What is mechanical advantage in a pulley system?

Mechanical advantage (MA) is the ratio of the load lifted to the effort force applied. A fixed pulley has MA = 1 (it only changes direction). A movable pulley has MA = 2. A block-and-tackle system with n stages has MA = 2^n. The trade-off is that you must pull more rope: distance pulled = MA × distance load moves.

Why does a block-and-tackle system have MA = 2^n?

Each movable pulley in the system doubles the mechanical advantage. With 1 stage (1 fixed + 1 movable pulley), MA = 2. With 2 stages, MA = 4. With 3 stages, MA = 8. This is because each movable pulley splits the tension between two rope segments supporting it, halving the effort needed at each stage.

How does an Atwood machine work?

An Atwood machine consists of two masses connected by a string over a pulley. The heavier mass accelerates downward while the lighter one accelerates upward. The acceleration is a = g(m₁ - m₂)/(m₁ + m₂), and the tension is T = 2m₁m₂g/(m₁ + m₂). When the masses are nearly equal, the acceleration is very small, making it useful for studying gravity in slow motion.

Pulley Systems

Explore how pulleys multiply force. From a simple fixed pulley to block-and-tackle systems with 2ⁿ mechanical advantage, and the classic Atwood machine for studying acceleration.

Pulley Parameters

Mode

Presets

Mass (Load) = 10 kg

Mass 2 = 5 kg

Stages (n) = 2

Efficiency = 100%

100

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Force arrows

Properties

Mode	Fixed Pulley
Mass (Load)	10 kg
Weight	98.1 N
MA	1
Effort	--
Stages	0
Efficiency	100%
Mass 2	--
Acceleration	--

The Physics Behind It

Pulley Formulas

Mechanical advantage: MA = Load / Effort
Block & tackle: MA = 2ⁿ (n stages)
Effort with efficiency: F = W / (MA × η)
Atwood acceleration: a = g(m&sub1; − m&sub2;) / (m&sub1; + m&sub2;)
Atwood tension: T = 2m&sub1;m&sub2;g / (m&sub1; + m&sub2;)

Key Concepts

Fixed pulley: changes force direction but MA = 1; you pull with the same force
Movable pulley: MA = 2; you pull with half the force but twice the rope length
Block & tackle: each stage doubles MA giving 2ⁿ; the trade-off is pulling more rope
Atwood machine: two masses on a string; the difference in weight drives acceleration while the sum determines inertia

Pulley Systems

Pulley Parameters

Properties

The Physics Behind It

Pulley Formulas

Key Concepts

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