Inclined Plane & Connected Masses: How acceleration and tension depend on the masses and the angle

Tilt the axes to the slope. Gravity still pulls m₂ straight down, but its weight splits into m₂g sin θ down the slope and m₂g cos θ into it. The frictionless surface pushes back on the second part only, so N = m₂g cos θ, not m₂g.

Find the winner before writing ΣF = ma. m₁g pulls the system one way and m₂g sin θ the other. Taken as one system, F_net = m₁g − m₂g sin θ accelerates the whole mass, so a = F_net ÷ (m₁ + m₂). With a light cord that does not stretch, over an ideal pulley, both blocks share one a and the cord pulls each with the same T.

Balanced is not stuck. When m₂g sin θ equals m₁g, a = 0: the blocks keep whatever velocity they have, and from rest they stay at rest, while T = m₁g — zero acceleration is not zero force.