Forceworks

The deck is flat, so the normal force is N = mg. Friction is capped: while the crate is still it can supply anything up to |f| ≤ μs N, which is why nothing moves until the thruster beats that limit. Once it slides, friction is fixed at f = μk N and always points against the velocity.

Along the deck that leaves ΣF = F − f = ma. Every frame the game solves for a, updates the velocity, then moves the crate with the new velocity — a semi-implicit Euler step at 120 Hz, the same integrator a real game engine uses.

The dashed ghost crate is the same model solved in closed form: from speed v, kinetic friction needs d = v² ÷ (2 μk g) of deck to bring the crate to rest. Release the thruster and the real crate glides exactly onto its ghost — that agreement is the whole model in one picture.

Each deck changes only m, μ and the thruster. Heavy Lift shows that doubling the mass halves the acceleration for the same net force. Ice Deck removes the friction that normally stops you, so the only way to brake is an equal and opposite force — Newton’s first and second laws in one move. Grip Deck does the opposite: friction stops the crate so fast that you must thrust nearly all the way in.

The rest of the chapter uses the same bookkeeping in other directions: tension resolves into components, gravitation supplies the force with Fg = GMm/r², and rotation balances moments with Στ = 0.