What is the fundamental difference between mass and weight?

Mass is a scalar quantity representing the amount of matter in an object and remains constant everywhere. Weight is a vector quantity representing the gravitational force on that mass and changes depending on the local gravitational field strength.

How does the weight of an object change if it is moved from Earth to a planet with double the gravitational field strength?

The weight would double because weight is directly proportional to the gravitational field strength ($W = mg$). Since the mass remains constant, doubling $g$ results in doubling $W$.

Why do a heavy object and a light object fall at the same rate in a vacuum?

Although the heavy object has a greater weight (force), it also has a greater mass (inertia). According to $a = F/m$, the ratio of weight to mass ($mg/m$) always simplifies to $g$, resulting in identical acceleration for both.

What is a common error when using the weight formula $W = mg$ with mass given in grams?

The most common error is failing to convert grams to kilograms. Since the Newton is defined using kilograms ($1 N = 1 kg \cdot m/s^2$), using grams will result in a weight value that is 1000 times too large.

Why is it incorrect to say an object 'weighs 50 kg' in a physics context?

Kilograms are a unit of mass, not weight. In physics, weight must be expressed in Newtons to reflect that it is a force; saying '50 kg' confuses an intrinsic property with a force interaction.

What mistake is made if weight is drawn horizontally on a free-body diagram of an object on a slope?

Weight must always be drawn vertically downwards toward the center of the Earth. Drawing it horizontally or perpendicular to the slope ignores the fundamental nature of gravity acting toward the center of the mass causing the field.

Define Gravitational Field Strength ($g$).

Gravitational field strength is the force exerted per unit mass at a specific point in a gravitational field. It is measured in Newtons per kilogram ($N/kg$) and is numerically equal to the acceleration of free fall.

What is the SI unit for weight and what are its base units?

The SI unit for weight is the Newton ($N$). Its base units are $kg \cdot m \cdot s^{-2}$, derived from the formula for force ($F = ma$).

What does the term 'Free Fall' imply about the forces acting on an object?

Free fall implies that the only force acting on the object is its weight. In this state, the object accelerates at the local value of $g$ because there are no opposing forces like air resistance or friction.

How is weight related to Newton's Second Law?

Weight is a specific application of Newton's Second Law ($F = ma$), where the force $F$ is the gravitational pull ($W$) and the acceleration $a$ is the acceleration due to gravity ($g$).

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3.3.2 Weight

Summary

Weight is the gravitational force acting on an object's mass within a gravitational field. Unlike mass, which is an intrinsic property of matter, weight is a vector quantity that varies depending on the local gravitational field strength ( $g$ ).

1. Definition & Core Concepts

Weight is defined as the force exerted on a mass due to the pull of gravity from a larger body, such as a planet or moon.
As a force, weight is a vector quantity, always acting vertically downwards toward the center of the gravitational source.
The standard unit of weight is the Newton (N), which is equivalent to $1 \text{ kg m s}^{-2}$ in base units.
Gravitational Field Strength ( $g$ ) represents the force per unit mass exerted by a gravitational field, measured in Newtons per kilogram ( $\text{N/kg}$ ) or meters per second squared ( $m/s^2$ ).

Comparison of weight on Earth vs Moon. The object (mass) remains identical in size, but the downward force vector (weight) is significantly larger on Earth due to higher gravitational field strength.

2. Underlying Principles

3. Methods & Techniques

4. Key Distinctions

5. Exam Strategy & Tips

6. Common Pitfalls & Misconceptions