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A-levelMechanics

Forces and equilibrium

For a particle in equilibrium, the resultant force is zero. Draw a force diagram, resolve along two perpendicular axes and balance the components in each direction. Try the questions below to check your method.

2 lessons6 worksheets18 questions

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Lessons

These free MathLab Learn guides are arranged in the order they are most useful for this stage.

  1. 01Newton's laws of motion
  2. 02How to resolve forces and solve equilibrium

Practise

Practice moves from direct fluency towards application, reasoning and synthesis.

  1. Intro

    Resolving Forces

    Step 1 · 1 worksheet · 3 questions

  2. Intro

    Particle Equilibrium

    Step 2 · 1 worksheet · 3 questions

  3. Practice

    Smooth Inclined Planes In Equilibrium

    Step 3 · 1 worksheet · 3 questions

  4. Practice

    Newton'S Second Law On A Horizontal Line

    Step 4 · 1 worksheet · 3 questions

  5. Practice

    Lifts And Apparent Weight

    Step 5 · 1 worksheet · 3 questions

  6. Challenge

    Newton'S Third Law And Contact Forces

    Step 6 · 1 worksheet · 3 questions

By MathLab · Updated

Draw a free-body diagram first. The questions below concern particles, so there is no separate turning-effect calculation. Extended rigid bodies also require a moments condition.

Forces and equilibrium questions with answers

These are original MathLab examples. Use g=9.8 m s−2g=9.8\text{ m s}^{-2} where needed, and try each question before revealing its worked answer.

Try a sample
01
MathLab practice

Foundation: resolve a force

Sample

A 2020 N force acts at 30∘30^\circ above the positive horizontal direction. Find its horizontal and vertical components.

Worked answer: use the angle measured from the horizontal

The horizontal component is 20cos⁡30∘=103 N20\cos30^\circ=\boxed{10\sqrt3\text{ N}} to the right. The vertical component is 20sin⁡30∘=10 N20\sin30^\circ=\boxed{10\text{ N}} upwards. Cosine gives the component adjacent to the marked angle.

02
MathLab practice

Standard: balance a particle

Sample

A particle of weight 3030 N is in equilibrium under a tension at 30∘30^\circ above the horizontal towards the right, and a horizontal force towards the left. Find the tension TT and horizontal force PP.

Worked answer: balance vertically, then horizontally

Vertical equilibrium gives Tsin⁡30∘=30T\sin30^\circ=30, so T=60T=60 N. Horizontal equilibrium gives P=Tcos⁡30∘=303 NP=T\cos30^\circ=\boxed{30\sqrt3\text{ N}}, approximately 52.052.0 N.

03
MathLab practice

Reasoning: is the reaction always equal to weight?

Sample

A 55 kg particle rests on a smooth plane inclined at 30∘30^\circ to the horizontal. A force parallel to the plane holds it in equilibrium. Find the normal reaction and explain why it is not 5g5g.

Worked answer: resolve perpendicular to the plane

The holding force has no component perpendicular to the plane. The normal reaction balances the perpendicular component of weight, so R=5gcos⁡30∘=4932 NR=5g\cos30^\circ=\boxed{\frac{49\sqrt3}{2}\text{ N}}, approximately 42.442.4 N. The remaining weight component acts down the slope and is balanced by the holding force. The full weight is not perpendicular to the surface.

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