Forces and equilibrium — AS & A Level Mathematics (9709) questions by topic
Finding the magnitude and direction of a resultant from three coplanar forces given as a ratio through tan alpha, resolving four forces at a point along perpendicular axes, and finding an unknown force that keeps a particle in equilibrium on a vertical wall drive the 18 forces and equilibrium questions from 2023 to 2025, worth 3 to 12 marks.
Find, calculate and show are the only three command words tracked here, each requiring forces resolved correctly along chosen axes before any equation is solved. Because a single mis-resolved component throws off an entire equilibrium equation, submit your resolved-forces working for instant marking, so a sign error or a wrongly assigned angle is caught the moment it is written down rather than after the whole system fails to balance.
May–June 2025, Paper 41
Three coplanar forces of magnitudes P N, 5 N and 10 N act at a point O, as shown in the diagram. The resultant of the three forces has magnitude Q N and acts in a direction…
Answer this question and get it marked →May–June 2025, Paper 42
A particle P of mass m kg is attached to one end of a light inextensible string of length 2.6 m. The other end of the string is attached to a fixed point on a horizontal ceiling,…
Answer this question and get it marked →May–June 2025, Paper 43
Three blocks P, Q and R, of masses 25 kg, 20 kg and m kg respectively, are held in equilibrium by three light inextensible strings OP, OQ and OR. The strings OP and OR both pass…
Answer this question and get it marked →May–June 2025, Paper 45
Coplanar forces of magnitudes 17 N, 51 N and 34 N act at a point O in the directions shown in the diagram, where tan(alpha) = 15/8. Find the magnitude and direction of the…
Answer this question and get it marked →Two particles A and B of masses 6.5 kg and m kg respectively are connected by a light inextensible string that passes over a smooth pulley. The pulley is fixed at the top of a…
Answer this question and get it marked →May–June 2024, Paper 41
Two forces of magnitudes 20 N and F N act at a point P in the directions shown in the diagram (the 20 N force acts at 60° above the positive x-axis; the F N force acts vertically…
Answer this question and get it marked →May–June 2024, Paper 42
Four coplanar forces of magnitude P N, 10 N, 16 N and 2 N act at a point in the directions shown in the diagram. It is given that the forces are in equilibrium. In the diagram, a…
Answer this question and get it marked →May–June 2024, Paper 43
A particle of mass 0.2 kg is attached to one end of a light inextensible string. The other end of the string is attached to a fixed point on a vertical wall. The particle is held…
Answer this question and get it marked →October–November 2024, Paper 41
Coplanar forces of magnitudes 52 N, 39 N and P N act at a point in the directions shown in the diagram. The system is in equilibrium. Find the values of P and θ. [4]
Answer this question and get it marked →October–November 2024, Paper 42
The diagram shows two particles, A and B, of masses 0.2 kg and 0.1 kg respectively. The particles are suspended below a horizontal ceiling by two strings, AP and BQ, attached to…
Answer this question and get it marked →October–November 2024, Paper 43
Coplanar forces of magnitudes 16 N, 12 N, 24 N and 8 N act at a point in the directions shown in the diagram. Taking the point as the origin with the 24 N force directed along the…
Answer this question and get it marked →May–June 2023, Paper 41
Four coplanar forces act at a point. The magnitudes of the forces are F N, 10 N, 50 N and 40 N. The directions of the forces are as shown in the diagram. Given that the forces are…
Answer this question and get it marked →May–June 2023, Paper 42
Coplanar forces of magnitudes 30 N, 15 N, 33 N and P N act at a point in the directions shown in the diagram, where tan α = 4/3. The system is in equilibrium. In the diagram a…
Answer this question and get it marked →May–June 2023, Paper 43
A smooth ring R of mass 0.2 kg is threaded on a light string ARB. The ends of the string are attached to fixed points A and B with A vertically above B. The string is taut and…
Answer this question and get it marked →October–November 2023, Paper 41
A particle of mass 2.4 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…
Answer this question and get it marked →October–November 2023, Paper 42
The diagram shows a smooth ring R, of mass m kg, threaded on a light inextensible string. A horizontal force of magnitude 2 N acts on R. The ends of the string are attached to…
Answer this question and get it marked →A particle P of mass 0.2 kg lies at rest on a rough horizontal plane. A horizontal force of magnitude 1.2 N is applied to P. Given that P is in limiting equilibrium, find the…
Answer this question and get it marked →October–November 2023, Paper 43
A light string AB is fixed at A and has a particle of weight 80 N attached at B. A horizontal force of magnitude P N is applied at B such that the string makes an angle theta…
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