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1.4.3Motion, Forces and Energy

Newton’s Second Law — Cambridge IGCSE Physics 0625 Revision Notes & Topical Questions

5 min read 9 parts Lesson 33 of 91 1 quiz

📚 Cambridge IGCSE Physics 0625 Hub / Topical Revision
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Curriculum Equation Key Newton Laws of Motion FormulasFast Exam Solution
F = m × a | W = m × g | F₁₂ = -F₂₁
Word Equation & Conditions: Force = Mass × Acceleration
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Lesson summary

1.4.3 Newton's Second Law — IGCSE PHYSICS notes: Use F = ma to calculate force, mass or acceleration and explain how acceleration depends on force and mass.Newton's second law = the acceleration of an object is directly proportional to the resultant force and inversely proportion…

  • What the symbols mean
  • Rearranged forms
  • If the resultant force is zero, a
  • Graph of a against F for fixed mass
  • Graph of a against m for fixed force
  • If speeds and times are given, find a

Part 1 of 7The law and equation

Newton's second law
Newton's second law the acceleration of an object is directly proportional to the resultant force and inversely proportional to its mass.
Equation
  • F = ma.
    What the symbols mean: F = resultant force (N) · m = mass (kg) · a = acceleration (m s−2)
  • F is the resultant force in N, m is mass in kg and a is acceleration in m/s2.
Rearranged forms
  • Rearranged forms a = F/m and m = F/a.
Direction
  • Direction the acceleration is in the same direction as the resultant force.
Newton
  • 1 N is the force that gives a mass of 1 kg an acceleration of 1 m/s2, so 1 N = 1 kg m/s2.

Part 2 of 7Effects of force and mass

Effects of force and mass
Doubling the resultant force on a given mass doubles the acceleration.
Doubling the mass for the same force halves the acceleration.
If the resultant force is zero, a
0 (the first law).
Graph of a against F for fixed mass
  • Graph of a against F for fixed mass a straight line through the origin with gradient 1/m.
Graph of a against m for fixed force
  • Graph of a against m for fixed force a curve showing an inverse relationship.

Part 3 of 7Always use the resultant force

F in F
F in F ma is the resultant (net) force.
Draw a force diagram first and find the resultant with direction.
Driving force minus friction and drag gives the resultant for a car.
Using the driving force alone is a common error.

Part 4 of 7Weight and free fall

Weight W
Weight W mg gives acceleration a = F/m = mg/m = g.
The mass cancels, so all objects fall with the same acceleration when air resistance is negligible.
With upward air resistance R the resultant is mg − R, so the acceleration is less than g.

Part 5 of 7Investigating the law

1
Pull a trolley along a bench with a string attached to a hanging weight.
2
Measure the acceleration with light gates or a ticker-timer.
3
To test a against F, move masses from the trolley to the hanger so the total mass stays constant.
4
To test a against m, keep the force constant and add masses to the trolley.
5
Compensate for friction by tilting the track slightly until the trolley moves at constant speed when pushed.

Part 6 of 7Problem-solving routine

Problem-solving routine
Write down the known quantities.
Find the resultant force with its direction.
Apply F = ma and check the units.
1If speeds and times are given, find a
Δv/Δt first, then the force.
2If force and mass are given and a speed or time is needed, find a and then use v
If force and mass are given and a speed or time is needed, find a and then use v u + at.

Part 7 of 7More from the specification

1Elastic proportional limit
  • Elastic proportional limit applied tensile forces produce linear extension according to Hooke's law until reaching the characteristic elastic limit.
2Extension
  • Increase in length over the original length.
3Length
  • Resistance is directly proportional to the length of a wire.
4Velocity
  • Rate of change of displacement.
5Balanced
  • Having equal and opposite moments.
6Elastic
  • Returns to original shape when force is removed.
7Spring constant
  • Stiffness k in N/m.
8Constant velocity
  • Zero acceleration.
9Circular motion
  • Motion along a circular path with a force towards the centre.
10One acceleration
  • One acceleration an object may have several forces acting on it, but it has only one acceleration, set by the resultant force.

Key terms

TermMeaning
Newton's second lawF = ma; acceleration is proportional to the resultant force and inversely proportional to mass.
NewtonForce that gives 1 kg an acceleration of 1 m/s².
Resultant forceNet force found by vector addition.
AccelerationRate of change of velocity, in m/s².
MassAmount of matter and a measure of inertia.

Avoid these mistakes

1
Using the driving force instead of the resultant force — subtract friction and drag first.
2
Forgetting to convert grams to kilograms — mass must be in kg.
3
Saying acceleration is larger for a larger mass — it is smaller for the same force.
4
Leaving out weight in vertical problems — include it in the resultant.

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