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# AS-Level Maths | Connected Particles
- URL: https://www.a-level-maths-tutor.com/as-level-maths-connected-particles/
- Published: 2026-02-26T10:52:57.000Z
- Updated: 2026-09-25T10:51:57.000Z
- Author: Jaisul Naik
- Tags: Mechanics

## Vertical pulleys

### Question 1

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/image-5.png)

Show Answers — Question 1 

a) $T = 33.6$ N

b) $a = 1.4$ ms⁻²

### Question 2

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/09/CleanShot-2026-09-11-at-15.37.49@2x.png)

Show Answers — Question 2 

a) $T = \\dfrac{12g}{7} = 16.8$ N

b) $m = 1.2$

### Question 3

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/image-7.png)

Show Answers — Question 3 

a) Using $s = \\frac{1}{2}at^2$: $2.5 = \\frac{1}{2} \\times a \\times 1.25^2 \\implies a = 3.2$ ms⁻²

b) $T = 39.0$ N

c) For $A$: $mg - T = ma \\implies m(9.8-3.2) = 39 \\implies m = \\dfrac{65}{11}$

### Question 4

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/image-6.png)

Show Answers — Question 4 

a) $T = 2mg$

b) For $P$: $T - kmg = km \\cdot \\dfrac{g}{3} \\implies 2mg = \\dfrac{4kmg}{3} \\implies k = 1.5$

## Horizontal pulleys

### Question 5

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/image-8.png)

Show Answers — Question 5 

a) $a = 2.0$ ms⁻²

b) $T = 14.0$ N

### Question 6

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/image-9.png)

Show Answers — Question 6 

a) Net force $= 1200 - 200 - 100 = 900$ N, total mass $= 1200$ kg, $a = \\dfrac{900}{1200} = 0.75$ ms⁻²

b) $T = 325$ N

### Question 7

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/image-10.png)

Show Answers — Question 7 

a) $a = 0.7$ ms⁻²

b) $T = 770$ N

## Mixed pulleys

### Question 8

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/09/CleanShot-2026-09-11-at-15.31.22@2x-1.png)

Show Answers — Question 8 

a) i) $a \\approx 2.84$ ms⁻²

a) ii) $T = 1.5g - 1.5a = 1.5(9.8) - 1.5(2.84) \\approx 10.4$ N

a) iii) $k \\approx 3.32$ N

### Question 9

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/09/CleanShot-2026-09-11-at-15.46.05@2x.png)

## 

Show Answers — Question 9 

a) $a = 3.2$ ms⁻²

b) $T = 5.28$ N

c) $F = 3.68$ N

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