Forces & equilibrium: A Level Mathematics questions with answers
Free Forces & equilibrium questions for A Level Mathematics (9709), part of Mechanics. Each question has the answer and the marking points an examiner would look for.
A particle of mass 2 kg rests on a rough plane inclined at angle α to the horizontal, where sin α = 0.28. The coefficient of friction between the particle and the plane is 0.3. A force of magnitude P N, acting up the plane along a line of greatest slope, keeps the particle in equilibrium.
(a)
Find the set of possible values of P.
[6]
(b)
The force P is removed. Determine whether the particle moves, and if it does, find its acceleration.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
0 ≤ P ≤ 11.4 (friction alone can hold the particle)
R = 2 × 10 × 0.96 = 19.2 B1 F = 0.3 × 19.2 = 5.76 B1 resolve parallel to the plane with friction up the plane (least P) M1 Pmin ≤ 0 so P ≥ 0 A1 friction down the plane (greatest P) M1 Pmax = 11.4 A1
6
(b)
does not move: friction limiting value exceeds weight component
component of weight down plane = 5.6 N M1 compare with maximum friction 5.76 N M1 remains at rest A1
3
Question 2Structured · 5 marksA* challenge
A particle is in equilibrium under three forces: its weight of 9 N, a horizontal force of 8 N, and a force of P N acting at an angle α above the horizontal. Find P and α.
[5]
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Part
Answer and marking points
Marks
P = 12, α = 48.4°
resolve horizontally: P cos α = 8 M1 resolve vertically: P sin α = 9 M1 tan α = 98M1 α = 48.4° A1 P = 12 A1
5
Question 3Structured · 5 marks
A particle of weight 51 N hangs in equilibrium from two strings. The strings make angles of 50° and 60° with the horizontal. Find the tensions in the strings.
A block A of mass 5 kg lies on a rough horizontal table (coefficient of friction 0.3). It is connected by a light inextensible string over a smooth pulley at the edge to a particle B of mass 5 kg hanging freely. The system is released from rest. Find the acceleration and the tension in the string.
[5]
Show answers and mark scheme
Part
Answer and marking points
Marks
a = 3.5 m s−2; T = 32.5 N
friction = μ × 5g B1 Newton II for A M1 Newton II for B M1 a = 3.5 A1 T = 32.5 A1
5
Question 5Structured · 6 marks
A block of mass 10 kg is released from rest on a rough plane inclined at 35° to the horizontal. The coefficient of friction is 0.23. Find the acceleration of the block and its speed after it has moved 3 m. [Use g = 10 m s−2]
[6]
Show answers and mark scheme
Part
Answer and marking points
Marks
a = 3.85 m s−2, v = 4.81 m s−1
R = 10g cos 35 B1 F = μR M1 Newton II along plane M1 a = 3.85 A1 v2 = 2as M1 4.81 A1
6
Question 6Structured · 7 marksA* challenge
A car of mass 1200 kg tows a trailer of mass 400 kg along a straight horizontal road using a light rigid tow-bar. The resistances to motion are 400 N on the car and 100 N on the trailer.
(a)
The driving force of the car is 3000 N. Find the acceleration and the tension in the tow-bar.
[4]
(b)
The car is now braking with a braking force of 2500 N and no driving force. Find the force in the tow-bar and state whether it is a tension or a thrust.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
1.56 m s−2, 725 N
whole system equation M1 a = 1.56 A1 trailer equation M1 T = 725 A1
4
(b)
650 N, thrust
deceleration 1.88 B1 trailer equation M1 650 N thrust A1
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Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in