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Friction and connected particles

Modelling friction with F ≤ μR and solving systems of connected particles.

  • Define and explain Friction and connected particles in your own words
  • Use key terms such as Friction accurately
  • Apply what you have learned to new examples and questions
  • Avoid the common mistakes learners make with this topic

This lesson focuses on Friction and connected particles: modelling friction with F ≤ μR and solving systems of connected particles.

Definition: Friction and connected particles

Modelling friction with F ≤ μR and solving systems of connected particles.

Key ideas

Newton's second law

The resultant force on a particle equals mass times acceleration (F = ma). Draw a force diagram, resolve along the direction of motion, and equate; mass in kg, acceleration in m/s² gives force in newtons.

SUVAT equations

For constant acceleration: v = u + at, s = ut + ½at², and v² = u² + 2as. Choose the equation containing the quantities you know and the one unknown you need; always define a positive direction first.

Key term — Friction: A force opposing relative motion between surfaces, modelled as F ≤ μR where μ is the coefficient of friction and R the normal reaction.

Worked example: Friction and connected particles

A box on rough ground has normal reaction 50 N and μ = 0.4. Find the maximum friction.

F_max = 0.4 × 50 = 20 N.

Answer: F_max = 0.4 × 50 = 20 N.

Common mistakes
  • Using F = ma with the wrong force It is the resultant (net) force that equals ma — add all forces vectorially first, including friction and weight components.
  • Confusing speed with velocity, or distance with displacement SUVAT uses vectors: fix a positive direction at the start and keep signs consistent, or the equations give nonsense.

Practice

A particle starts from rest and accelerates at 3 m/s² for 5 s. Find its final velocity.
v = u + at.

v = 0 + 3 × 5 = 15 m/s.

Find the distance travelled in the previous question.
s = ut + ½at².

s = 0 + ½ × 3 × 25 = 37.5 m.

A 2 kg mass experiences a resultant force of 10 N. Find its acceleration.
F = ma.

a = 10/2 = 5 m/s².

A ball is dropped from rest. How far does it fall in 2 s? (g = 9.8 m/s²)
s = ut + ½gt² with u = 0.

s = ½ × 9.8 × 4 = 19.6 m.

Quick check

Friction and connected particles — quick check

Which of these best defines "Friction"?

A force opposing relative motion between surfaces, modelled as F ≤ μR where μ is the coefficient of friction and R the normal reaction.

A projectile is launched horizontally at 20 m/s from a 45 m cliff. How long until it hits the sea? (g = 9.8 m/s²)

t² = 90/9.8 ≈ 9.18; t ≈ 3.03 s.
Key takeaways
  • Friction and connected particles: modelling friction with F ≤ μR and solving systems of connected particles.
  • Newton's second law: The resultant force on a particle equals mass times acceleration (F = ma).
  • Displacement: Distance measured in a straight line from a starting point, with direction included; unlike distance, it can be negative.
  • Watch out for: using F = ma with the wrong force
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