Mass and weight
Weight is a force. Specifically, it is the gravitational force exerted on an object that has mass. Weight depends on the strength of the gravitational field where the object is located. Therefore, weight changes if you move to a different planet.
| Property | Mass | Weight |
|---|---|---|
| Definition | Quantity of matter in an object | Gravitational force on an object with mass |
| Type of Quantity | Scalar (magnitude only) | Vector (magnitude and direction towards center of gravity) |
| SI Unit | Kilogram (kg) | Newton (N) |
| Changes with Location? | No | Yes |
The equation linking weight, mass, and gravitational field strength is:
g = \frac{W}{m}
Where:
- g is the gravitational field strength (measured in newtons per kilogram, N/kg, or meters per second squared, m/s²)
- W is the weight of the object (measured in newtons, N)
- m is the mass of the object (measured in kilograms, kg)
Key Conceptual Link: The value of g is equivalent to the acceleration of free fall. This means that if an object falls freely under gravity alone (ignoring air resistance), it accelerates at a rate equal to the local gravitational field strength.
- A massive body (like Earth) creates a gravitational field around it.
- When another object with mass enters this field, the field exerts a force on that object.
- This force is what we call weight.
Therefore, weight is not an inherent property of the object itself, but rather the result of the interaction between the object's mass and the external gravitational field. Without the field, there is no weight.
- Gravitational field strength on Earth (g_{Earth}) = 9.8 N/kg
- Gravitational field strength on Mars (g_{Mars}) = 3.7 N/kg
Step 1: Calculate Weight on Earth
Using W = m \times g:
W_{Earth} = 80 , \text{kg} \times 9.8 , \text{N/kg} = 784 , \text{N}
Step 2: Calculate Weight on Mars
The mass remains 80 kg (mass does not change).
W_{Mars} = 80 , \text{kg} \times 3.7 , \text{N/kg} = 296 , \text{N}
Conclusion: The astronaut weighs less on Mars because the gravitational field strength is weaker, even though their mass (quantity of matter) is unchanged.
Answer: Use a balance (specifically a beam balance or lever balance).
Reasoning: A balance compares the weight of two objects. Since W = mg, if the balance is level, then:
m_1 g = m_2 g
Because g is the same for both objects at the same location, it cancels out:
m_1 = m_2
Thus, a balance compares masses directly. A spring balance (which measures force/weight) would give different readings if moved to a different planet.
Correction: Weight is a force. The quantity of matter is mass. Weight is the effect of gravity acting on that mass.
Error: Assuming weight changes when mass changes, or vice versa, independently.
Correction: Weight is directly proportional to mass (W \propto m). If you double the mass, you double the weight (in the same field).
Error: Thinking a spring balance measures mass.
Correction: A spring balance measures force (weight). To get mass from a spring balance reading, you must divide by g (m = W/g).
Why examiners accept this: The definition is strictly 'force per unit mass'. Simply saying 'gravity' or 'acceleration due to gravity' is often insufficient for full marks unless explicitly linked to force.
Correct phrasing: "Gravitational field strength is the gravitational force per unit mass acting on a mass placed in the field."
Example Answer:
Q: Define gravitational field strength.
A: It is the force per unit mass experienced by a mass in a gravitational field.
Why examiners accept this: They want to see the causal link: Field exists -> Mass interacts with field -> Force results.
Correct phrasing: "Weight is the force exerted on a mass by a gravitational field."
Example Answer:
Q: Describe weight as an effect of a gravitational field.
A: A massive body creates a gravitational field. When another object with mass is in this field, the field exerts a force on it. This force is the object's weight.
W = 5.0 \times 1.6
W = 8.0 , \text{N}
- Mass is a scalar quantity; weight is a vector quantity.
- Mass is measured in kilograms (kg); weight is measured in newtons (N).
(Or: Mass does not change with location; weight changes with location.)
m = 4.9 / 9.8
m = 0.50 , \text{kg}