Atwood Machine — Newton's Second Law for Connected Bodies
1 · Predict
Two unequal masses hang from a pulley. As the system runs, does its acceleration speed up, slow down, or stay constant?
- Acceleration increases over time
- Acceleration stays constant
- Acceleration decreases over time
2 · Set Up
- 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.
3 · Collect Data
| Heavy mass m₂ (kg) | Light mass m₁ (kg) | Elapsed time t (s) | Predicted acceleration a (m/s²) | Net force on heavy mass F (N) | Measured speed v (m/s) |
|---|---|---|---|---|---|
| 5 | 3 | 0.4 | |||
| 5 | 3 | 0.8 | |||
| 5 | 3 | 1.2 |
Plot measured speed v (y-axis) against elapsed time t (x-axis). The slope of your best-fit line is the system's acceleration.
4 · Analyze
- 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.
5 · Extend
- 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.
The Physics Behind This Experiment
Atwood Machine Acceleration
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
The net force on the heavier mass equals its mass times the system's shared acceleration — the same acceleration you predicted above.