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Course: SQA National 5 Physics
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SQA National 5 Physics

1. Dynamics

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2. Space

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3. Electricity

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4. Properties of Matter

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5. Waves

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6. Radiation

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Text lesson

1.4.2 Newton’s Laws and Unbalanced Forces

1.4.2 Newton's Laws and Unbalanced Forces: Use F = m a to link the resultant force on an object to its mass and acceleration, and describe the effect of unbalanced forces.

1.4.2 Newton's Laws and Unbalanced Forces

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.
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
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.
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.

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?

  1. Resultant force = 3000 − 600 = 2400 N.
  2. a = F ÷ m = 2400 ÷ 1200 = 2.0 m/s².
  3. Trolley: F = 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.

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.
  • 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.
YOUR STUDY PATH

1.4.2 Newton's Laws and Unbalanced Forces

SQA National 5 Physics / 1. Dynamics

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