Physics·Laws of Motion

Pulley Simulator — Atwood Machine

Two masses, one rope, one ideal pulley. Change the masses and see the tension and acceleration update.

T (tension)

mg (weight)

a (accel)

Right-click drag = draw arrow · single-click = mark

m₁2.00 kg

m₂3.00 kg

m₁g19.62 N

m₂g29.43 N

Tension T23.54 N

|a|1.96 m/s²

m₂ accelerates down · m₁ rises

Mass m₁ (left)2kgMass m₂ (right)3kg

The Atwood machine — two masses connected by a light rope over a frictionless pulley — is the simplest system where constraint forces really matter. The rope forces both masses to move together, so a single acceleration governs the whole system. Once you write $F = ma$ for each mass, tension pops out algebraically. Adjust the two masses. The heavier side falls, the lighter one rises, and the tension is always between the two weights.

Key equations

Acceleration

$a = \dfrac{(m_2 - m_1)\,g}{m_1 + m_2}$

Tension

$T = \dfrac{2 m_1 m_2 g}{m_1 + m_2}$

For mass 1 (going up)

$T - m_1 g = m_1 a$

For mass 2 (going down)

$m_2 g - T = m_2 a$

Key ideas to remember

1
The constraint (inextensible rope, ideal pulley) forces both masses to share one acceleration magnitude — opposite in direction.
2
Tension is the same everywhere along a massless rope — that's why a single $T$ appears in both equations.
3
If $m_1 = m_2$ : $a = 0$ and $T = mg$ . The system is in equilibrium regardless of position.
4
Tension always lies strictly between the two weights: $m_1 g < T < m_2 g$ (when $m_1 < m_2$ ).

Pulley Simulator — Atwood Machine

Key equations

Key ideas to remember

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