Forces of Resistance

Forces of Resistance

A ball rolling on the ground would soon stop. A feather falling through the air does not accelerate under its own weight. These everyday observations often appear to be at odds with what we learn in physics. Newton's first law says that a moving body would continue moving in a straight line. Why does the ball stop? The acceleration of free fall is a constant at 9.81 m/s². Why does the feather not accelerate?

The reason is because of resistive forces. The ball slows down because of friction from the ground. The feather falls gently because of air resistance. We could even imagine that it is by thinking about resistive forces that led Newton to formulate his first law of motion.

Suppose a ball is given a push on a concrete ground. The ball would roll, slow down, and stop. Suppose instead that it is on very slippery ice, and given the same push. It would roll for a much longer time before it stops. In both cases, we have started with the same ball and the same push. Only the grounds are different. If the concrete ground somehow produces a larger force that resists the motion, then this could explain why the ball slows down more quickly.

Assuming that this is the correct explanation, lets try and take this further. The ball on ice goes a lot further. This must be because the force of resistance is much smaller. What if we can somehow make the ground perfectly smooth, so that there is zero force of resistance? Then, surely, the ball must keep going in a straight line at the same speed, since there is nothing to resist it. This is just what Newton's first law says.

Today, we call this force of resistance the friction. The strength of this friction depends very much on the surfaces in contact. The ground would be rough, and would give more friction than the ice. We can imagine that a rough ground may look flat, but have many small lumps or kinks jutting out randomly. These could be very obvious, like small gravels on the main road. They may only be visible under a microscope, as on the smooth kitchen tiles. The uneven surface is only one possible cause of friction. Another cause could be direct attraction between the atoms on the two surfaces. An extreme case of this would be when both surfaces are sticky.

In the case of a feather falling through air, the force of resistance is called air resistance. It is also called viscous force or damping. These last two terms are used for forces of resistance in liquids and gases in general. It is never called friction, a word that is reserved for solids.

There is indeed an important difference between fluid resistance and solid resistance. Solid resistance happens because of the nature of the solid surfaces in contact when bodies move against each other. The surfaces could be uneven or sticky. When a feather moves through air, however, the air does not really have a surface. The molecules in contact with the surface of the feather can easily move around, unlike the solid surface of the ground. When the feather moves through air, it collides with these molecules.

Recall Newton's third law. If the feather pushes at an air molecule, the air molecule also push back at the feather - with an equal and opposite force. Since the feather is falling, it would be pushing downwards. So the air molecules that pushed would react by pushing upwards at the feather. This is in the opposite direction to the falling feather. In this way, the feather experiences resistance from the air.

There is another feature of air resistance that is difference from friction. If the feather falls faster, it pushes harder at the air molecules. Since the air molecules push back with equal and opposite forces, the air resistance would also be larger. This means that the air resistance increases if the velocity of the feather increases.

In the case of a ball moving on the ground, the friction tends to stay relatively constant even if the velocity of the ball is increased. This friction would normally change only if the ball is pressed harder against the ground - say if we use a heavier ball.

The Physics Notes