Weight Formula

Weight is a measure of the gravitational force applied to an object by its mass and the gravitational environment in which it resides. It is a fundamental idea in physics that is used in a variety of applications including engineering and scientific study. Learn more about weight and its formula in this article.

What is Weight?

Weight is the force imposed on an object by the gravitational pull of a celestial body, such as the Earth. It is a measurement of an object’s mass and gravity-induced acceleration at its current location. Weight is a measure of how heavy an object is.

Weight influences many facets of everyday life, including how items interact with one another and their surroundings. It governs the force exerted by items on supporting structures, like as floors, and influences the performance of cars, buildings, and other engineered systems.

An object’s weight is determined by the strength of the gravitational field at its location. For example, an object will weigh less on the Moon.

Weight Formula

The weight formula is a mathematical expression used to calculate the force exerted on an object due to gravity. It relates an object’s weight to its mass and the strength of the gravitational field in which it is located.

The weight formula is given by:

W = m×g

Where:

• W is the weight of the object (measured in newtons, N).
• m is the mass of the object (measured in kilograms, kg).
• g is the acceleration due to gravity (measured in meters per second squared, m/s²

Here’s what each term represents:

Weight (W): Weight is the force with which an object is attracted towards the center of the Earth (or another celestial body) due to gravity. It is a vector quantity and is typically measured in newtons (N) or pounds (lbs).

Mass (m): Mass is a measure of the amount of matter in an object. It is a scalar quantity and remains constant regardless of the object’s location. Mass is typically measured in kilograms (kg) or grams (g).

Acceleration due to Gravity (g): The acceleration due to gravity represents the strength of the gravitational field at the location of the object. It determines the rate at which objects accelerate towards the Earth’s surface. The standard value for g on or near the surface of the Earth is approximately \( 9.81 \, m/s^2 \).

Weight Formula Derivation

A freely falling body would undergo acceleration regardless of mass, as is widely known from experiments. This acceleration is indicated by the letter “g” and is brought on by the pull of gravity. Additionally, this acceleration pulls toward the Earth’s centre. As a result, the Second Law of Motion provides us with: 

F = ma 

Here, m stands for mass, F for force, and a for acceleration. 

Now for bodies that are falling freely 

a = g

F = w 

Here, w = mg since g = gravity and w = weight.

Solved Examples on Weight Formula

Example 1. An individual weighs 70 kg, and the Earth’s gravity is 9.8 m/s2. Find out this person’s weight. 

Solution:

One must use the weight formula in order to determine the Weight Formula. 

Here, g = 9.8 m/s2 and m = 70 kg. 

W = mg 

W = 70 × 9.8\sW = 637 Nw 

As a result, the guy is 637 N in weight.

Example 2. On the moon, a person weighs 250 N. Calculate the person’s mass while assuming a gravity of 1.6 m/s² for the mass. 

Solution:

Here, g = 1.6 m/s² and w = 250 N 

156.25kg is equal to 250Nw/1.6m/s² m when W = mg m = w/g 

As a result, the person weighs 156.25 kg.

Example 3. How much does a body on the moon weigh if its mass is 60 kg? The value for g is 1.625 m/s². 

Solution: 

The values of m = 60 kg and 

g = 1.625 m/s² 

W = mg is the Weight Formula. 

W = 60×1.625 = 97.5 N