1.4.2Dynamics
Newton’s Laws and Unbalanced Forces — SQA National 5 Physics Revision Notes & Topical Questions
5 min read 6 parts Lesson 12 of 22
Curriculum Equation Key Newton Laws of Motion FormulasFast Exam Solution
F = m × a | W = m × g | F₁₂ = -F₂₁
Word Equation & Conditions: Force = Mass × Acceleration
Part 1 of 6Newton's Second Law
Newton's first law tells us what happens when forces balance; the second law tells us exactly what happens when they do not.
Statement
- When a resultant force acts on an object it accelerates in the direction of the force.
Equation
- The relationship is F = m a, where F is the resultant force in newtons, m is the mass in kg and a is the acceleration in m/s².
Proportionality
- For a fixed mass, doubling the resultant force doubles the acceleration.
Mass
- For a fixed force, doubling the mass halves the acceleration, so heavier objects are harder to accelerate.
Part 2 of 6Finding the Resultant First
Finding the Resultant First
Step one
- Identify all the horizontal forces such as the driving force and friction acting on the object.
Step two
- Subtract the smaller from the larger when they oppose each other, to get the unbalanced force.
Step three
- Divide this resultant force by the mass to find the acceleration, using a = F ÷ m.
Direction
- The acceleration is in the same direction as the resultant force, so a force opposite to motion gives a deceleration.
| Quantity | Symbol | Unit |
|---|---|---|
| resultant force | F | N |
| mass | m | kg |
| acceleration | a | m/s² |
Part 3 of 6Investigating the Relationship
1
Fix a trolley on a runway and pull it with a known force from a newton balance or weights on a string.
2
Use light gates to measure the acceleration for each force while keeping the mass the same.
3
Plot acceleration against force and observe a straight line through the origin showing direct proportionality.
4
Then keep the force the same and add mass to the trolley, noticing that acceleration decreases as mass increases.
Part 4 of 6Exam Technique
Exam Technique
Draw a diagram
- Sketch the object and label every force with an arrow before choosing which forces to combine.
Resultant first
- Always work out the resultant force before using F = m a, since the equation applies to the unbalanced force only.
Units
- Use kilograms for mass; a mass given in grams must be divided by 1000 before substituting.
Check direction
- A resultant force opposing the direction of motion gives a negative acceleration, meaning the object is slowing down.
Part 5 of 6Worked Example
Question
- A car of mass 1200 kg has an engine force of 3000 N while friction and air resistance total 600 N.
- Find its acceleration.
- What resultant force gives a 0.50 kg trolley an acceleration of 4.0 m/s²?
- Resultant force = 3000 − 600 = 2400 N.
- a = F ÷ m = 2400 ÷ 1200 = 2.0 m/s².
- TrolleyF = m a = 0.50 × 4.0 = 2.0 N.What the symbols mean: F = resultant force (N) · m = mass (kg) · a = acceleration (m s−2)
Answer Car 2.0 m/s²; trolley needs 2.0 N.
Part 6 of 6Exam Checklist & Tips
1.4.2 – Key Points for the Exam
- Resultant force The overall unbalanced force acting on an object.
- Newton The force that gives a 1 kg mass an acceleration of 1 m/s².
- Mass
- The amount of matter in an object;
- a measure of its inertia.
- The amount of matter in an object;
- Direct proportionality When doubling one quantity doubles the other.
Common Mistakes
- Using one of the forces instead of the resultant in F = m a.
- Forgetting to subtract friction from the driving force.
- Using weight in newtons where mass in kilograms is needed.
- Writing the acceleration unit as N or kg instead of m/s².
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