Forces and equilibrium: past paper questions

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• Question 1May/June 2026, paper 41Structured6 marksHas a diagram

  Coplanar forces of magnitudes $55\text{ N}$, $23\text{ N}$, $20\text{ N}$ and $16\text{ N}$ act at a point in the directions shown in the diagram. Find the magnitude and direction of the resultant force.

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• Question 3Oct/Nov 2025, paper 41Structured6 marksHas a diagram

  Coplanar forces of magnitudes $45\text{ N}$, $28\text{ N}$, $72\text{ N}$ and $35\text{ N}$ act at a point in the directions shown in the diagram. Find, in either order, the magnitude and direction of the resultant force.

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• Question 3Oct/Nov 2024, paper 41Structured4 marksHas a diagram

  Coplanar forces of magnitudes $52\text{ N}$, $39\text{ N}$ and $P\text{ N}$ act at a point in the directions shown in the diagram. The system is in equilibrium. Find the values of $P$ and $\theta$.

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• Question 2Oct/Nov 2023, paper 41Structured5 marksHas a diagram

  A particle of mass $2.4\text{ kg}$ is held in equilibrium by two light inextensible strings, one of which is attached to point $A$ and the other attached to point $B$. The strings make angles of ${35}^{\circ }$ and ${40}^{\circ }$ with the horizontal (see diagram).

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• Question 5May/June 2026, paper 41Structured10 marksHas a diagram

  A particle of mass $3.6\text{ kg}$ is placed on a rough plane inclined at an angle of ${30}^{\circ }$ to the horizontal. The particle is held at rest on the plane by a horizontal force of magnitude $24\sqrt{3}\text{ N}$.

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• Question 5Oct/Nov 2025, paper 41Structured6 marksHas a diagram

  A particle $P$ of mass $m\text{ kg}$ is in equilibrium on a rough plane inclined at an angle ${\theta }^{\circ }$ to the horizontal. The equilibrium of $P$ is maintained by a force of magnitude $8mg\text{ N}$ making an angle ${\theta }^{\circ }$ with a line of greatest slope (see diagram).

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• Question 6Oct/Nov 2024, paper 41Structured6 marksHas a diagram

  A particle of mass $1.2\text{ kg}$ is placed on a rough plane which is inclined at an angle $\theta$ to the horizontal, where $\sin \theta =\frac{7}{25}$.

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• Question 5Oct/Nov 2023, paper 41Structured7 marksHas a diagram

  The diagram shows a particle $A$, of mass $1.2\text{ kg}$, which lies on a plane inclined at an angle of ${40}^{\circ }$ to the horizontal and a particle $B$, of mass $1.6\text{ kg}$, which lies on a plane inclined at an angle of ${50}^{\circ }$ to the horizontal.

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• Question 3May/June 2026, paper 42Structured10 marksHas a diagram

  Two particles, $A$ and $B$, of masses $0.5\text{ kg}$ and $0.8\text{ kg}$ respectively are attached to the ends of a light inextensible string. The string passes over a small smooth pulley fixed at the end of a rough horizontal plane and to the top of a smooth inclined plane.

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• Question 8Oct/Nov 2025, paper 41Structured8 marksHas a diagram

  A block $A$ of mass $2\text{ kg}$ and a particle $B$ of mass $0.5\text{ kg}$ are connected by a light inextensible string inclined at ${15}^{\circ }$ to the horizontal.

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• Question 4Oct/Nov 2024, paper 42Structured6 marksHas a diagram

  The diagram shows two particles, $A$ and $B$, of masses $0.2\mathrm{k}\mathrm{g}$ and $0.1\mathrm{k}\mathrm{g}$ respectively. The particles are suspended below a horizontal ceiling by two strings, $AP$ and $BQ$, attached to fixed points $P$ and $Q$ on the ceiling.

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• Question 2Oct/Nov 2023, paper 42Structured5 marksHas a diagram

  The diagram shows a smooth ring $R$, of mass $m\text{ kg}$, threaded on a light inextensible string. A horizontal force of magnitude $2\text{ N}$ acts on $R$. The ends of the string are attached to fixed points $A$ and $B$ on a vertical wall.

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• Question 6May/June 2026, paper 42Structured8 marksHas a diagram

  A crate of weight $W\text{ N}$ is at rest on rough horizontal ground. The crate is pulled at a constant acceleration of $1.5{\text{ ms}}^{-2}$ along the ground in a straight line by a light rope.

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• Question 5Oct/Nov 2025, paper 42Structured6 marksHas a diagram

  A block of mass $5\text{ kg}$ is being pulled straight down a line of greatest slope of a rough plane by a force of magnitude $20\text{ N}$.

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• Question 2Oct/Nov 2024, paper 43Structured6 marksHas a diagram

  Coplanar forces of magnitudes $16\text{ N}$, $12\text{ N}$, $24\text{ N}$ and $8\text{ N}$ act at a point in the directions shown in the diagram. Find the magnitude and direction of the single additional force acting at the same point which will produce equilibrium.

