Pulley System Calculator
Work out pulley system instantly with clear inputs, formula shown and shareable results.
About Pulley System Calculator
In an Atwood machine the weight difference drives the system while the total mass resists it, so a = (m1 - m2)g/(m1 + m2). The rope tension sits between the two weights at 2.m1.m2.g/(m1+m2). With 8 kg against 5 kg the acceleration is 2.26 m/s2 and the tension 60.3 N - more than the light weight, less than the heavy one.
Formulas
Acceleration
a = (m1 - m2) g / (m1 + m2)
Tension
T = 2 m1 m2 g / (m1 + m2)
Worked example
With the default values below, Pulley System Calculator returns System Acceleration of 2.2631. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Heavier massminimum 0 kg
- 8 kg
- Lighter massminimum 0 kg
- 5 kg
Results
- System Acceleration
- 2.2631 m/s2
- Rope Tension
- 60.349 N
- Net Driving Force
- 29.420 N
- Speed After One Second
- 2.2631 m/s
Step by step
- 1Values used
- 2Acceleration
- 3Tension
- 4System Acceleration= 2.2631 m/s2
- 5Rope Tension= 60.349 N
- 6Net Driving Force= 29.420 N
- 7Speed After One Second= 2.2631 m/s
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why is tension the same throughout the rope?
Because an ideal rope has no mass and the pulley no friction. A real heavy rope or a stiff bearing breaks that assumption.
What if the masses are equal?
The acceleration is zero and the tension equals either weight - the system will stay wherever you leave it.