Mechanical · Experiment

The Atwood Machine

Two masses hang from a string over a pulley. The heavier one falls, dragging the lighter one up — but gently, because both masses share the same acceleration. A classic way to "slow down" gravity.

tension Tweight mgvelocity

Controls

Acceleration a1.96 m/s²
Tension T₁ (left)47.0 N
Tension T₂ (right)47.0 N
Speed0.0 m/s
Elapsed0.0 s
The heavier mass falls; both share the same acceleration.
About this experiment ›

What you are looking at

Two masses, m₁ and m₂, hang from the ends of a single string that runs over a pulley. Because the string can't stretch, the two masses always move together — as one goes down, the other comes up by the same amount, at the same speed and the same acceleration. Release them and the heavier side wins.

Finding the acceleration

Apply Newton's second law to each mass. For the falling mass, gravity beats the tension; for the rising mass, tension beats gravity. Writing both and eliminating the tension gives the acceleration of the whole system (for a light, frictionless pulley):
a = (m₁ − m₂) g / (m₁ + m₂)
Notice what this says: if the masses are equal, a = 0 and nothing moves; if they are very different, a approaches g. The Atwood machine "dilutes" gravity — the tiny difference (m₁ − m₂) does the pulling, but the whole combined mass (m₁ + m₂) has to be accelerated. That is exactly why George Atwood built it in 1784: it let him measure g accurately with slow, easily-timed motion.

The tension in the string

With a massless pulley the string tension is the same on both sides:
T = 2 m₁ m₂ g / (m₁ + m₂)
This tension sits between the two weights — bigger than the light weight (so it accelerates upward) and smaller than the heavy weight (so it accelerates downward).

Giving the pulley mass

A real pulley has to be spun up too. Turn up the pulley mass and it adds rotational inertia (for a uniform disc, I = ½M_p r²), so the system accelerates more slowly:
a = (m₁ − m₂) g / (m₁ + m₂ + ½M_p)
Now the pulley needs a net torque to spin, which means the two tensions are no longer equal — T₁ (heavy side) exceeds T₂ (light side), and their difference (T₁ − T₂) is exactly what angularly accelerates the wheel. Watch the two tension readouts split apart as you add pulley mass.

Things to try

Set the masses nearly equal for a slow, stately fall; make them very different to approach free-fall. Then add pulley mass and watch the acceleration drop and the two tensions separate. Use slow-motion to read the motion, and the velocity graph to confirm the speed climbs in a straight line — constant acceleration.