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Statics of a particle practice problems Edexcel IAL Mechanics 1, Chapter 4

Written by STEM-Tutor's tutors · Updated October 2026 · 8 questions and 1 structured exam question

Particles in equilibrium: resolving forces in two directions, strings at angles, limiting friction and particles held on inclined planes. Try each question before you look: use the hint if you are stuck, then reveal the worked solution one step at a time.

On this page
  1. Key equations
  2. Warm-up questions
  3. Exam-style questions
  4. Exam question practice
  5. Common mistakes
  6. Keep going

Key equations for statics of a particle

ΣFx = 0, ΣFy = 0equilibrium: resolve in two directions
F cos θ, F sin θcomponents of a force at θ to the horizontal
F = μRlimiting equilibrium (on the point of moving)
μ = tan αparticle on the point of slipping on a plane at α, with no other forces

Take g = 9.8 m s−2, as the WME01 paper asks, and give answers to 2 or 3 significant figures. Answers within 2.5% are marked correct, so rounding along the way is fine. Revise the methods in our A level Maths mechanics guide.

Warm-up questions

Quick checks on the core ideas. If these feel easy, go straight to the exam-style questions.

Q1Warm-up
A particle of mass 2 kg hangs at rest on the end of a light vertical string. Find the tension in the string.
N

Hint

In equilibrium the forces balance.

Worked solution
  1. T = 2g = 2 × 9.8.
  2. T = 19.6 N.
Q2Warm-up
A particle is on the point of sliding along a rough surface. The friction force F and normal reaction R satisfy:

Hint

This is called limiting equilibrium.

Worked solution
  1. When the particle is about to move, friction has reached its maximum value.
  2. So F = μR: C. Before that point, F < μR.
Q3Warm-up
A force of 10 N acts at 30° above the horizontal. Find its horizontal component.
N

Hint

The horizontal component is next to the angle, so use cosine.

Worked solution
  1. 10 cos 30° = 10 × 0.866.
  2. = 8.66 N.

Exam-style questions

Questions at the level of the Edexcel IAL Mechanics 1 exam. The ones marked Challenge combine more than one idea.

Q4Exam-styleLimiting friction
A particle rests on a rough plane inclined at 25° to the horizontal and is on the point of slipping down it. Find the coefficient of friction.

Hint

Resolve along and perpendicular to the plane, with friction acting up the plane.

Worked solution
  1. Perpendicular: R = mg cos 25°. Along the plane: F = mg sin 25°.
  2. Limiting, so F = μR: mg sin 25° = μmg cos 25°.
  3. μ = tan 25° = 0.466 (3 s.f.).
Q5Exam-style
A particle of mass 5 kg rests on a smooth plane inclined at 20° to the horizontal. It is held in equilibrium by a horizontal force P. Find P.
N

Hint

Resolve along the plane so that R does not appear.

Worked solution
  1. Along the plane: P cos 20° = 5g sin 20°.
  2. P = 49 tan 20°.
  3. P = 17.8 N (3 s.f.).
Q6Exam-style
A particle of mass 4 kg hangs in equilibrium from two light strings. One string makes 30° with the horizontal and the other makes 60° with the horizontal. Find the tension in the string at 60°.
N

Hint

Resolve horizontally and vertically, then solve the two equations simultaneously.

Worked solution
  1. Horizontally: T1 cos 30° = T2 cos 60°, so T2 = √3 T1.
  2. Vertically: T1 sin 30° + T2 sin 60° = 4g, so 0.5T1 + 1.5T1 = 39.2 and T1 = 19.6 N.
  3. T2 = 19.6√3 = 33.9 N (3 s.f.).
Q7Exam-style
Forces (3i − 2j) N, (ai + 5j) N and (−4i + bj) N act on a particle in equilibrium. Find a and b.

Hint

In equilibrium the resultant is zero, so each component adds to zero.

Worked solution
  1. i: 3 + a − 4 = 0, so a = 1.
  2. j: −2 + 5 + b = 0, so b = −3.
  3. The answer is A.
Q8Challenge
A box of mass 2 kg rests on rough horizontal ground, with coefficient of friction 0.5. A force P acting at 20° above the horizontal is just enough to make the box start to move. Find P.
N

Hint

P reduces the normal reaction. Write R in terms of P first.

Worked solution
  1. Vertically: R + P sin 20° = 2g, so R = 19.6 − P sin 20°.
  2. Horizontally, limiting: P cos 20° = 0.5(19.6 − P sin 20°).
  3. P(cos 20° + 0.5 sin 20°) = 9.8, so P = 9.8/1.1107 = 8.82 N (3 s.f.).

Exam question practice

One original structured question in the style of the WME01 paper. Answer it in full, with working, before you open the mark scheme: M marks are for a correct method, A marks for accurate answers that follow from it, and B marks for a correct statement on its own.

Structured exam question style · 7 points · about 12 minutes

A particle of mass 2 kg rests on a rough plane inclined at 30° to the horizontal. The coefficient of friction between the particle and the plane is 0.25. The particle is held in equilibrium by a force of magnitude P newtons acting up the plane, along a line of greatest slope.

  1. (a) Find the normal reaction on the particle.
  2. (b) Find the least value of P for which the particle stays at rest.
  3. (c) Find the greatest value of P for which the particle stays at rest.

Write your full answer on paper first, then open the scoring guide and tick each point you earned.

Scoring guide and model answer

Part (a)

R = 2g cos 30° = 16.97… = 17.0 N.

Part (b)

About to slip down, so friction acts up the plane: P + 0.25R = 2g sin 30°, P = 9.8 − 4.24 = 5.56 N.

Part (c)

About to move up, so friction acts down the plane: P = 9.8 + 4.24 = 14.0 N.

Your mark: 0 of 7

Common mistakes in statics of a particle

Keep going

Revise the ideas behind these questions:

Then try real exam questions: Edexcel IAL Mechanics 1 past papers, with official scoring guidelines. · All Edexcel IAL Mechanics 1 units