Air resistance is just one example of the resistive force (or viscous force) that objects experience when they move through a fluid, a liquid or a gas. If you have ever run down the beach and into the sea, or tried to wade quickly through the water of a swimming pool, you will have experienced the force of drag. The deeper the water gets, the more it resists your movement and the harder you have to work to make progress through it. In deep water, it is easier to swim than to wade.
You can observe the effect of drag on a falling object if you drop a key or a coin into the deep end of a swimming pool. For the first few centimetres, it speeds up, but for the remainder of its fall, it has a steady speed. (If it fell through the same distance in air, it would accelerate all the way.) The drag of water means that the falling object reaches its terminal velocity very soon after it is released. Compare this with a skydiver, who has to fall hundreds of metres before reaching terminal velocity.

Moving through air

We rarely experience drag in air. This is because air is much less dense than water; its density is roughly that of water. At typical walking speed, we do not notice the effects of drag. However, if you want to move faster, the effects can be important. Racing cyclists, like the one shown in Figure 3.11, wear tight-fitting clothing and streamlined helmets.

Other athletes may take advantage of the drag of air. The runner in Figure 3.12 is undergoing resistance training. The parachute provides a backwards force against which his muscles must work. This should help to develop his muscles.

WORKED EXAMPLES

3) A car of mass $500 kg$ is travelling along a flat road. The forward force provided between the car tyres and the road is $300 N$ and the air resistance is $200 N$. Calculate the acceleration of the car.
Step 1: Start by drawing a diagram of the car, showing the forces mentioned in the question (Figure 3.13). Calculate the resultant force on the car; the force to the right is taken as positive:
resultant force $= 300 − 200 = 100 N$
Step 2: Now use F = ma to calculate the car’s acceleration:
$\begin{array}{l}
a = \frac{F}{m}\\
 = \frac{{100}}{{500}}\\
 = 0.20\,m\,{s^{ - 2}}
\end{array}$
So the car’s acceleration is $0.20\,m\,{s^{ - 2}}$.

4) The maximum forward force a car can provide is $500 N$. The air resistance F that the car experiences depends on its speed according to $F = 0.2{v^2}$, where v is the speed in $m\,{s^{ - 1}}$. Determine the top speed of the car.
Step 1: From the equation $F = 0.2{v^2}$, you can see that the air resistance increases as the car goes faster. Top speed is reached when the forward force equals the air resistance. So, at top speed:
$500 = 0.2{v^2}$
Step 2: Rearranging gives:
$\begin{array}{l}
{v^2} = \frac{{500}}{{0.2}}\\
 = 2500\\
v = \sqrt {2500} \\
 = 50\,m\,{s^{ - 1}}
\end{array}$
So the car’s top speed is $50\,m\,{s^{ - 1}}$ (this is about $180\,km\,{h^{ - 1}}$).

Contact forces and upthrust

We will now think about the forces that act when two objects are in contact with each other. When two objects touch each other, each exerts a force on the other. These are called contact forces. For example, when you stand on the floor (Figure 3.14), your feet push downwards on the floor and the floor pushes back upwards on your feet. This is a vital force – the upward push of the floor prevents you from falling downwards under the pull of your weight.
Where do these contact forces come from? When you stand on the floor, the floor becomes slightly compressed. Its atoms are pushed slightly closer together, and the interatomic forces push back against the compressing force. At the same time, the atoms in your feet are also pushed together so that they push back in the opposite direction. (It is hard to see the compression of the floor when you stand on it, but if you stand on a soft material such as foam rubber or a mattress you will be able to see the compression clearly.)

You can see from Figure 3.14 that the two contact forces act in opposite directions. They are also equal in magnitude. As we will see shortly, this is a consequence of Newton’s third law of motion.
When an object is immersed in a fluid (a liquid or a gas), it experiences an upward force called upthrust.
It is the upthrust of water that keeps a boat floating (Figure 3.15), and the upthrust of air that lifts a hot air balloon upwards.
The upthrust of water on a boat can be thought of as the contact force of the water on the boat. It is caused by the pressure of the water pushing upwards on the boat. Pressure arises from the motion of the water molecules colliding with the boat and the net effect of all these collisions is an upwards force.
An object in air, such as a ball, has a very small upthrust acting on it, because the density of the air around it is low. Molecules hit the top surface of the ball pushing down, but only a few more molecules push upwards on the bottom of the ball, so the resultant force upwards, or the upthrust, is low. If the ball is falling, air resistance is greater than this small upthrust but both these forces are acting upwards on the ball.