Weight
Calculate weight from mass and gravitational field strength.
This public page keeps the free explanation visible and leaves premium worked solving, advanced walkthroughs, and saved study tools inside the app.
Core idea
Overview
Weight is the measure of the gravitational force acting on an object's mass, specifically defined as the product of mass and local gravitational acceleration. Unlike mass, which is a scalar and intrinsic property of matter, weight is a vector quantity that varies depending on the strength of the surrounding gravitational field.
When to use: Use this equation when calculating the downward force an object exerts on a support or the force it experiences due to a planet's gravity. It assumes the object is in a region where the gravitational field strength is known and relatively uniform.
Why it matters: Understanding weight is essential for structural engineering, where load-bearing capacities must exceed the weight of materials, and for aerospace, where engines must overcome weight to achieve lift. It clarifies the distinction between an object's physical quantity of matter and the external force pulling on it.
Symbols
Variables
m = Mass, g = Gravitational Field Strength, W = Weight
Walkthrough
Derivation
Derivation of W = mg (Weight)
Weight is the force on a mass due to gravity, found using Newton’s second law.
- Gravitational field strength g is approximately constant over the height change.
- The object is small compared with the Earth.
Start with Newton’s second law:
Resultant force equals mass multiplied by acceleration.
Use gravitational acceleration:
For weight, the acceleration is g, so the gravitational force is W = mg.
Note: Weight is a force (newtons). Mass is in kilograms.
Result
Source: Edexcel GCSE Physics — Forces and their effects
Free formulas
Rearrangements
Solve for
Make W the subject
W is already the subject of the formula.
Difficulty: 1/5
Solve for
Make m the subject
To make mass () the subject of the formula for Weight (), divide both sides of the equation by gravitational field strength ().
Difficulty: 2/5
Solve for
Make g the subject of the formula for Weight
Rearrange the formula for Weight, W=mg, to solve for gravitational field strength, g.
Difficulty: 2/5
The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.
Visual intuition
Graph
This graph is a straight line passing through the origin with a slope equal to g, showing that weight increases at a constant rate as mass increases for all values greater than zero. For a physics student, this means that larger mass values correspond to a proportionally greater weight, while smaller mass values result in a smaller weight. The most important feature is the linear relationship, which means that doubling the mass will always result in doubling the weight.
Graph type: linear
Why it behaves this way
Intuition
Imagine an object resting on a surface or suspended, being pulled downwards by an invisible force field, with the strength of this pull (its weight)
Free study cues
Insight
Canonical usage
This equation is used to calculate the weight (gravitational force) of an object given its mass and the local gravitational field strength, ensuring consistent units for force, mass, and acceleration.
Common confusion
The most frequent error is confusing mass (a scalar quantity measured in kilograms) with weight (a vector force measured in Newtons).
One free problem
Practice Problem
A scientific rover on the surface of Mars has a mass of 150 kg. If the gravitational acceleration on Mars is 3.7 m/s², what is the rover's weight on the Martian surface?
Solve for:
Hint: Multiply the mass of the rover by the Martian gravitational acceleration.
The full worked solution stays in the interactive walkthrough.
Where it shows up
Real-World Context
Weighing scales (measure N, show kg).
Study smarter
Tips
- Ensure mass is in kilograms (kg) to produce weight in Newtons (N).
- Remember that weight changes on different planets even if the mass stays the same.
- On Earth, the standard value for gravitational acceleration (g) is roughly 9.8 m/s².
- The weight vector always points toward the center of the mass creating the gravity.
Avoid these traps
Common Mistakes
- Confusing mass (kg) and weight (N).
- Using g=10 without checking question.
Common questions
Frequently Asked Questions
Weight is the force on a mass due to gravity, found using Newton’s second law.
Use this equation when calculating the downward force an object exerts on a support or the force it experiences due to a planet's gravity. It assumes the object is in a region where the gravitational field strength is known and relatively uniform.
Understanding weight is essential for structural engineering, where load-bearing capacities must exceed the weight of materials, and for aerospace, where engines must overcome weight to achieve lift. It clarifies the distinction between an object's physical quantity of matter and the external force pulling on it.
Confusing mass (kg) and weight (N). Using g=10 without checking question.
Weighing scales (measure N, show kg).
Ensure mass is in kilograms (kg) to produce weight in Newtons (N). Remember that weight changes on different planets even if the mass stays the same. On Earth, the standard value for gravitational acceleration (g) is roughly 9.8 m/s². The weight vector always points toward the center of the mass creating the gravity.
References
Sources
- Halliday, Resnick, Walker, Fundamentals of Physics
- Britannica: Weight (physics)
- Wikipedia: Weight (physics)
- Halliday, Resnick, Walker, *Fundamentals of Physics*
- Bird, Stewart, Lightfoot, *Transport Phenomena*
- Wikipedia: Newton (unit)
- Halliday, Resnick, Walker, Fundamentals of Physics, 11th Edition
- Britannica, The Editors of Encyclopaedia. 'Weight'. Encyclopedia Britannica, 20 Jul. 2023.