IGCSE Physics 0625 – Motion: Weight and Gravitational Field
1.2 Motion – Weight as the Effect of a Gravitational Field
Learning Objective
Describe, and use the concept of, weight as the effect of a gravitational field on a mass.
Key Definitions
Mass (m): The amount of matter in an object. It is a scalar quantity and does not change with location. Unit: kilogram (kg).
Weight (W): The force exerted on a mass by a gravitational field. It is a vector quantity acting towards the centre of the attracting body. Unit: newton (N).
Gravitational field strength (g): The force per unit mass experienced in a gravitational field. On the surface of the Earth, \$g \approx 9.8\ \text{N kg}^{-1}\$ (or \$9.8\ \text{m s}^{-2}\$).
Relationship Between Mass, Weight and Gravitational Field
The weight of an object is directly proportional to its mass and the local gravitational field strength:
\$W = m\,g\$
where
\$W\$ = weight (N)
\$m\$ = mass (kg)
\$g\$ = gravitational field strength (N kg⁻¹ or m s⁻²)
Units and Direction
Weight is measured in newtons (N). 1 N = 1 kg·m s⁻².
The direction of weight is always towards the centre of the attracting body (e.g., towards the centre of the Earth).
Mass vs. Weight – A Comparison
Property
Mass
Weight
Physical nature
Scalar quantity (amount of matter)
Vector quantity (force)
Symbol
\$m\$
\$W\$
Unit
kilogram (kg)
newton (N)
Depends on location?
No
Yes – varies with \$g\$
Formula
–
\$W = m\,g\$
Effect of Changing Gravitational Field Strength
Since \$W = mg\$, if the gravitational field strength changes, the weight changes proportionally while the mass remains constant.
On the Moon, \$g_{\text{Moon}} \approx 1.6\ \text{N kg}^{-1}\$.
On Earth, \$g_{\text{Earth}} \approx 9.8\ \text{N kg}^{-1}\$.
Example: A 10 kg object has a weight of \$W{\text{Earth}} = 10 \times 9.8 = 98\ \text{N}\$ on Earth, but only \$W{\text{Moon}} = 10 \times 1.6 = 16\ \text{N}\$ on the Moon.
Weightlessness
Weightlessness occurs when the net force due to gravity on a body is zero. This can happen in two situations:
In deep space far from any massive body, \$g \approx 0\$, so \$W = 0\$.
In free‑fall, such as an astronaut orbiting Earth, the astronaut and the spacecraft are both accelerating at \$g\$, so there is no contact force and the sensation of weight disappears.
Measuring Weight
Weight is commonly measured with a spring (or elastic) scale. The scale is calibrated to read the force exerted by the object, which is proportional to the extension of the spring:
\$F = k\,x\$
where \$k\$ is the spring constant and \$x\$ is the extension. The scale converts this force directly into a weight reading (N) or, by dividing by \$g\$, into a mass reading (kg) for convenience.
Suggested diagram: A free‑body diagram showing a mass \$m\$ with the weight vector \$W = mg\$ acting downwards, and a normal reaction \$R\$ acting upwards when the mass rests on a horizontal surface.
Common Misconceptions
“Weight is the same as mass.” – Weight depends on \$g\$, while mass does not.
“If an object feels lighter, its mass has decreased.” – The object’s mass is unchanged; only the gravitational field strength or the net force acting on it has changed.
“A scale measures mass directly.” – Most classroom scales are calibrated to read mass by assuming a constant \$g\$; they actually measure weight and then divide by \$g\$.
Summary
Weight is the force exerted on a mass by a gravitational field and is given by \$W = mg\$. It varies with the strength of the gravitational field, unlike mass which is invariant. Understanding the distinction between mass and weight, and how to calculate weight in different gravitational environments, is essential for solving many physics problems in the IGCSE syllabus.