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Weight

2.8 Weight
PHYSICS • Form 4 • Chapter 2: Force and Motion I

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".

1

What is meant by gravitational field strength?

Check Answer
Answer: Gravitational field strength is the force acting per unit mass caused by gravitational pull (\(g = \frac{W}{m}\)).
2

State two differences between mass and weight.

Check Answer
Answer: 1. Mass is a scalar quantity, whereas weight is a vector quantity directed towards the centre of the planet. 2. Mass has the unit kilogram (\(\mathrm{kg}\)) and is constant regardless of location, whereas weight has the unit newton (\(\mathrm{N}\)) and varies depending on the local gravitational field strength.
3

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
Answer: \(g = \dfrac{W}{m} = \dfrac{150\ \mathrm{N}}{10\ \mathrm{kg}} = 15\ \mathrm{N\,kg^{-1}}\).

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

Misunderstanding

An astronaut feels lighter on the Moon because their mass has decreased.

Correct Concept

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).

Misunderstanding

Weight and mass are the same physical quantity.

Correct Concept

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.

Quantity / Concept
Mass
Weight
Gravitational field strength
9.81 N kg⁻¹
Description / Unit
Scalar quantity measured in kg that remains constant regardless of locationCorrect ✓Try againEmpty
Vector quantity representing the gravitational force acting on an object towards the centre of EarthCorrect ✓Try againEmpty
Force acting per unit mass caused by gravitational pull, with the unit N kg⁻¹Correct ✓Try againEmpty
Value of the gravitational field strength on the surface of the EarthCorrect ✓Try againEmpty
 

Keywords

Weight (\(W\)) Mass (\(m\)) Gravitational field strength (\(g\)) Newton's Second Law of Motion
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of Pandai.

Weight

2.8 Weight
PHYSICS • Form 4 • Chapter 2: Force and Motion I

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".

1

What is meant by gravitational field strength?

Check Answer
Answer: Gravitational field strength is the force acting per unit mass caused by gravitational pull (\(g = \frac{W}{m}\)).
2

State two differences between mass and weight.

Check Answer
Answer: 1. Mass is a scalar quantity, whereas weight is a vector quantity directed towards the centre of the planet. 2. Mass has the unit kilogram (\(\mathrm{kg}\)) and is constant regardless of location, whereas weight has the unit newton (\(\mathrm{N}\)) and varies depending on the local gravitational field strength.
3

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
Answer: \(g = \dfrac{W}{m} = \dfrac{150\ \mathrm{N}}{10\ \mathrm{kg}} = 15\ \mathrm{N\,kg^{-1}}\).

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

Misunderstanding

An astronaut feels lighter on the Moon because their mass has decreased.

Correct Concept

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).

Misunderstanding

Weight and mass are the same physical quantity.

Correct Concept

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.

Quantity / Concept
Mass
Weight
Gravitational field strength
9.81 N kg⁻¹
Description / Unit
Scalar quantity measured in kg that remains constant regardless of locationCorrect ✓Try againEmpty
Vector quantity representing the gravitational force acting on an object towards the centre of EarthCorrect ✓Try againEmpty
Force acting per unit mass caused by gravitational pull, with the unit N kg⁻¹Correct ✓Try againEmpty
Value of the gravitational field strength on the surface of the EarthCorrect ✓Try againEmpty
 

Keywords

Weight (\(W\)) Mass (\(m\)) Gravitational field strength (\(g\)) Newton's Second Law of Motion
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of Pandai.
Chapter : Force and Motion I
Topic : Describe weight as the gravitational force that acts on an object, W = mg
Form 4 Physics
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