Edexcel International A Level Maths: Mechanics 1

Revision Notes

3.2.4 Connected Bodies - Pulleys

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Connected Bodies - Pulleys

What is a pulley (or peg)?

  • A pulleyĀ 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)Ā 

3-2-4-fig1-pulley-examples

How do I solve pulley questions?

  • In all pulley questions the particles are moving in different directions so are considered separatelyĀ rather than the system being treated as one
  • If a particle is in motion in the direction being considered then Newtonā€™s Laws of Motion apply so use ā€œF = maā€ (N2L)
  • For constant acceleration the ā€˜suvatā€™ 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 ā€œF = maā€
    • Equations 1 and 2: Treating each particle separately

(ā†‘) T - m1g = m1a

(ā†“) 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-1

sAI7SOiJ_3-2-4-fig5-we-solution-2

Exam Tip

  • Sketch a diagram or add to a diagram given in a question.
  • All pulleys are smooth and light; in many questions the pulley itself can be ignored.
  • In pulley questions the particles will be moving in different directions - so each particle needs 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 involvedĀ (since F = Ī¼R and R is related to weight).

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Paul

Author: Paul

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 ā€“ if itā€™s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams ā€“ one of the many reasons he is excited to be a member of the SME team.