How to use F = ma
Find the resultant force first, then apply F = ma. A worked example with two opposing forces, plus the unit errors that lose marks.
What the examiner is testing
Whether you can find the resultant force before you use it. Almost every lost mark on this topic comes from putting the applied force into the formula while ignoring the force opposing it.
The method
- Draw the forces. Mark each with its size and direction.
- Pick a positive direction — usually the direction of motion.
- Add the forces with their signs. This is the resultant, \( F \).
- Convert units: mass in kg, force in N, acceleration in m/s².
- Apply \( F = ma \), rearranging first if you are solving for \( m \) or \( a \).
Worked example
A van of mass 1800 kg has a driving force of 4500 N. Air resistance and friction together oppose it with 1200 N. Find its acceleration.
Step 1 — forces. Driving force 4500 N forwards; resistive forces 1200 N backwards.
Step 2 — positive direction. Forwards.
Step 3 — resultant.
$$ F = 4500 - 1200 = 3300 \text{ N} $$
This is the step that carries the marks. The 4500 N on its own is not the resultant.
Step 4 — units. Mass is already in kilograms. Nothing to convert.
Step 5 — apply the formula. Rearranging \( F = ma \) gives \( a = F/m \):
$$ a = \frac{3300}{1800} = 1.83 \text{ m/s}^2 $$
Answer: \( 1.83 \text{ m/s}^2 \) (3 s.f.), forwards.
Sanity check: a van accelerating at a couple of metres per second squared is believable. An answer of 0.0018 or 1830 would tell you a unit went wrong.
The same question in reverse
If the van is travelling at a constant 25 m/s, what is the resistive force?
Constant velocity means zero acceleration, so \( F = ma = 1800 \times 0 = 0 \). The resultant is zero, so the resistive force must equal the driving force exactly: 4500 N. No calculator needed — and this is a question type that appears every year.
The three mistakes that lose marks
1. Using the applied force instead of the resultant. If anything opposes the motion, subtract it first.
2. Using weight where mass belongs. If a question gives you a weight of 7000 N, divide by \( g = 9.8 \text{ N/kg} \) to get the mass in kilograms before using \( F = ma \).
3. Grams instead of kilograms. A 500 g trolley is 0.5 kg. Putting 500 into the formula makes the acceleration a thousand times too small.
30-second recap
Resultant force first, then \( F = ma \). Mass in kilograms, force in newtons, acceleration in m/s². Constant velocity means zero resultant, which is a shortcut worth spotting rather than a calculation to do. Always ask whether the size of your answer is believable.