Connected Bodies - Pulleys | AQA AS Maths: Mechanics Revision Notes 2018

Connected Bodies - Pulleys

A pulley is a wheel like device that rotates as a string passes over it allowing motion of any particles attached to the string
Pulleys allow a (inextensible) string to change its orientation.
In A level mathematical models, pulleys will always be smooth and light, so there is no friction involved at the pulley and its mass is negligible
A peg is similar to a pulley but is a fixed point that a particle can be suspended from (like a nail in a wall)

3-2-4-fig1-pulley-examples

In all pulley questions the particles are moving in different directions so it is best if they are considered separately as opposed to treating them as one object
If a particle is in motion in the direction being considered then Newton’s Laws of Motion apply so use “F = ma” (N2L)
For constant acceleration the ‘suvat’ equations could be involved
Step 1. Draw a series of diagrams
- - Label the forces and the positive direction of motion for each particle.
  - Colour coding forces acting on each particle may help.

3-2-4-pulleys-diagram-2

Step 2. Write equations of motion, using “F = ma"
- - Equations 1 and 2: Treating each particle separately

(↑) T - m₁g = m₁a
(↓) m₂g - T = m₂a

Step 3. Solve the relevant equation(s) and answer the question
- - Some trickier problems may lead to simultaneous equations

3.2.4_WE_Pulleys_1

Find the tension, T N , in the string and the acceleration, a m s^-2 , of the system.

3-2-4-fig5-we-solution-aqa-1

zclMSsLK_3-2-4-fig5-we-solution-aqa-2

Sketch a diagram or add to a diagram given in a question.
All pulleys are smooth and in most (but not all) the pulley itself can be ignored.
In pulley questions the particles will be moving in different directions - so each particle will need to be considered separately.
If one particle is on a horizontal surface (such as a desk or table) then the weight only need be considered if friction is involved (since F = μR and R is related to weight).
Unless told otherwise, use g = 9.8 m s^-2 and round your final answer to two significant figures.
Some questions may direct you to use g = 10 m s^-2 in which case round your final answer to one significant figure.