A resultant force accelerates a mass
Definition
Newton
The unit of force: one newton (1 N1\ \text{N}1 N) is the resultant force that gives a mass of 1 kg1\ \text{kg}1 kg an acceleration of 1 m/s21\ \text{m/s}^21 m/s2.
Key Idea
The resultant force on an object equals its mass multiplied by its acceleration, with the force and the acceleration in the same direction.
- In symbols, F=maF = maF=ma, where FFF is the resultant force in N\text{N}N, mmm is the mass in kg\text{kg}kg and aaa is the acceleration in m/s2\text{m/s}^2m/s2.
- For a fixed mass, the acceleration is directly proportional to the resultant force, so doubling the force doubles the acceleration.
- For a fixed force, a larger mass gives a smaller acceleration, because the same force is shared over more mass.
- The acceleration is always in the same direction as the resultant force, so a backward resultant force gives a backward (slowing) acceleration.
Common Mistake
- Use the resultant force in F=maF = maF=ma, not one single applied force while ignoring friction.
- Mass must be in kilograms: a mass given in grams has to be converted first.
- Do not confuse mass and weight: mass in kg\text{kg}kg goes in F=maF = maF=ma, while weight is a force in N\text{N}N from W=mgW = mgW=mg.
- Acceleration is a rate of change of velocity, not the velocity itself, so a large acceleration does not mean a large speed.
Exam technique
- Write F=maF = maF=ma from memory, then rearrange before putting numbers in, so a rearrangement error is easy to spot.
- Check the unit of every quantity (N\text{N}N, kg\text{kg}kg, m/s2\text{m/s}^2m/s2) before substituting, as a wrong unit usually means a wrong answer.
- If a question gives several forces, first work out the resultant along the line of motion, then use it in F=maF = maF=ma.
Self review
- State the equation linking resultant force, mass and acceleration.
- A 4.0 kg4.0\ \text{kg}4.0 kg mass has a resultant force of 10 N10\ \text{N}10 N on it. Find its acceleration.
- For a fixed force, what happens to the acceleration if the mass increases?
- In which direction is the acceleration compared with the resultant force?
- Define the newton.
