Force and Mass

Hook a 20 kg crate under the drone and full throttle suddenly feels sluggish. The rotors push just as hard as before; there is simply more mass to move and more weight to hold up. A physics engine turns that feeling into one line of arithmetic.

The rule

Add every force, divide by mass: that's the acceleration.

Newton's second law, $\mathbf{F} = m\mathbf{a}$, read the way an engine uses it: $\mathbf{a} = \mathbf{F}_{\text{net}} / m$. Forces are vectors measured in newtons (N), mass is in kilograms, and $\mathbf{F}_{\text{net}}$ is the sum of every force acting on the body during this step.

• Weight is gravity's force, $m\mathbf{g}$, pointing down. A 20 kg crate weighs $20 \times 9.8 = 196$ N.
• Thrust, wind, a spring or a rope are other forces. Each is a vector, and all of them go into the sum.

Weight grows with mass and acceleration divides by mass, so the two cancel: every object falls with the same 9.8 m/s². That is why engines often apply gravity directly as an acceleration rather than as a force.

A sudden kick, such as an explosion or a collision, is an impulse $\mathbf{J}$, measured in N·s. It changes velocity instantly: $\Delta\mathbf{v} = \mathbf{J} / m$.

The shortcut

Make a force list: write every force as a vector, add them all, and divide once by the total mass.

To hover, thrust must exactly match the weight: 245 N. Anything less and the pair sinks.

The trap is applying gravity twice: once as an acceleration of −9.8 and again as a weight force in the list. Pick one. Its twin is forgetting the crate's mass, so the drone lifts a heavy load as if it were empty.

Drills

Answer fast — trust the rule.

Remember

• Acceleration = (sum of forces) ÷ mass; weight is mass × g, pointing down.
• Make a force list, add the vectors, and divide once by the total mass.
• Apply gravity once, as a force or as an acceleration, never both.