2.8 Weight
Weight is the gravitational force acting on an object towards the centre of the Earth. According to Newton's Second Law of Motion, this force is expressed as \(W = mg\), where \(W\) is weight, \(m\) is mass, and \(g\) is gravitational acceleration or gravitational field strength.
Learning Objectives
- State the definition of weight as the gravitational force acting on an object.
- Explain the relationship between Newton's Second Law of Motion (\(F = ma\)) and weight (\(W = mg\)).
- Define gravitational field strength, \(g\), and state its SI unit (\(\mathrm{N\,kg^{-1}}\)).
- Differentiate between mass and weight in terms of physical quantity type, base/derived quantity, units, and dependency on location.
- Calculate weight and gravitational field strength using the formula \(W = mg\) on Earth and other celestial bodies (such as the Moon).
Comparison between Mass, Weight, and Gravitational Field Strength
See how an object's mass remains the same on Earth and the Moon, while its weight changes due to differences in gravitational field strength, \(g\).
Earth
Mass, \(m = 60\ \mathrm{kg}\)
Gravitational field strength, \(g = 9.81\ \mathrm{N\,kg^{-1}}\)
Weight, \(W = mg = 60 \times 9.81 = 588.6\ \mathrm{N}\)
Moon
Mass, \(m = 60\ \mathrm{kg}\)
Gravitational field strength, \(g = \frac{1}{6} \times 9.81 = 1.635\ \mathrm{N\,kg^{-1}}\)
Weight, \(W = mg = 60 \times 1.635 = 98.1\ \mathrm{N}\)
Short Explanation
What is Weight?
Weight is the gravitational force acting on an object towards the centre of the Earth. It is a vector quantity and is measured in newtons (\(\mathrm{N}\)).
From Newton's Second Law to Weight
Newton's Second Law of Motion states \(F = ma\). For a falling object, the force is its weight, \(W\), and the acceleration is gravitational acceleration, \(g\). Therefore, \(W = mg\).
Gravitational Field Strength
Gravitational field strength, \(g\), is the force acting per unit mass caused by gravitational pull: \(g = \dfrac{W}{m}\). Its SI unit is \(\mathrm{N\,kg^{-1}}\).
Earth's Gravitational Field Strength
On the surface of the Earth, \(g = 9.81\ \mathrm{N\,kg^{-1}}\). This means each \(1\ \mathrm{kg}\) mass experiences a gravitational force of \(9.81\ \mathrm{N}\).
| Quantity | Mass | Weight |
|---|---|---|
| Definition | Amount of matter in an object | Gravitational force acting on an object |
| Physical quantity type | Scalar quantity | Vector quantity (towards the centre of the Earth) |
| Base / derived quantity | Base quantity | Derived quantity |
| SI unit | kilogram (\(\mathrm{kg}\)) | newton (\(\mathrm{N}\)) |
| Dependency on location | Constant everywhere | Changes with gravitational field strength |
Try to Answer First
Answer in your mind, then press "Check Answer".
What is meant by gravitational field strength?
Check Answer
State two differences between mass and weight.
Check Answer
A box has a mass of \(10\ \mathrm{kg}\) and a weight of \(150\ \mathrm{N}\) on Planet X. Calculate the gravitational field strength on Planet X.
Check Answer
Common Mistakes
- Confusing the units of mass and weight (using \(\mathrm{kg}\) for weight instead of \(\mathrm{N}\)).
- Assuming that an object's mass decreases when it travels to the Moon (mass stays strictly constant; only weight changes).
- Treating weight as a scalar quantity without direction (weight is a vector pointing towards the centre of the Earth).
- Confusing gravitational field strength unit (\(\mathrm{N\,kg^{-1}}\)) with force unit (\(\mathrm{N}\)) or acceleration unit (\(\mathrm{m\,s^{-2}}\)), although numerically equivalent on Earth.
Concept Misunderstandings
An astronaut feels lighter on the Moon because their mass has decreased.
Mass is the amount of matter in a body and remains constant. The astronaut feels lighter because the Moon's gravitational field strength is \(\frac{1}{6}\) of Earth's, which reduces the downward gravitational force (weight).
Weight and mass are the same physical quantity.
Mass is a base, scalar quantity measured in kilograms (\(\mathrm{kg}\)), while weight is a derived, vector quantity (force) measured in newtons (\(\mathrm{N}\)).
Summary
- Formula: \(W = mg\)
- Gravitational field strength: \(g = \dfrac{W}{m}\)
- Earth's gravitational field strength: \(g = 9.81\ \mathrm{N\,kg^{-1}}\)
- Moon's gravitational field strength: \(g_{\mathrm{Moon}} = \frac{1}{6} g_{\mathrm{Earth}} \approx 1.635\ \mathrm{N\,kg^{-1}}\)
- Mass (\(m\)): Scalar quantity, unit \(\mathrm{kg}\), constant everywhere.
- Weight (\(W\)): Vector quantity, unit \(\mathrm{N}\), directed towards the centre of the Earth, varies with \(g\).
Short Activity
Objective: Test your understanding of weight, mass and gravitational field strength.
A. Objective Quiz
1 What is the weight of an astronaut with a mass of \(60\ \mathrm{kg}\) on the surface of the Moon if the Moon's gravitational field strength is \(\frac{1}{6}\) of Earth's gravitational field strength (\(g = 9.81\ \mathrm{N\,kg^{-1}}\))?
2 Which of the following statements correctly describes gravitational field strength?
B. Fill in the Blanks
3 Weight is a vector quantity that is always directed towards the of the Earth.
4 The SI unit for gravitational field strength, \(g\), is .
C. Matching / Drag and Drop
Drag each term to the correct description. If using a phone, tap the answer first, then tap the matching box.
