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Newton's Second Law - Atwood Machines

Instructions for Students & Teachers

Use the simulator above to explore systems of masses connected by a string over a pulley. Choose from four machine types, adjust the masses and gravity, and see how the acceleration of the system and the tension in the string depend on them.

How to Use the Atwood Machine Simulator
 

Machine Type

  • Standard: two masses hang on either side of a single pulley.

  • Flat Table: one mass sits on a table and is pulled by a hanging mass. You can add friction between the block and the table.

  • Inclined: one mass sits on a ramp. Set the Ramp Angle (θ), and the simulator shows the parallel and perpendicular components of its weight (Fg∥ and Fg⊥).

  • Two-Pulley: a mass on a table (m₃) is connected to a hanging mass on each side, with a separate tension in each string.
    Note for teachers: All four machines come down to the same idea. Treat the masses as one system, find the net external force, and divide by the total mass. Moving through the machine types in order is a natural way to build that skill.
     

Playback & Speed

  • Press Play to release the system and watch it accelerate.

  • Use Speed to run the simulation at 0.1×, 0.25×, 0.5×, 1×, 2×, or 4×. Slower speeds make it easier to watch the motion and the graphs together.
     

Parameters

  • Set Mass m₁ and Mass m₂ (and m₃ on the Two-Pulley machine) in kilograms.

  • Start offset sets where m₁ begins, which controls how far the system can move before a mass reaches the pulley, table, or floor.

  • Gravity (g) changes the gravitational field strength.
     

Physics

  • This section gives a live readout of the system's acceleration (a) and the string tension (Fₜ). The Two-Pulley machine shows both tensions, Fₜ₁ and Fₜ₂.
    Mastery tip: On the Standard machine, compare the tension to the weight of each mass. While the system accelerates, the tension is always between the two weights, never equal to either one. Can you explain why?
     

View & Display

  • Use View to switch between Dark and Light mode.

  • Force Arrows draws the forces on each mass, and Tension Labels adds the tension values to the strings.

  • Motion Graphs adds live x(t), v(t), and a(t) graphs below the canvas.
    Note for teachers: Turning on Force Arrows and pausing the simulation gives you a ready-made free body diagram for every machine type.
     

Challenge Mode (Test your understanding!)

  • Difficulty: Easy, Medium, or Hard.

  • Click New Challenge to get a problem. The given values are listed (for example, both masses and g), along with what you need to find.

  • Enter your answer and click Check. If you're stuck, use Get a Hint.
    Mastery tip: If you need hints, use them! Just keep working new challenges until you can solve them without the hints.
     

Lab

  • Choose a lab to investigate:

    • a vs Δm: the total mass is locked. Vary m₁ (m₂ adjusts automatically) to change the mass difference, and record the acceleration for each Δm. The mass difference is your independent variable, the acceleration is your dependent variable, and the total mass is your constant variable.

    • a vs M: the mass difference is locked. Vary the total mass and record the acceleration. The total mass is your independent variable, the acceleration is your dependent variable, and the mass difference is your constant variable. This graph is not linear, so plot a vs 1/M to linearize it.

  • Enter your name in the Student Name field, set your independent variable, and click Record Data Point. Your data is added to the table.

  • In each lab, figure out the physical meaning of the slope and use it to find a value you didn't set directly, such as g.

  • Use Export PDF to save your data and graph to submit to your teacher, and Back to lab selection to switch labs.

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