CAIE A-Level Mathematics 4.1 Forces and Equilibrium Question Bank

CAIE A-Level Mathematics 4.1 Forces and Equilibrium Question Bank
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise drawing force diagrams, resolving coplanar forces and applying equilibrium or limiting-friction equations to particles, strings, pulleys and inclined planes.

Exam points

  • draw every force with its correct direction before resolving along chosen axes
  • resolve horizontally and vertically or parallel and perpendicular to an inclined plane
  • apply resultant zero and F = μR at limiting equilibrium to solve tensions, angles or masses

Covered syllabus points

4.1.1—Forces4.1.2—The vector nature of force4.1.3—Forces4.1.4—Friction4.1.5—The model of a 'smooth' contact4.1.6—Equilibrium4.1.7—Newton's laws

Question 1

[Maximum number: 5]
Figure for Question 1 — CAIE A-Level Mathematics

Coplanar forces of magnitudes P N,Q N,32 NP \mathrm{~N}, Q \mathrm{~N}, 32 \mathrm{~N} and 21 N act at a point in the directions shown in the diagram. The forces are in equilibrium.

Find the value of P and the value of Q.

Question 3(a)

[Maximum number: 1]

A block of mass 8 kg slides down a rough plane inclined at 30∘30^{\circ} to the horizontal, starting from rest. The coefficient of friction between the block and the plane is μ\mu. The block accelerates uniformly down the plane at 2.4 m s−22.4 \mathrm{~m} \mathrm{~s}^{-2}.

Draw a diagram showing the forces acting on the block.

Question 3

[Maximum number: 6]
Figure for Question 3 — CAIE A-Level Mathematics

Coplanar forces of magnitudes 45 N,28 N,72 N45 \mathrm{~N}, 28 \mathrm{~N}, 72 \mathrm{~N} and 35 N act at a point in the directions shown in the diagram.

Find, in either order, the magnitude and direction of the resultant force.

Question 5

[Maximum number: 6]
Figure for Question 5 — CAIE A-Level Mathematics

A particle P of mass m kgm \mathrm{~kg} is in equilibrium on a rough plane inclined at an angle θ∘\theta^{\circ} to the horizontal. The equilibrium of P is maintained by a force of magnitude 8mg N8 m g \mathrm{~N} making an angle θ∘\theta^{\circ} with a line of greatest slope (see diagram). The coefficient of friction between P and the plane is 0.5 and P is on the point of slipping down the plane.

Find the value of θ\theta.