Journal II — The Dark Beyond

Check 01 · Newton's second law

Why does the rover accelerate when you open the throttle?

Because it is moving, and anything moving keeps accelerating. Because the vector sum of all forces on it is non-zero: ΣF = m·a. Because the engine is physically larger than the rover.

Check 02 · Traction on a low-g world

Here g ≈ 4.2 m/s². Why does the rover skid in a turn far sooner than on Earth?

Because max friction is μN = μmg, and a smaller g means less grip to spare. Because the rover's mass grows during a storm. Because turning a vehicle involves no forces at all.

Check 03 · Wind as an external force

A gust shoves the rover sideways off your line. The cleanest correction is to…

Floor the throttle to outrun the wind. Steer into the wind and ease off, cutting speed so the centripetal demand stays under the grip you have left. Brake hard and hold the wheel perfectly straight.

Check 04 · Impulse & momentum

You kiss a rock at 15 m/s and bounce off. Why does hitting the same rock slower hurt the hull less?

The impulse J = m·Δv is smaller at lower speed — less momentum is ripped away in the same instant, so less force, less damage. The rock becomes physically softer when you approach it slowly. Momentum is always conserved, so the impact speed cannot matter.

Check 05 · Power & fuel

Why does holding full throttle at top speed drain the tank far faster than coasting?

Fuel evaporates faster the hotter the engine runs. Power is P = F·v: at high speed a large drive force times a large v spends energy fast, while coasting needs almost no drive force. Coasting increases drag, which burns extra fuel.

Check 06 · Frenet decomposition

The rover holds speed steady through a bend. What are a_T and a_N?

a_T = 0 (speed constant) and a_N = v²/ρ ≠ 0 (direction changing). Both are zero because the speed is not changing. a_T = v²/ρ and a_N = 0.

Check 07 · Work–energy theorem

Climbing a rise at constant speed, the drive does positive work yet KE is unchanged. Where did it go?

Into potential energy and heat: W_nc = ΔKE + ΔPE + |W_diss|, with ΔKE = 0. It vanished, so the work–energy theorem fails on slopes. Into kinetic energy that is simply hidden.

Check 08 · Circular motion limit

With μ = 0.20 in the storm and a turn of radius ρ = 30 m, the fastest safe speed is about…

v_crit = √(μgρ) = √(0.20 × 4.2 × 30) ≈ 5.0 m/s. v_crit = μgρ ≈ 25 m/s. Any speed, because friction does not limit turns.

Check 09 · Rolling & rotational KE

Why do the spinning wheels make the rover harder to accelerate than its mass alone suggests?

Because part of the work stores rotational KE = ¼M_wv², acting like extra inertial mass ½M_w. Because wheels add no energy, only friction. Because rotational energy is negative.

Drive into the dark.

You brought the light with you.

—

Prove you understand the drive.

Why does the rover accelerate when you open the throttle?

Here g ≈ 4.2 m/s². Why does the rover skid in a turn far sooner than on Earth?

A gust shoves the rover sideways off your line. The cleanest correction is to…

You kiss a rock at 15 m/s and bounce off. Why does hitting the same rock slower hurt the hull less?

Why does holding full throttle at top speed drain the tank far faster than coasting?

The rover holds speed steady through a bend. What are a_T and a_N?

Climbing a rise at constant speed, the drive does positive work yet KE is unchanged. Where did it go?

With μ = 0.20 in the storm and a turn of radius ρ = 30 m, the fastest safe speed is about…

Why do the spinning wheels make the rover harder to accelerate than its mass alone suggests?

Unknown traveller.

Drive into the dark.

You brought the light with you.

—

Prove you understand the drive.

Why does the rover accelerate when you open the throttle?

Here g ≈ 4.2 m/s². Why does the rover skid in a turn far sooner than on Earth?

A gust shoves the rover sideways off your line. The cleanest correction is to…

You kiss a rock at 15 m/s and bounce off. Why does hitting the same rock slower hurt the hull less?

Why does holding full throttle at top speed drain the tank far faster than coasting?

The rover holds speed steady through a bend. What are aT and aN?

Climbing a rise at constant speed, the drive does positive work yet KE is unchanged. Where did it go?

With μ = 0.20 in the storm and a turn of radius ρ = 30 m, the fastest safe speed is about…

Why do the spinning wheels make the rover harder to accelerate than its mass alone suggests?

The rover holds speed steady through a bend. What are a_T and a_N?