Tekneτέχνη

T-16 · Newton's laws

Force, mass, acceleration.

F = ma, set loose on the mathematics of the earlier sheets. A thrown ball is integrated step by step and measured against the parabola it must follow; drag is checked against the energy it takes away. Collisions are solved in exact fractions, and Pythagoras turns up in the middle of one: equal masses meeting off-centre always leave at a right angle.

green: integrated (Runge–Kutta 4, Δt = 0.01 s), a dot every half seconddashed: the vacuum parabolavelocity at t = 0.95 s: across (blue), up (violet), and the hypotenuse25.08 mTEKNE · T-16 NEWTON'S LAWS · PROJECTILEv₀ = 20 m/s · θ = 50° · g = 9.81 m/s²a = −g ŷ − k|v|v · k = 0.02/m