Terminal velocity

When an object is falling through a fluid (or, less commonly, accelerating across a solid surface with friction), it will eventually reach a point where the resistive forces (drag or friction) are equal in magnitude to the driving force (usually gravity), and the object will stop accelerating and continue to move at a constant velocity.

This velocity is called the terminal velocity of the object.

we’ll focus on terminal velocity in the context of an object falling through a fluid under the force of gravity. The same principles apply to an object accelerating across a solid surface with friction.

What happens when an object is falling?

When any object falls through any fluid, it speeds up because of the force of gravity causing it to accelerate downwards. The velocity increases.

However, as velocity increases, the drag force (or frictional force) also increases. It increases at a faster rate than the velocity, so the drag force will eventually increase so much to the point where it becomes equal in magnitude to the gravity.

Basically, when an object gets fast enough, the air resistance becomes equal to the weight of the object.

What happens at terminal velocity?

When the drag force becomes equal in magnitude to the weight of the object, the object will stop accelerating and will continue to fall at a constant velocity - the terminal velocity.

So it stops accelerating but it doesn’t stop moving - it continues to fall, but at a constant velocity (doesn’t speed up anymore).

What affects terminal velocity?

• The object’s mass:
  • A heavier object has a greater weight force
  • It needs a greater drag force to balance the weight
  • So it needs to fall faster to generate that drag force
  • So it has a higher terminal velocity
• The surface area of the object (and how streamlined it is):
  • A larger surface area increases the drag force for a given velocity
  • So it can balance the weight at a lower velocity
  • So it has a lower terminal velocity
• The density of the fluid:
  • A denser fluid increases the drag force for a given velocity
  • So it can balance the weight at a lower velocity
  • So it has a lower terminal velocity