Weight (W = mg)
Forces in Action - OCR A-Level Physics
Key Definition
Weight
The gravitational force exerted on an object by a planet or other massive body. Always acts vertically downwards through the centre of mass. The unit is the newton (N).
The gravitational force exerted on an object by a planet or other massive body. Always acts vertically downwards through the centre of mass. The unit is the newton (N).
$$W = mg$$
- $m$ is mass in $\text{kg}$; $g$ is the gravitational field strength in $\text{N kg}^{-1}$ (or equivalently $\text{m s}^{-2}$).
- Near the Earth's surface, $g = 9.81 \text{ N kg}^{-1}$. On the Moon, $g \approx 1.62 \text{ N kg}^{-1}$, so a $60 \text{ kg}$ astronaut weighs $\approx 97 \text{ N}$ on the Moon vs $589 \text{ N}$ on Earth.
- Mass is a scalar and is invariant; weight is a vector and depends on the local field strength.
- 1 N is the resultant force required to accelerate a $1 \text{ kg}$ mass at $1 \text{ m s}^{-2}$: $1 \text{ N} = 1 \text{ kg} \times 1 \text{ m s}^{-2}$.
Other contact and field forces
Normal contact forceThe perpendicular push exerted by a surface on an object in contact with it. ($N$): perpendicular to the surface, opposes the push of the object on the surface.
TensionThe pulling force transmitted along a rope, string or cable; the same magnitude everywhere along an ideal rope. ($T$): transmitted along a rope or cable, same size everywhere along an ideal rope, changes direction over a pulley.
FrictionA resistive contact force opposing relative motion or attempted motion between two surfaces. ($F_f$): resistive contact force opposing relative motion or attempted motion.
UpthrustThe upward force on an object immersed in a fluid, equal to the weight of fluid displaced (Archimedes' principle). ($U$): upward force from a displaced fluid.
TensionThe pulling force transmitted along a rope, string or cable; the same magnitude everywhere along an ideal rope. ($T$): transmitted along a rope or cable, same size everywhere along an ideal rope, changes direction over a pulley.
FrictionA resistive contact force opposing relative motion or attempted motion between two surfaces. ($F_f$): resistive contact force opposing relative motion or attempted motion.
UpthrustThe upward force on an object immersed in a fluid, equal to the weight of fluid displaced (Archimedes' principle). ($U$): upward force from a displaced fluid.
Diagram pending
Free-body diagram of a box on a horizontal surface: weight $W$ down, normal contact force $N$ up, applied force $F$ horizontal, friction $F_f$ opposing motion. Arrows start inside the box and scale with magnitude.
Will be replaced with a GeoGebra SVG in stream 2.
Common Mistake
MEDIUM
Students often: confuse mass and weight, or quote weight in $\text{kg}$.
Instead: mass is in $\text{kg}$, weight is a force in $\text{N}$. Always multiply by $g$ when the question gives you a mass and asks for a force.
Instead: mass is in $\text{kg}$, weight is a force in $\text{N}$. Always multiply by $g$ when the question gives you a mass and asks for a force.
Examiner Tips and Tricks
- In free-body diagram questions, label every arrow with the name of the force, not just a symbol.
- Only draw forces exerted ON the object; never draw forces it exerts on something else.
- Use arrow length to indicate relative size where the question asks for a scaled diagram.