Newton’s Laws Part 1 – Falling

Newton’s laws first written in Newton’s Principia are the foundation of science and engineering. This article will look how Newton’s laws applies to falling.

When dropping an apple there are two forces at work. Gravity pulls the apple towards the earth. Drag slows the apple down. The gravitational force is equal to the mass of the apple times the earth’s acceleration (Newton’s second law). The force of drag is a bit more complicated but depends on the downward velocity of the apple.

Force : $F_{net} = mg - cv^2$      Acceleration : $a = \frac{ mg - cv^2}{m}$

• $F_{net}$ – Net Force
• $m$ – Mass of the apple
• $g$ – earth’s gravitational acceleration ( $9.8 \frac{m}{s^2}$)
•  $c$ – drag coefficient, this depends on the shape of the apple
• $v$ – the velocity of the apple

The faster the apple falls, the stronger drag becomes. If an apple is dropped from a high enough distance, drag will eventual equal the gravitational force. Drag cannot grow any stronger because the apple is no longer accelerating. This situation is called terminal velocity.

Parachutes have high drag coefficients which means the user reaches terminal velocity quickly, thus allowing a slower and safer descent.