Two-Block Contact Force: How a Push Splits Between Touching Blocks

One push, one acceleration. The touching blocks move as one system: a = F ÷ (m₁ + m₂). Only block 1 pushes block 2, so the contact force is block 2's share: F_c = m₂a. With no friction and F = 0, F_c = 0, yet a moving pair keeps its speed.

F_c is a fixed fraction of F, F × m₂ ÷ (m₁ + m₂), the slope of the graph. Make m₂ large and m₁ small: F_c nears F but never reaches it. The orange arrows are a Newton's third law pair, equal and opposite, one on each block.

Friction slows the pair but leaves the split alone while it slides: each block's μmg comes out of its own share. At rest the pair holds until F passes μ(m₁ + m₂)g; this sim lets block 1's grip take the push first, up to μm₁g, and block 2 feels only the rest.