Forces, the difference between mass and weight, the weight relationship W equals mg, and the force-mass-acceleration relationship F equals ma.

What this key area is asking

The SQA wants you to understand what a force is, distinguish mass from weight, use $W = mg$ to find weight, and use $F = ma$ to link an unbalanced force to acceleration.

Forces

Forces are vectors, meaning they have both a size and a direction. When several forces act on an object, what matters is the resultant (the overall, combined force).

Mass and weight

A 10 kg bag always has a mass of 10 kg, but its weight on Earth ($98 \text{ N}$) is about six times its weight on the Moon, because the Moon's gravitational field strength is much smaller. Confusing mass with weight is one of the most common errors, so always check whether a question wants kilograms (mass) or newtons (weight).

Balanced and unbalanced forces

When the forces on an object are balanced (the resultant is zero), the object stays at rest or keeps moving at a steady speed in a straight line. When the forces are unbalanced (there is a resultant force), the object accelerates in the direction of the resultant.

A larger unbalanced force gives a larger acceleration; a larger mass gives a smaller acceleration for the same force. The force in $F = ma$ must always be the resultant, not just one of the forces acting.

Why this matters

Forces underpin the whole of mechanisms and structures. Mechanisms use input forces to produce useful output forces; structures must safely carry the forces (loads) placed on them. Getting mass, weight and $F = ma$ right is the foundation for everything that follows, including moments, mechanical advantage and structural analysis.

Try this

Q1. A 20 kg object is on Earth ($g = 9.8 \text{ N/kg}$). Calculate its weight. [2 marks]

• Cue. $W = mg = 20 \times 9.8 = 196 \text{ N}$.

Q2. State the unit of force. [1 mark]

• Cue. The newton (N).

Q3. A $5.0 \text{ kg}$ mass accelerates at $3.0 \text{ m/s}^2$. Calculate the unbalanced force. [2 marks]

• Cue. $F = ma = 5.0 \times 3.0 = 15 \text{ N}$.