Pulley and String Constraints
For an inextensible string, L=sum l_i is constant; differentiating gives velocity and acceleration constraints.
Why this shows up in the exam
Compound pulleys · Moving ends · Load-speed ratios
Learn the idea
A constant string length creates exact displacement, velocity, and acceleration relations. Moving pulleys have several changing segments, so geometry must precede dynamics.
🧠 Memory hook: Write length first; differentiate later.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- L = sum l_i = constant — length constraint
- sum s_i v_i = 0 — velocity constraint
- sum s_i a_i = 0 — acceleration constraint
How to approach it
- 1Mark variable segments
- 2Write constant length
- 3Differentiate consistently
Common slip-ups that cost marks
- •Guessing equal accelerations
- •Missing a segment
- •Changing signs between derivatives
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A 2 kg block moves on a horizontal rough surface with coefficient of kinetic friction 0.2. A horizontal force of 10 N acts on it. Take g = 10 m/s^2. What is its acceleration?
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