MY SIMULATOR

Brass Beam Balance
Archimedes Bob

Weigh it in air. Weigh it in water.

INTERACTIVE 3D

Reading 0.0 div

Left minus right 0.0 g

State arrested

Add brass weights on the right pan · raise the jack to submerge the bob · drag to orbit · wheel to zoom

Water bath height

0 cm

Sim speed

Mechanical model · 1 scene unit = 5 cm

Scale (1 div = 0.25°)

Right pan weights

Bob and bath

Bob material (same size, 28.3 cm³)

Bath liquid

Beam

Centre of gravity below pivot d

Knife-edge offset s (below pivot line)

Damper

Presets

Camera & quality

Live readouts

Pointer angle vs time

■ angle ■ static equilibrium ● turning points

Experiment: density of a mystery bob

Choose Mystery bob (hidden density). 1) Balance it in air with the weights, press Record air. 2) Raise the jack until the bob is fully submerged, re-balance, press Record in liquid. 3) Compute density, then Reveal.

Recorded value = weights − (turning-point equilibrium reading ÷ sensitivity), so you do not have to wait for the beam to settle exactly.

The science

What you see. A beam of mass M, half-length L and centre of gravity d below the pivot carries two equal pans on knife edges at height s below the pivot line. The left pan also carries a bob on a wire dipping into a bath that sits on a jack, so the bob is partly or fully in the liquid.

I θ'' = g[ m_R (L cosθ − s sinθ) − m_L(L cosθ + s sinθ) ] − g M d sinθ − c θ'
m_L = m_pan + m_bob − ρ_f V_sub(θ) − F_drag/g      (Archimedes: buoyancy = ρ_f V g)
static: tanθ = L (m_R − m_L) / ((m_R + m_L) s + M d)
small oscillation: T = 2π √( I / K ),  K = g[(m_R+m_L)s + M d] (+ ρ_f g A L² if the bob is only partly immersed)
density by two weighings:  ρ_bob = ρ_f m_air / (m_air − m_liquid)

Why partial immersion stiffens the beam. When the left end rises the bob lifts out of the liquid, buoyancy drops, the left side gets heavier and pulls the beam back: an extra restoring torque ρ_f g A L²θ.

Turning points. Real analytical balances are read without waiting for the beam to stop: with three successive extremes x1, x2, x3 the rest point is (½(x1+x3) + x2)/2.

Simplifications. Pans hang vertically and are lumped into I; vertical motion of the pans and the added mass of the liquid are ignored; drag on the bob is quadratic (C_d = 1, end-on area) and only present while the bob is in the liquid; the liquid level rises by the displaced volume (included); air buoyancy (about 0.03 g here) is ignored; damper strength is an illustrative constant; mechanical stops at ±8° with restitution 0.25. Densities are typical values at about 20°C (spot-check against a table).

Checks. running…

Virtual model for education. Not a calibrated instrument.

Brass Beam BalanceArchimedes Bob

Brass Beam Balance
Archimedes Bob