Mechanics
Atwood machine
Watch the heavier mass fall while the lighter one rises at the same rate — a=(m2−m1)g/(m1+m2).
Analyze an Atwood machine with two masses over a pulley. Calculate acceleration from unequal masses and verify Newton's second law for connected bodies.
Atwood's machine
Two masses over a pulley accelerate together. The heavier mass descends while the lighter rises with the same magnitude of acceleration.
The net force on the system is the weight difference (m_heavy − m_light)g, accelerating both masses. Because total mass is m_heavy + m_light, a = (m_heavy − m_light)g / (m_heavy + m_light).
- a = (m₁ − m₂)g / (m₁ + m₂)
- T is the same on both sides
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
Two unequal masses hang from a pulley. As the system runs, does its acceleration speed up, slow down, or stay constant?
Predictions to weigh
- Acceleration increases over time
- Acceleration stays constant
- Acceleration decreases over time
Variable roles
What you set:
- Heavy mass m₂ (kg)
- Light mass m₁ (kg)
- Elapsed time t (s)
What you measure:
- Predicted acceleration a (m/s²)
- Net force on heavy mass F (N)
- Measured speed v (m/s)
How the investigation runs
- Open the Atwood machine simulation and press Reset.
- Enable the speed probe on the heavier mass.
- For each trial below, press Play, pause the sim at the listed elapsed time, and record the probe's speed reading.
Governing equation
Atwood Machine Acceleration — a = |m₂ − m₁|·g / (m₁ + m₂)
Applying Newton's second law to both hanging masses gives a single system acceleration that depends on the mass difference, not the masses individually.
Newton's Second Law — F = m·a
The net force on the heavier mass equals its mass times the system's shared acceleration — the same acceleration you predicted above.
What the printable worksheet asks students to work out
- Show your work computing the predicted acceleration a = (m₂ − m₁)g/(m₁ + m₂) for the system, and compare it to the slope of your v–t graph.
- How closely does your measured speed at each time match the predicted speed v = at? Is the relationship linear? Cite numbers from your table.
Where this shows up beyond the lab
- The formula a = (m₂ − m₁)g/(m₁ + m₂) assumes a massless, frictionless pulley and an inextensible string. Which of these idealizations would most affect your measured results, and why?
- Predict what would happen to the system's acceleration if the two masses were equal (m₁ = m₂). Explain your reasoning using the formula.
- AP Physics 1 — Unit 3: Work, Energy, and Power
- AP Physics C: Mechanics — Unit 3: Work, Energy, and Power
- IB Physics — A.3 Work, energy and power
- General High School Physics — Work, energy & power
- NGSS High School Physics — Energy accounting in systems
- Middle School Physical Science — Force, mass, and motion
- Welcome to Atwood Machine
- Select the mass
- Press Play
- Opposite motion
- Open the data
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.