Determining g with an Atwood Machine

Time a known drop of the heavier mass at several mass ratios. Recover a = 2s/t² and fit a versus (m₁−m₂)/(m₁+m₂) to get g.

Kids· 22 min·Related simulator: Classical MechanicsAtwood Machine

Goal

Determine g from timed Atwood runs: acceleration a = 2s/t² from rest, then the slope of a versus (m₁−m₂)/(m₁+m₂) equals g.

Equipment

Atwood pulley (massless)
Masses m₁, m₂
Metre scale (drop s)
Stopwatch

Experiment

Time the drop of m₁ over a fixed distance. The bench hides acceleration and tension.Stopwatch: —

Known (fixed)

m₂ = 0.20 kg
s = 0.80 m

Heavier mass m₁m₁ = 0.32 kg

Take at least 6 points across the m₁ range.

Measurements

№	Mass m₁ kg	Time t s	a = 2s/t² m/s²	(m₁−m₂)/(m₁+m₂)
No measurements yet — take your first reading.

Data processing

Add at least 2 measurements to compute the fit.

Uncertainty

Lab report

Opens the system print dialog — choose “Save as PDF” or your printer. Header and footer are hidden when printing.

One click opens the print dialog — choose “Save as PDF”.

Determining g with an Atwood Machine

Generated: 24 Aug 2026, 22:29

Goal

Determine g from timed Atwood runs: acceleration a = 2s/t² from rest, then the slope of a versus (m₁−m₂)/(m₁+m₂) equals g.

Measurement table

#	Mass m₁ (kg)	Time t (s)	a = 2s/t² (m/s²)	(m₁−m₂)/(m₁+m₂)
No measurements yet — take your first reading.

Fit and derived value

Add at least 2 measurements to compute the fit.

Conclusion

The fitted g agrees with standard gravity within tolerance. Main uncertainties: stopwatch noise, a massless frictionless pulley, and treating the drop as uniformly accelerated from rest.

PhysSandbox virtual lab — values come from your session; add your own discussion of error sources.

Theory

For a massless frictionless pulley, a = g (m₁−m₂)/(m₁+m₂). From rest, s = a t²/2 so a = 2s/t². Plotting a against x = (m₁−m₂)/(m₁+m₂) is a straight line through the origin with slope g. The bench hides a and the string tension; you only time the drop.

Procedure

m₂ and the drop distance s are fixed and known. You only change the heavier mass m₁.
Release from rest and record the stopwatch time t for the drop. Small timing noise is added.
The notebook computes a = 2s/t² and x = (m₁−m₂)/(m₁+m₂).
Repeat for at least 6 different m₁ values spread across the slider range.
Fit a versus x; the slope is g. Compare with the reference 9.81 m/s².

Conclusion

The fitted g agrees with standard gravity within tolerance. Main uncertainties: stopwatch noise, a massless frictionless pulley, and treating the drop as uniformly accelerated from rest.