PhysicsSolver360 logoPhysicsSolver360°
Powered by Solver360°

Atwood Machine Calculator

Find acceleration and rope tension for two masses connected over an ideal pulley

Parameters

kgⓘ
kgⓘ
kgⓘ
Set 0 for ideal pulley (ignored in calculation)
Show Trail

Controls

xⓘ

Calculated Values

Acceleration:
2.45;m/s22.45;m/s²
Tension:
36.79;N36.79;N
Net Force on System:
19.62;N19.62;N
Mass Difference:
2.00;kg(+→m1descends)2.00;kg (+ → m₁ descends)

Examples

5 kg and 3 kg

Standard Atwood machine.

  • Acceleration: 2.452.45
  • Tension: 29.4329.43

Visualization

The Atwood Machine

An Atwood machine has two masses connected by a string over a pulley. Ideal assumptions: massless string, frictionless pulley, no air drag.

Both masses share the same magnitude of acceleration a (string inextensible). Heavier mass accelerates downward if m₁ > m₂.

From Newton’s second law on each mass and eliminating tension: a = g(m₁ − m₂)/(m₁ + m₂). Equal masses → a = 0 (equilibrium).

String tension T = 2m₁m₂g/(m₁ + m₂). T is always between m₂g and m₁g when m₁ > m₂ and the system accelerates.

Real pulleys have rotational inertia and friction; this calculator uses the ideal model (pulley mass input is for reference only).

Key Concepts

  • a = g(m₁ − m₂)/(m₁ + m₂) — acceleration
  • T = 2m₁m₂g/(m₁ + m₂) — string tension
  • Same |a| for both masses
  • Equal masses: static equilibrium
  • Heavier mass descends (standard setup)
  • Ideal pulley: same T on both sides

Real-World Applications

  • Introductory lab measurement of g
  • Teaching Newton’s second law
  • Elevator counterweight analogy
  • Dynamics of connected bodies
  • JEE/NEET pulley systems (basic case)

Explore Further

More mechanics tools

Physics Equations

Acceleration:
a=gm1−m2m1+m2a = g\frac{m_1 - m_2}{m_1 + m_2}
Tension:
T=2m1m2gm1+m2T = \frac{2m_1 m_2 g}{m_1 + m_2}

Step-by-Step Solution

See how the main results are calculated.

1

Draw Free-Body Diagrams

For each mass: weight mg down, tension T up. Heavier mass accelerates down.

Equation:

m1g−T=m1a,T−m2g=m2am_1 g - T = m_1 a, \quad T - m_2 g = m_2 a

Calculation:

m1=5 kg,m2=3 kgm_1 = 5 \text{ kg}, \quad m_2 = 3 \text{ kg}

Result:

Two equations, two unknowns (T and a)

Explanation:

Assume m₁ > m₂ so m₁ descends. String is inextensible → |a₁| = |a₂| = a. Ideal pulley → same tension on both sides.

2

Solve for Acceleration

Add the two equations to eliminate T:

Equation:

a=gm1−m2m1+m2a = g\frac{m_1 - m_2}{m_1 + m_2}

Calculation:

a=9.81×5−35+3a = 9.81 \times \frac{5 - 3}{5 + 3}
a=2.45 m/s2a = 2.45 \text{ m/s}^2

Result:

a=2.45 m/s2a = 2.45 \text{ m/s}^2

Explanation:

Net driving force on the system = |m₁ − m₂|g = 19.62 N. Total inertia = m₁ + m₂.

3

Calculate String Tension

Substitute a into either force equation:

Equation:

T=2m1m2gm1+m2T = \frac{2m_1 m_2 g}{m_1 + m_2}

Calculation:

T=2(5)(3)(9.81)5+3=36.79 NT = \frac{2(5)(3)(9.81)}{5 + 3} = 36.79 \text{ N}

Result:

T=36.79 NT = 36.79 \text{ N}

Explanation:

T is between m₂g = 29.43 N and m₁g = 49.05 N. Equal masses → a = 0, T = mg.

Frequently Asked Questions (FAQ)

What if masses are equal?

Acceleration is zero and tension T = mg for either mass—the system is in equilibrium.

Is tension equal on both sides?

Yes for an ideal massless pulley and massless string.

Why is a smaller than g?

The net driving force is (m₁ − m₂)g but total inertia is (m₁ + m₂), so a < g.

Can the lighter mass accelerate upward?

Yes—if it is on the side that rises when the heavier mass descends.

Practice MCQs

  1. Heavier mass is 5 kg, lighter 3 kg. Heavier mass:
  2. Equal masses give acceleration:
  3. Tension in accelerating Atwood machine is:

Related Calculators

These tools connect to the same physics concepts used in this calculator.

Projectile MotionCalculate and visualize the path of objects under the influence of gravity.Newton's LawsApply the three laws of motion to solve force and acceleration problems.Circular MotionAnalyze objects moving in circular paths with centripetal acceleration.Conservation of MomentumSolve problems involving collisions and momentum conservation.Error PropagationCombine measurement uncertainties for sums, products, quotients, and powers in experimental formulas.Related Measurement & Uncertainty topic.Ideal Gas LawCalculate pressure, volume, temperature, and moles for ideal gases.Related Thermodynamics topic.Bernoulli's PrincipleCalculate fluid velocities, pressures, and flow rates using Bernoulli's equation.Related Fluid Mechanics topic.