Weight

Weight is the force of gravity acting on a body. It is a vector quantity with magnitude and direction. Weight changes with different gravitational forces at different places. It is an important concept in physics that is used in many equations. It also has many uses in day-to-day life. In this guide, we will look at the concept of weight and many characteristics in great detail.

1.0What is Weight?

If you are wondering about the Weight definition in physics, it is the force of gravity acting on a body. It is calculated by multiplying mass by gravitational pull.

Mathematically:

Weight = Mass × Acceleration due to gravity

W = m × g

2.0Weight vs Mass: What’s the Difference?

There is a common misconception that weight and mass are interchangeable. Let’s look at the table below to understand weight vs mass characteristics.

3.0Formula for Weight

As outlined above, the formula for weight in physics is:

Weight (W)=Mass (m)×Acceleration due to gravity (g)

$$\begin{gathered} \text{On Earth}g\approx 9.8m/s^2 \\ \text{On the Moon}g\approx 1.6m/s^2 \\ \text{On Jupiter}g\approx 24.8m/s^2 \end{gathered}$$

So, the same object will have different weights on different planets, even though its mass stays constant.

4.0Units of Weight

In the International System of Units (SI), weight is measured in Newtons (N). Here's a quick overview of units of weight: 

1 Newton is the force required to accelerate 1 kg of mass at 1 m/s².

Therefore, 1 N = 1 kg × 1 m/s².

Other units used in non-SI systems include:

• Pound-force (lbf): Common in the US Customary System.
• Dyne: Used in the CGS (centimetre-gram-second) system (1 N = 10⁵ dyne).

5.0Gravitational Force and Weight

Gravitational force and weight are connected. The gravitational force is the attractive force between two masses. Weight is simply the gravitational force exerted by a planet on an object’s mass.

Using Newton’s Universal Law of Gravitation:

$F=\frac{G\cdot m_1\cdot m_2}{r^2}$

Here, 

• F is the gravitational force.
• G is the universal gravitational constant.
• m1 and m2 are interacting masses. 
• R is the distance between the centres. 

When one of the masses is the Earth, this equation simplifies into the familiar W = mg, where the gravitational pull of the Earth is considered as g. 

6.0How to Calculate Weight

To answer how to calculate weight, you will need: 

• The mass of the object (in kilograms).
• The gravitational acceleration (in m/s²) at the location.

Step-by-Step Example: 

Question: What is the weight of a 70 kg person on:

• Earth (g = 9.8 m/s²)
• Moon (g = 1.6 m/s²)
• Jupiter (g = 24.8 m/s²)

Solution:

Thus, a person’s weight is highest on Jupiter and lowest on the Moon, but the mass remains constant at 70 kg.

7.0Factors Affecting Weight

Several factors can influence an object's weight:

Gravitational Field Strength (g)

Varies across planets or even altitudes on Earth.

Higher g results in higher weight.

Altitude or Elevation

Gravity decreases with height above Earth’s surface.

At Mount Everest, the weight is slightly less than at sea level.

Shape of Earth

The Earth is not a perfect sphere. Gravity is slightly stronger at the poles than at the equator due to Earth’s oblateness.

8.0Misconceptions About Weight

• Weight is the same as mass: False. As explained, mass is constant; weight varies with gravity.
• Your weight is constant everywhere: No. It depends on where you are in the universe.
• Weight is measured in kilograms: Incorrect. Kilograms measure mass, Newtons measure weight.

9.0Real-World Applications of Weight

• Engineering and Construction: Structures are designed to bear the weight (force) of materials, machines, and occupants. Engineers must calculate these loads precisely.
• Space Exploration: Weight plays a crucial role in launching and landing spacecraft.
• Weighing Systems: Scales use gravitational pull to determine weight.
• Transport and Logistics: Transportation systems consider the weight of cargo, especially in air travel.