Section 1 of 5The Relationship
Newton's second law links the resultant force on an object to its mass and the acceleration it produces.
Resultant force
- The acceleration of an object is in the direction of the non-zero resultant force that acts on it.
Proportional to force
- For a fixed mass, the acceleration is directly proportional to the resultant force,
- so doubling the force doubles the acceleration.
Inversely proportional to mass
- For a fixed resultant force, the acceleration is inversely proportional to the mass,
- so heavier objects accelerate less.
The equation
- F = m × a, with F in newtons, m in kilograms and a in m/s².What the symbols mean: F = resultant force (N) · m = mass (kg) · a = acceleration (m s−2)
Section 2 of 5Solving Problems
A consistent method prevents most errors in second-law calculations.
1
List the known quantities, converting the mass into kilograms and any other values into SI units.
2
Select the form of F = m × a that finds the unknown, such as a = F ÷ m when the acceleration is wanted.
3
Substitute the values into the equation and calculate the answer, giving it to a sensible number of significant figures.
4
Check that the direction of the acceleration matches the direction of the resultant force.
Section 3 of 5Mass, Force and Motion
Mass, Force and Motion
Doubling the force
- Doubling the resultant force on the same mass doubles the acceleration.
Doubling the mass
- Doubling the mass for the same resultant force halves the acceleration.
Definition of the newton
- One newton is the force that gives a 1 kg mass an acceleration of 1 m/s².
Link to weight
- Weight is given by W = m × g, which is the same equation with the acceleration of free fall in place of a.
Section 4 of 5Worked Example
Question
- A car of mass 1200 kg accelerates uniformly from rest to 15 m/s in 5 seconds.
- Calculate (a) the acceleration of the car and (b) the resultant force needed to produce it.
- (a) Use a = Δv ÷ t with Δv = 15 − 0 = 15 m/s and t = 5 s, so a = 15 ÷ 5 = 3 m/s².
- (b) Write F = m × a.
- (b) Substitute: F = 1200 × 3 = 3600 N, acting in the direction of motion.
Answer
- (a) The acceleration is 3 m/s².
- (b) The resultant force is 3600 N forwards.
Section 5 of 5Exam Checklist & Tips
1.3.6 – Key Points for the Exam
- Newton's second law The resultant force on an object equals its mass multiplied by its acceleration.
- Resultant force The single force equivalent to all the forces acting on an object.
- Acceleration The rate of change of velocity, in m/s².
- Inverse proportion A relationship in which one quantity increases as the other decreases by the same factor.
- Newton (N) The SI unit of force, equal to 1 kg m/s².
Common Mistakes
- Using the mass in grams without converting it into kilograms.
- Using the sum of all forces, including those that balance, instead of the resultant force in F = m × a.
- Forgetting that force and acceleration are vectors and must point in the same direction.
- Using weight in place of mass in the equation F = m × a.