I. Hypothesis → II. Experiment → III. Proof

Section § 27 — Dynamics of Connected Bodies · Atwood's Machine t = 0.00 s

Atwood's Machine: Dynamics of Connected Masses & Pulley Inertia

Two weights connected by an inextensible thread over a pulley move with a single common acceleration determined by the difference in weight and total system inertia.

Prediction Problem

On an ideal massless pulley (m_{\text{pulley}} = 0), two loads m_1 = 3\text{ kg} and m_2 = 1\text{ kg} are suspended. What is the acceleration a of the system and how does thread tension T compare to the weights of the loads?

Your hypothesis: Option B

Writing Newton's second law for both loads: m_1 g - T_1 = m_1 a and T_2 - m_2 g = m_2 a, plus the pulley torque equation (T_1 - T_2)R = I\varepsilon = \frac{1}{2}m_{\text{pulley}}R^2(a/R), yields a = \frac{(m_1 - m_2)g}{m_1 + m_2 + \frac{1}{2}m_{\text{pulley}}}. For the descending heavier load m_1, tension is **less** than its weight (T_1 = m_1(g - a) m_2 g).

Analytical Law Formula

System Energy Balance E = 0.0 J

Kinetic E_k

0.0 J

Potential E_p

0.0 J

Heat Q

0.0 J

Fig. 27.1 — Precision vertical Atwood stand with graduated scale, rotating pulley, and force vectors T₁, T₂, m₁g, m₂g

Fundamental Relations Theory

Apparatus Parameters

Diagram Overlays

Force & Velocity Vectors Vector Symbol Labels Trajectories & Guide Lines Wavefronts & Thermal Particles

Velocity ($\vec{v}$)

Momentum / Projections

Gravity ($m\vec{g}$)

Normal / Tension / Pressure