Connected Bodies - Pulleys (AQA A Level Maths: Mechanics)

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Connected Bodies - Pulleys

What is a pulley (or peg)?

  • 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

How do I solve pulley questions?

  • 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

Worked example

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

Examiner Tip

  • 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.

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Paul

Author: Paul

Expertise: Maths

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.