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Leaving Cert Applied Maths: Connected particles & pulleys

How often Connected particles & pulleys comes up on the Applied Maths papers, every year it was asked, and questions to try.

HL Asked on 3 of the last 3 Higher Level papers, most recently in 2025. banker

OL Asked on 3 of the last 3 Ordinary Level papers, most recently in 2025. banker

Connected particles & pulleys, Higher Level(8 marks)

Quick ones on Connected particles & pulleys.

(a)Why is a string in a pulley problem modelled as light and inextensible?
  1. So there is no friction at the pulley or on the table
  2. So tension is uniform and both masses share one acceleration
  3. So the two masses have equal weights and balance
(b)Masses of 3 kg and 4 kg hang over a smooth light pulley (g = 9.8). Acceleration?
  1. 2.45 m/s²
  2. 9.8 m/s²
  3. 1.4 m/s²
(c)A string over a fixed smooth pulley has both parts vertical, tension T. Force on the pulley?
  1. 2T
  2. T/2
  3. T
Show the answers

(a) So tension is uniform and both masses share one acceleration

(b) 1.4 m/s²

(c) 2T

Your turn: Higher Level questions on Connected particles & pulleys.

Higher Level

Asked on 3 of the last 3 Higher Level papers, most recently in 2025. banker

Every paper, year by year

YearWhere it came up
2025Q3
2024Q2
2023Q5

Links open the State Examinations Commission’s paper for that year.

More Connected particles & pulleys questions

Connected particles & pulleys, 3 marks

In an Atwood machine, why is the tension less than the weight of the heavier (falling) mass?

  1. The tension always equals the lighter weight
  2. The pulley takes part of the weight
  3. That mass accelerates down, so its net force is down
Show the answer

That mass accelerates down, so its net force is down

For the heavier mass, m₁g − T = m₁a with a > 0, so T < m₁g. For the lighter one, T − m₂g = m₂a, so T > m₂g. The tension lies between the two weights.

Connected particles & pulleys, 3 marks

Masses 3 kg and 2 kg hang over a smooth light pulley, released from rest (g = 9.8). Speed after moving 0.98 m?

  1. 4.38 m/s
  2. 1.96 m/s
  3. 3.84 m/s
Show the answer

1.96 m/s

a = (3 − 2)(9.8)/5 = 1.96 m/s². v² = 2(1.96)(0.98) = 3.8416, so v = 1.96 m/s. 3.84 is v², and 4.38 m/s is free fall, as if the lighter mass were not there.

Connected particles & pulleys, 3 marks

A block on a smooth table is pulled by a hanging mass, which then hits the floor. What does the block do next?

  1. Moves on at constant speed
  2. Stops at once, as the pull ends
  3. Keeps accelerating at the same rate
Show the answer

Moves on at constant speed

Once the mass lands, the string goes slack and the tension is 0. On a smooth table no horizontal force acts, so the block keeps the speed it had. On a rough table it would slow down.

Ordinary Level

Asked on 3 of the last 3 Ordinary Level papers, most recently in 2025. banker

Every paper, year by year

YearWhere it came up
2025Q1
2024Q8
2023Q9

Links open the State Examinations Commission’s paper for that year.

More Connected particles & pulleys questions

Connected particles & pulleys, 3 marks

Masses of 3 kg and 4 kg hang over a smooth pulley. Tension in the string? (g = 9.8 m s⁻²)

  1. 29.4 N
  2. 39.2 N
  3. 33.6 N
Show the answer

33.6 N

a = 1.4 m s⁻². For the 3 kg (rising): T − 29.4 = 3 × 1.4, so T = 33.6 N. It lies between the two weights, 29.4 N and 39.2 N.

Connected particles & pulleys, 2 marks

Two equal masses hang at rest over a smooth pulley. What happens?

  1. They accelerate at g ÷ 2
  2. They stay at rest
  3. They accelerate at g
Show the answer

They stay at rest

The weights are equal, so the net force on the system is zero. By Newton's first law, masses at rest stay at rest.

Connected particles & pulleys, 3 marks

A 3 kg block on a smooth table is joined over a pulley to a hanging 2 kg mass. Acceleration? (g = 9.8)

  1. 3.92 m s⁻²
  2. 9.8 m s⁻²
  3. 6.53 m s⁻²
Show the answer

3.92 m s⁻²

Only the hanging weight drives the system: 2 × 9.8 = 19.6 N on a total mass of 5 kg. a = 19.6 ÷ 5 = 3.92 m s⁻².

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