The mass of an object is 6,000 pounds.

Calculate its mass in tons.

Solution

We know that 1 ton = 2000 pounds.

Thus,\[  6000 \text { pounds} = \dfrac {6000}{2000}=3 \text { tons}\].

\( \therefore\) The mass of the object is 3 tons.
Example 4

 

 

Joe wants to know which is heavier, a jug of water or a bucket of water.

Can you tell him the right answer?

Solution

Mass represents the heaviness of an object.

The mass of the water in the bucket is greater than the mass of the water in the jug.

\(\therefore\) Bucket of water is heavier than a jug of water.
Example 5

 

 

Sam weighs 1000 lbs on Earth.

On some other planet, the weight of Sam would be 38% of that on Earth.

How much would Sam weigh on that planet?

Solution

We know that Sam's weight on earth is 1000 lbs and his weight on another planet would be 38% of that on Earth

\(\therefore\) \( \text { Sam's weight on another planet} \)= \(38 \% \times \text { his weight on the Earth}\) = \(0.38 × 1000 \text{ lbs} = 380 \text{ lbs} \)

\(\therefore\) Sam's weight on another planet is 380 lbs.
 
Challenge your math skills
Challenging Questions
  1. What do we use to measure mass?
  2. What is the mass of one electron and proton?
  3. What is the weight of the moon?

Interactive Questions on Mass

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

 
 
 
 
 
 

Let's Summarize

The mini-lesson targeted the fascinating concept of mass. The math journey around mass starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. Here lies the magic with Cuemath.

About Cuemath

At Cuemath, our team of math experts are dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it problems, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.


Frequently Asked Questions (FAQs)

1. Does air have mass?

Air has mass. A small volume of air, such as the air in balloons, has a very small amount of mass.

2. Are mass and volume the same?

Mass is how much matter that object is made of. Volume is how much vacant space an object takes up.

Hence, mass and volume are not the same.

3. Are density and mass the same?

Mass measures the amount of matter present in a substance.

Density shows the amount of matter in a given space for a substance.

Density and mass can be the same as unit volume.

  
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