Forces & equilibrium: AS Level Mathematics questions with answers
Free Forces & equilibrium questions for AS Level Mathematics (9709), part of Mechanics. Each question has the answer and the marking points an examiner would look for.
Particle A of mass 2 kg lies on a rough horizontal table. It is attached to a light inextensible string that passes over a smooth pulley at the edge of the table. Particle B of mass 3 kg hangs from the other end, 1 m above the floor. The coefficient of friction between A and the table is 0.1. The system is released from rest with the string taut. A does not reach the pulley.
(a)
Find the acceleration of the system and the tension in the string.
[5]
(b)
Find the speed of B when it hits the floor.
[2]
(c)
B does not rebound. Find the total distance moved by A before it comes to rest.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
5.6 m s−2, 13.2 N
friction = 0.1 × 20 = 2 B1 Newton’s second law for A M1 Newton’s second law for B M1 a = 5.6 A1 T = 13.2 A1
5
(b)
3.35 m s−1
v2 = 2as M1 3.35 A1
2
(c)
6.6 m
deceleration of A = 1 m s−2B1 extra distance = 5.6 m M1 total 6.6 A1
3
Question 2Structured · 9 marksA* challenge
A particle of mass 5 kg rests on a rough plane inclined at angle α to the horizontal, where sin α = 0.8. The coefficient of friction between the particle and the plane is 0.5. 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)
25 ≤ P ≤ 55
R = 5 × 10 × 0.6 = 30 B1 F = 0.5 × 30 = 15 B1 resolve parallel to the plane with friction up the plane (least P) M1 Pmin = 25 A1 friction down the plane (greatest P) M1 Pmax = 55 A1
6
(b)
moves: a = 5 m s−2 down the plane
component of weight down plane = 40 N M1 compare with maximum friction 15 N M1 a = 5 A1
3
Question 3Structured · 5 marks
A particle of weight 27 N hangs in equilibrium from two strings. The strings make angles of 30° and 45° with the horizontal. Find the tensions in the strings.
A block of mass 4 kg is released from rest on a rough plane inclined at 25° to the horizontal. The coefficient of friction is 0.19. 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 = 2.5 m s−2, v = 3.88 m s−1
R = 4g cos 25 B1 F = μR M1 Newton II along plane M1 a = 2.5 A1 v2 = 2as M1 3.88 A1
6
Question 5Structured · 5 marks
A block A of mass 5 kg lies on a rough horizontal table (coefficient of friction 0.1). 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 = 4.5 m s−2; T = 27.5 N
friction = μ × 5g B1 Newton II for A M1 Newton II for B M1 a = 4.5 A1 T = 27.5 A1
5
Question 6Structured · 7 marksA* challenge
A car of mass 1800 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 200 N on the trailer.
(a)
The driving force of the car is 2500 N. Find the acceleration and the tension in the tow-bar.
[4]
(b)
The car is now braking with a braking force of 2000 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)
0.864 m s−2, 545 N
whole system equation M1 a = 0.864 A1 trailer equation M1 T = 545 A1
4
(b)
273 N, thrust
deceleration 1.18 B1 trailer equation M1 273 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