Mechanics & Simple Machines · GCSE Physics Forces & Machines
Pulley System Block & Tackle Simulator
Block & tackle golden rule: If load-bearing rope strands n is odd, anchor at the movable block; if even, anchor at the fixed block. Effort F = (G + G_mov)/n.
- Client-side
- No Sign-up
- Live Derivation
- Projector Mode
- Print Worksheet
3D Simulation Stage● 60 FPS
Parameter Controls
N
N
m
N
Live Derivations & Metrics
Effort Force F
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Rope Distance s
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Mechanical Efficiency η
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Total Work W_total
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Real-Time Formula Derivation
Governing Formula:
--Substitution:
--Regime: --
Related Tool:
⚙️ Standard Tool: V-Belt Pulley Calculator ↗
Worked Examples & Exam Question Deep Dive
Worked Problem
Problem: A block and tackle with n=3 lifts 400N. Movable pulley weighs 50N, friction negligible. Find effort F and efficiency η.
Step-by-Step Derivation:
- Effort F = (G + G_mov)/n = (400 + 50)/3 = 150N; efficiency η = G / (n*F) = 400 / (3*150) ≈ 88.9%.
Worked Problem
Problem: A pulley lifts 600N by 3m with effort 250N moving 9m. Find useful work, total work, and efficiency.
Step-by-Step Derivation:
- W_useful = 600*3 = 1800J; W_total = 250*9 = 2250J; η = 1800 / 2250 = 80%. Here n = s/h = 3.
Student Inquiry Worksheet & Practice Problems
Q1. Variant 1: An operator on the ground pulls downward to lift 500N with G_mov=60N. What is the minimum n and effort?
Answer Key: Pulling downward requires rope from fixed pulley (n=2). Effort F = (500+60)/2 = 280N.
Q2. Variant 2: Does the same pulley have identical efficiency lifting 200N vs 600N?
Answer Key: No, efficiency is higher with 600N because useful work G*h forms a larger fraction of total work.
Q3. Variant 3: A pulley with η=75% lifts a load at 0.2m/s with power 40W. Find the load weight G.
Answer Key: Useful power P_useful = 0.75*40W = 30W. Since P_useful = G*v, G = 30 / 0.2 = 150N.
Frequently Asked Questions & Misconceptions
What is the "odd movable, even fixed" rigging rule?
If the number of load-bearing strands n is odd (3, 5), the fixed end of the rope must be anchored to the movable block. If even (2, 4), anchor to the fixed block.
Does pulling downward from the ground change mechanical advantage?
Yes. The final rope segment coming off the fixed pulley changes direction rather than supporting the load, yielding n=2 strands from two pulleys.
Can a pulley system save work or energy?
No. By the law of conservation of energy, no machine saves work. Effort is reduced by factor n (F=G/n), but distance increases by factor n (s=nh). Total work always exceeds useful work due to friction and pulley weight.
How do you maximize pulley efficiency?
1) Minimize movable pulley weight; 2) lubricate bearings to reduce friction; 3) operate near rated capacity so useful work dominates total work.