Atwood Machine Calculator
Calculate acceleration and tension using a = (m₁−m₂)g/(m₁+m₂).
What Is Atwood Machine Calculator?
The formula Calculate acceleration and tension using a = (m₁−m₂)g/(m₁+m₂)., derives directly from fundamental physics principles.
Understanding this relationship enables both analytical calculation and intuitive reasoning about physical systems.
Applications span multiple fields of science and engineering. This calculator handles the arithmetic while you focus on the physics.
Ensure inputs are in SI units for correct results.
Formula Reference Table
| Solve For | Formula | Notes |
|---|---|---|
| Acceleration | a = (m₁−m₂)g/(m₁+m₂) | m/s² |
| Tension | T = 2m₁m₂g/(m₁+m₂) | N; same throughout ideal rope |
| When m₁=m₂ | a = 0, T = mg | Static equilibrium |
| With friction (pulley) | Effective a is less | Friction reduces net force |
| Net force | F_net = (m₁−m₂)g | N |
| Total mass | m_total = m₁+m₂ | Both masses accelerate |
3 Worked Examples
m₁=5 kg, m₂=3 kg.
- a = (5-3)×9.81/(5+3) = 2×9.81/8 = 2.45 m/s²
- T = 2×5×3×9.81/(5+3) = 294.3/8 = 36.8 N
m₁=0.51 kg, m₂=0.49 kg, measured a=0.196 m/s².
- g = a×(m₁+m₂)/(m₁−m₂) = 0.196×1.0/0.02 = 9.8 m/s²
- Atwood machine traditionally used to measure g accurately
m₁=10.1 kg, m₂=9.9 kg.
- a = 0.2×9.81/20 = 0.098 m/s² (very slow acceleration)
- T ≈ mg = 9.81×10 = 98.1 N — almost equal to each weight
Real-World Applications
Common Mistakes to Avoid
Use SI.
Check geometry/conditions.
Formula assumes ideal conditions.
Check conventions.
Verify squared/sqrt terms.
Frequently Asked Questions
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Interpretation: This relationship connects motion, force, momentum, work or energy in a mechanical system. Assumption: Choose a consistent reference direction and unit system. The model may assume constant acceleration, rigid bodies, negligible losses or an isolated system.