3.2.2 Motion with non-uniform acceleration

If an object is moving through a fluid it will experience a drag force from the fluid. Drag is a frictional force that opposes the motion of the object. Its magnitude is mainly affected by:

• the speed of the object
• the cross-sectional area of the object
• the shape of the object
• the density of the fluid
• the texture of the object

Objects with larger cross-sectional areas will experience a greater drag force. This is because drag ∝ speed². 

Often, we call the drag force experienced by objects in air air resistance. We are able to reduce air resistance. For example, modern vehicles have streamlined shapes as this increases their top speed and reduces their fuel consumption.

During a vertical fall (e.g through air) the weight of an object will of course remain constant but the speed will increase so the drag force will increase. At the instant objects start to fall the object will experience no drag force and the total force is equal to the weight (as this is the only force acting on the object). As the object falls its speed increases so drag increases. The resultant force on the object decreases (as drag opposes the motion ie is in the opposite direction to weight). At terminal velocity, drag = weight and the object has zero acceleration and its speed is constant.

We can investigate the motion of an object falling affected by drag force by using a motion sensor and data-logger:

• attach the object to a light polystyrene ball using a thin thread passing over a pulley.
• Drop the object through a cylinder of liquid (e.g water or glycerol). This will pull the polystyrene ball vertically upwards (the motion of this ball is equal to the motion of the object)
• when the ball is moving up with constant velocity, the object is moving down with terminal velocity