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• Question 4Oct/Nov 2023, paper 42Structured7 marks

  A particle $P$ of mass $0.2\text{ kg}$ lies at rest on a rough horizontal plane. A horizontal force of $1.2\text{ N}$ is applied to $P$. Given that $P$ is in limiting equilibrium, find the coefficient of friction between $P$ and the plane.

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• Question 6May/June 2026, paper 43Structured8 marksHas a diagram

  Three coplanar forces of magnitudes $F\mathrm{N}$, $65\mathrm{N}$ and $50\mathrm{N}$ act at a point in the directions shown in the diagram. It is initially given that $F=40$. Find the magnitude and direction of the resultant force.

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• Question 3Oct/Nov 2025, paper 43Structured7 marks

  A block of mass $4\text{ kg}$ is pulled along a rough horizontal road by a constant force of magnitude $25\text{ N}$ acting at an angle of ${36}^{\circ }$ above the horizontal.

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• Question 5Oct/Nov 2024, paper 43Structured8 marks

  A particle of mass $12\text{ kg}$ is going to be pulled across a rough horizontal plane by a light inextensible string. The string is at an angle of ${30}^{\circ }$ above the plane and has tension $T\text{ N}$ (see diagram).

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• Question 5Oct/Nov 2023, paper 43Structured8 marksHas a diagram

  A light string $AB$ is fixed at $A$ and has a particle of weight $80\text{ N}$ attached at $B$. A horizontal force of magnitude $P\text{ N}$ is applied at $B$ such that the string makes an angle ${\theta }^{\circ }$ to the vertical (see diagram).

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• Question 7Oct/Nov 2025, paper 43Structured7 marksHas a diagram

  A particle $P$ of mass $6\text{ kg}$ lies on a rough plane inclined at an acute angle $\theta$ to the horizontal. A horizontal force of magnitude $12\text{ N}$ acts on $P$ as shown in the diagram.

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• Question 2May/June 2024, paper 41Structured7 marksHas a diagram

  Two forces of magnitudes $20\text{ N}$ and $F\text{ N}$ act at a point $P$ in the directions shown in the diagram. Given that the resultant force has no component in the $y$-direction, calculate the value of $F$.

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• Question 7Oct/Nov 2023, paper 43Structured13 marksHas a diagram

  Particles $A$ and $B$, of masses $2.4\text{ kg}$ and $3.3\text{ kg}$ respectively, are connected by a light inextensible string that passes over a smooth pulley which is fixed to the top of a rough plane. The plane makes an angle of ${\theta }^{\circ }$ with horizontal ground.

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• Question 2May/June 2025, paper 41Structured4 marks

  Three coplanar forces of magnitudes $P\text{ N}$, $5\text{ N}$ and $10\text{ N}$ act at a point $O$, as shown in the diagram. The resultant of the three forces has magnitude $Q\text{ N}$ and acts in a direction perpendicular to the force of magnitude $P\text{ N}$.

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• Question 3May/June 2024, paper 42Structured6 marksHas a diagram

  Four coplanar forces of magnitude $P\text{ N}$, $10\text{ N}$, $16\text{ N}$ and $2\text{ N}$ act at a point in the directions shown in the diagram. It is given that the forces are in equilibrium. Find the values of $\theta$ and $P$.

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• Question 5May/June 2023, paper 41Structured9 marksHas a diagram

  Four coplanar forces act at a point. The magnitudes of the forces are $F\text{ N}$, $10\text{ N}$, $50\text{ N}$ and $40\text{ N}$. The directions of the forces are as shown in the diagram.

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• Question 3May/June 2025, paper 42Structured4 marksHas a diagram

  A particle $P$ of mass $m\text{ kg}$ is attached to one end of a light inextensible string of length $2.6\text{ m}$. The other end of the string is attached to a fixed point on a horizontal ceiling, and the string is taut.

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• Question 5May/June 2024, paper 42Structured8 marksHas a diagram

  A particle of mass $0.8\text{ kg}$ lies on a rough plane which is inclined at an angle of ${28}^{\circ }$ to the horizontal. The particle is kept in equilibrium by a force of magnitude $T\text{ N}$.

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• Question 6May/June 2023, paper 41Structured8 marksHas a diagram

  Two particles $P$ and $Q$, of masses $0.2\text{ kg}$ and $0.1\text{ kg}$ respectively, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley at $B$ which is attached to two inclined planes.

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• Question 4May/June 2025, paper 43Structured6 marks

  Three blocks $P$, $Q$ and $R$, of masses $25\text{ kg}$, $20\text{ kg}$ and $m\text{ kg}$ respectively, are held in equilibrium by three light inextensible strings $OP$, $OQ$ and $OR$.

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