In the last post, we discussed how to find mass with acceleration and force. So in this post, we will discuss its special case, which is how to calculate mass from weight. So let us go into depth.

**Sir Isaac Newton established numerous principles that make it simple to calculate the mass of an object. Finding the mass of an object from its weight is a special case of Newton’s Second Law, in which the object experiences force due to the earth’s gravitational pull.**

In our daily lives, we use the terms “weight” and “mass.” Most people believe that mass equals weight. But no, they are completely different and have different interpretations. The amount of matter in an object or particle is measured by its mass, which is a fundamental property of any object or particle. While the weight of an object or body is simply the force experienced by the matter of the body due to gravity.

Let’s look at a special case of Newton’s second law to determine the mass of any object from its weight.

**How to calculate mass from weight using Newton’s Second law:**

Newton’s Second Law establishes the relationship between an object’s mass, the net force acting on it, and the acceleration the object experiences due to this force. Thus, according to Newton’s Second Law, the acceleration that an object will experience due to a force applied to it will be directly proportional to the net force exerted on it. Moreover, it has an inverse relationship with the object’s mass.

Putting these statements into the equation, we can write it as:

a ∝ F

a ∝ 1/m

Thus,

Or,

F = ma

Making mass the subject of the equation, it can be expressed as:

However, we wish to figure out mass from the weight. Let’s see how Newton’s Law can assist us.

**As previously stated, weight is the gravitational force exerted on an object. Because the gravitational force is the cause of the object’s acceleration, it is referred to as gravitational acceleration. **It is represented by the letter g. As a result, in Newton’s Second Law, force F is replaced by weight W, and acceleration a is replaced by gravitational acceleration g. As a result, Newton’s law can be written as follows:

W = mg

As a result, the mass of an object in terms of weight is given by:

As we all know, an object’s mass remains constant until its speed approaches that of light. In the case of weight, however, this is not true. This occurs due to variations in the value of gravitational acceleration. The earth’s gravitational acceleration is 9.8 m/s^{2}. However, its value, as well as the weight of an object, changes on the surface of the moon. **According to the above equation, if an object or body has a large mass, it will weigh a lot and accelerate slowly. And if it has a smaller mass, it will be lighter and accelerate more quickly.**

**Newton, Kilogram, and m/s ^{2} are the**

**SI units of weight (as it is also a force), mass, and gravitational acceleration, respectively.**

**Problems of finding mass from weight:**

**Problem: A body is experiencing 294 N gravitational force on the earth. Then determine the mass of the body.**

**Given:**

Gravitational force on body (weight of body) W = 294 N

Gravitational acceleration g = 9.8 m/s^{2}

**To find:**

Mass of body m = ?

**Solution:**

Mass of body

∴ m = 30 kg

**On the earth’s surface, a body of mass 30** **kg experiences a gravitational force of 294 N.**

**Problem: The gravitational force exerted on a body on the moon’s surface is 71.5 N, and the gravitational acceleration on the moon is 1.625 m/s2. What would be the body’s mass then?**

**Given:**

Gravitational force acting on body (weight of body) W = 71.5 N

Gravitational acceleration on Moon’s surface g = 1.625 m/s^{2}

**To find:**

Mass of body m = ?

**Solution:**

Mass of body

∴ m = 44 kg

**Thus, if a body weighs 71.5 kg on the moon’s surface, its mass is 44 kg.**

**FAQs on Mass & Weight:**

**Q. Distinguish between mass and weight.**

**Ans:** Both mass and weight are scientific and mathematical quantities used to describe objects in space. However, they are not the same, and the following are the differences:

Mass | Weight |

The quantity of matter contained by the body is its mass. | The weight of an object or a body is just the force exerted by gravity on the matter of the body. |

It is a scalar quantity with only value. | It is a vector quantity since it is essentially force with direction and magnitude. |

Its value does not change wherever you go. | When gravitational acceleration changes, it causes a change in the weight of an object. |

A beam balance is used to determine an object’s mass. | A spring balance is used to determine an object’s weight. |

SI unit: kg | SI unit: Newton |

**Q. Why is mass, rather than weight, a better way to measure matter?**

Ans: Mass and weight are two quantities that are used to describe an object in space.

**The gravitational pull, or weight, is felt by an item because of its mass. The mass of any body or object does not depend on its location. So its value remains the same. However, the weight of an object changes as its location is changed. Flying on an airplane reduces your weight. When you travel to another planet or space, it alters even more. Thus, due to its unchanged characteristics, mass is a better way to measure matter than weight.**

**Q. How does the earth’s gravitational acceleration, g, get to be 9.8?**

Ans: Gravitational acceleration can be calculated using the universal law of gravitation.

The gravitational force between two objects, according to the universal law of gravitation, can be given by:

But here, G – gravitational constant = 6.67 X 10^{-11 }Nm^{2}/kg^{2 }

m_{1} = Me (mass of earth) = 5.98 X 10^{24} kg

m_{2} = m (mass of object)

R (radius of earth as object is on the surface of the earth) = 6.38 X 10^{6} m

Thus, gravitational force on the object due to earth is:

But,

F = mg

Where,

∴ g = 9.8 m/s^{2}

**Q. The gravity of the moon is lower than that of the Earth. How would your weight change if you were on the moon compared to Earth?**

**Ans:** On the earth and the moon, measuring the weight of an object or body yields different results.

On the surface of the Earth, the weight of an object is given by:

On the surface of the Earth, the weight of an object is given by:

Thus, from the above equations, we can write:

However, the earth’s mass and radius are 100 times and 4 times, respectively, greater than those of the moon, i.e., M_{e }= 100 M_{m} and R_{e} = 4 R_{m}.

Thus,

∴ W_{m} = (1/6) W_{e}

**As a result, we may conclude that if you weigh yourself on the moon, it will be 1/6th of what you weigh on Earth. Your mass on the moon and on Earth, however, remains the same.**