How to Calculate Weight Based on Mass

The weight of an object is the force of gravity acting on that object. The mass of an object is the amount of substance that the object has. Mass is a constant of the object and does not depend on gravity. That is why an object with a mass of 20 kg on earth would also have a mass of 20 kg on the moon. The same object’s weight on the moon is only one-sixth of the weight on the earth because gravity on earth is 6 times stronger than gravity on the moon. The next section of the article will give you more information as well as some ways to calculate weight based on volume.

Table of Contents

Calculate the mass

Use the “w = mxg” formula to calculate weight from volume. Weight is defined as the value of gravity acting on an object, generalizing in mathematical terms as w = mxg or w = mg .

Since weight is a force, scientists also write this formula another way as F = mg .
F = weight symbol, measured in Newtons, N .
m = symbol for mass, in kilograms, kg .
g = symbol for acceleration due to gravity, unit is m/s ² , ie meters per second squared.
- When you use the unit ‘ meters , the acceleration due to gravity on the earth’s surface will be 9.8 m/s ² . This is a value with international standard units and you should use this value.
- If you must use feet , the value of the acceleration due to gravity you need to use is 32.2 f/s ² , essentially unchanged but only in feet instead of meters.

Determine the mass of an object. Since we are looking to find the weight based on the mass, that is, we already know the mass value. Mass is the amount of substance present in that object, expressed in kilograms.

Determine the acceleration due to gravity. In other words define g . On the earth’s surface, g is 9.8 m/s ² . Depending on your location on the earth, the acceleration of gravity can change. However, you will know this value because in most cases this value is often mentioned in the problem.

The acceleration due to gravity on the moon is different from the acceleration due to gravity on the earth. The acceleration caused by gravity on the moon has a value of about 1.622 m/s ² , which is about 1/6 of the corresponding value on earth. That’s why your weight on the moon is only 1/6 of the weight on earth.
The gravitational acceleration on the sun is also different from the gravitational acceleration on the moon and earth. On the sun, the acceleration caused by gravity is about 274.0 m/s ² , which is about 28 times the acceleration caused by gravity on earth. So you would be 28 times heavier if you could survive on the sun.

Substitute the values into the formula. Once you have the values for m and g , you substitute these values into the formula F = mg . The result of this calculation will have the unit of Newton, denoted by N .

For example

Example 1. “An object has a mass of 100 kilograms. What is the weight of the object on the earth?”

We already have the values of both m and g . Since we are looking for the weight of the object on the earth, so m is 100kg and g is 9.8 m/s ² .
Substituting the value into the formula we get: F = 100 kg x 9.8 m/s ² .
Do this calculation to get the final result. On the earth’s surface, an object with a mass of 100 kg would have a weight of about 980 Newtons. F = 980 N.

Example 2. “An object has a mass of 40 kilograms. What is the weight of the object on the moon?”

We already have the values of m and g . In which, m is 40 kg, g is 1.6 m/s ² because we are considering the object on the moon.
Substituting these two values into the formula, we have: F = 40 kg x 1.6 m/s ² .
Do the multiplication to get the final result. On the moon, an object with a mass of 40 kg would weigh about 64 Newtons. F = 64 N.

Example 3. “An object weighs 549 Newtons on earth. What is the mass of the object?”

This example is an inverse problem, where we have the values of F and g in advance. We need to calculate m .
Substituting the known values into the formula we have: 549 = m x 9.8 m/s ² .
Instead of multiplying, we’ll do division. More specifically, we divide F by g . An object weighing 549 Newtons on earth has a mass of about 56 kilograms. m = 56 kg.

Proofreading

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Avoid confusion between mass and weight. The most common mistake in this type of question is confusing mass with weight. Remember that mass is the amount of “substance” of an object, this is a constant value, independent of the object’s position. In contrast, weight is the force of gravity acting on the amount of “substance” of an object and can vary in different places. Here are some tips to help you distinguish these two quantities:

Mass has units of grams or kilograms. In English, both mass ( m ass ) and gram ( gram m ) have the letter m . Weight has units of Newton. In English, both weight ( w eight) and Newton (ne w ton) have the letter w .
For those of you who study in English or use English fluently, you can remember this sentence: You only have weight while you’re ” wait “ing on Earth, but even ” mass “tronauts have mass.

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Use the international system of measurement. Most physics problems use Newtons (N) for weight, meters per second squared (m/s ² ) for gravity, and kilograms (kg) for mass. If you use other units, you cannot apply the formulas given in this article if you have not converted the values to the international system of measurement. Here are some common conversion values:

1 pound force = ~4,448 newton
1 foot = ~0.3048 meters

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Expand newton for unit testing. If you’re working on a complex math problem, double-check the units while solving the problem. Remember that 1 newton is equivalent to 1 (kg*m)/s ² . If necessary, you can use units of this form to suppress units during the calculation.

Example: On the ground, An has a weight of 880 newtons. What is the mass of An?
Mass = (880 newtons)/(9.8 m/s ² )
Mass = 90 newtons/(m/s ² )
Mass = (90 kg*m/s ² )/(m/s ² )
After eliminating units we have: mass = 90 kg
Kg is the unit of mass, so we got it right.

Appendix: Weight in kgf

Newton is the international system of measurement (SI-unit). However, in some documents and in some countries, weight is also expressed in kilogram-force (kgf). This is not a standard unit, and is therefore less commonly accepted. However, using kgf is very convenient for comparing weights elsewhere with weights on earth.
1 kgf = 9,80665 N.
Divide the value in Newtons by 9,80665 or include the digit after the last comma when you know the value.
The weight of a 101 kg astronaut is 101.3 kgf at the North Pole and 16.5 kgf when he is on the moon.
What is the International System of Units (SI-units)? SI-unit is an abbreviation of Systeme International d’Unites (translated into Vietnamese as the International System of Measurements), which is a system of stipulating units of measurement in science.

Advice

Figuring out the difference between mass and weight is the hardest part of this type of exercise, as we tend to use the two terms interchangeably. In everyday life, we often use kilograms when it comes to weight instead of Newton or kgf. Even if your doctor wants to talk about your weight, they really want to talk about your mass.
The acceleration due to gravity g can also be written in units of N/kg. 1N/kg = 1 m/s ² . So changing the unit of the acceleration due to gravity does not change its value.
An astronaut with a mass of 100 kg would weigh 982.2 N at the North Pole and 162.0 N on the moon. If standing on a neutron star, this person would be even heavier, but he probably wouldn’t feel it.
A scale is an instrument that measures mass (in kilograms), where your weight is calculated based on the compression or relaxation of a spring.
The Newton unit is preferred over kgf because it makes it easier to calculate other values.

Warning

The term ‘atomic weight’ has nothing to do with the weight (weight) of the atom, but with the mass (mass). This designation probably won’t change, since ‘atomic mass’ is already being used for a different quantity.

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