Physics
Double Award
Double Award
Cambridge IGCSE
TOPIC 1B: ENERGY and PRESSURE
An aerosol can contains a liquid. Every time you press the button, a fine spray of liquid jets out. But what makes it come out of the bottle?
The liquid inside is under pressure. That means it is pushing outwards in all directions. This is why it is dangerous to puncture an aerosol bottle as the pressure will force the liquid out of the hole at a high speed.
Figure 1. An aerosol spray
PiccoloNamek [GFDL or CC-BY-SA-3.0], via Wikimedia Commons
Fizzy drinks contain a gas that produces a pressure. The pressure pushes outwards on all sides of the container. An easy test to identify a bottle of sparkling fizzy water compared to a flat, still water bottle is to squeeze the sides. The sparkling water bottle will be hard to compress, because of the pressure pushing outwards, as shown in figure 2.
Figure 2. Pressure in a fizzy drink bottle
In figure 2, the fizzy water produces a pressure in all directions. This pushes on the sides, and a 'push' is a force. As can be seen in the image, there is a force of 4 N acting on two small 1cm2 sections of the sides of the bottle. In total, there is a force of 8 N on these two sections, and a much large force on the whole bottle's surface. However, we say that the pressure is producing 4 newtons per centimetre squared. (4 N/cm2). Pressure as a quantity is simply the force acting on a unit area, either a cm2 for small surfaces or a m2 for larger areas.
Any fluid can move freely, so the pressure in a fluid is the same at all points and is distributed evenly. if you push the sides of a bottle of water, you are increasing the pressure under your fingers, but this increase spreads throughout the liquid and is the same at all points.
To calculate pressure we use the following formula:
pressure (N/cm2 or N/m2) |
= | force (N) |
| area (cm2 or m2) |
| p = | F |
| A |
Notes:
Example:
A steel block rests on a desk. The weight of the block pushing down on the desk is 40.0 N. The area touching the desk is 95.0 cm3. Calculate the pressure acting on the desk.
Answer:
We know that:
| p = | F | and therefore:- | P = | 40.0 |
| A | 96.0 |
This gives a pressure of 0.417 N/cm2 to 3 sig. figs.
Try the practice questions below, to check you understand how to use this formula:
Questions:
1. A syringe is used to squeeze a liquid down a tube. A force of 5N is applied to an area of 0.8 cm2. Calculate the pressure on the liquid.
We know that
| p = | F |
| A |
| p = | 5 |
| 0.8 |
2. A classroom stool has a weight of 160 N. Each of the 4 stool legs produces a pressure of 8.0 N/cm2 on the floor.
Calculate the area of each stool leg that is in contact with the floor.
Each stool takes ¼ of the weight. This means the force on each leg is ¼ of 160 N, or 40 N each.
We know that:
| p = | F |
| A |
| A = | F | and therefore | A = | 40 |
| p | 8 |
A = 5.0 cm2 (The pressure was given in N/cm2 so the answer must be in cm2, not m2).
When putting in a fence in a field, a farmer must drive thick wooden stakes into the ground. What shape should the end of the stake be to make it easy to push into the soil?
The answer is that the stake should have a sharp point on the end, and this seems like common sense. However, the reason the sharp point is used is that the surface area of the end is very small. When the stake is hammered downwards, a force is applied on a very small surface area, and this makes
a large pressure. The large pressure applied makes it much easier to drive the stake into the ground.
Figure 3: A fence post driven into hard soil
A tractor, on the other hand, has very large wheels with a large surface area. Even though the tractor is very heavy and the force on the ground is large, the surface area of the wheels in contact with the ground is also large so that the pressure is small. This prevents the wheels sinking into the soft, muddy ground and getting stuck. Note that you should always state the equation (shown above) to prove this relationship between area and pressure is true in exam questions.
You should be aware of some other applications where large or small surface areas make a small or large pressure:
Large area, therefore small pressure:
Small area, therefore large pressure:
