Pressure: Why Sharp Knives Cut and Snowshoes Do Not Sink
Hello, young scientists! Why does a sharp knife slice bread easily while a blunt one squashes it? Why do your ears feel blocked in a fast lift? The answer to both is pressure.
In this chapter you will learn: (1) what pressure is and how to calculate it, (2) how we make pressure bigger or smaller in daily life, (3) how atmospheric pressure changes with height, (4) how water pressure changes with depth, and (5) how suction cups, straws and syringes use air pressure.
1. What Is Pressure?
Same force, different effect
Press a balloon gently with your palm. Nothing happens. Now press it with the same force using the tip of a pin. Pop! The force was the same, but the pin squeezed it onto a tiny spot.
Pressure tells us how concentrated a force is on a surface. It is the force acting on each unit of area (for example, on each square metre). A force spread over a large area gives a small pressure. The same force on a small area gives a large pressure.
The pressure formula
\(\text{pressure} = \dfrac{\text{force}}{\text{area}}\) or, in short, \(P = \dfrac{F}{A}\)
Force is measured in newtons (N) and area in square metres \((\text{m}^2)\), so pressure is measured in \(\text{N/m}^2\). This unit has a special name, the pascal (Pa): \(1\ \text{Pa} = 1\ \text{N/m}^2\).
Memory aid: "Force sits on top of Area", just like you sit on top of a chair.
Two ways to change pressure
1. Change the force – With the same area, a bigger force gives a bigger pressure. Pushing harder on a drawing pin helps it go into the board.
2. Change the area – With the same force, a smaller area gives a bigger pressure, and a larger area gives a smaller pressure.
Worked examples
Example 1: A box weighs 600 N. It rests on a face with an area of \(2\ \text{m}^2\). What pressure does it put on the floor?
\(P = \dfrac{F}{A} = \dfrac{600\ \text{N}}{2\ \text{m}^2} = 300\ \text{Pa}\)
Example 2: The same box is turned onto a smaller face with an area of \(0.5\ \text{m}^2\).
\(P = \dfrac{F}{A} = \dfrac{600\ \text{N}}{0.5\ \text{m}^2} = 1200\ \text{Pa}\)
The weight is the same, but the area is only one-quarter as large, so the pressure is 4 times as large.
Key takeaway: \(\text{pressure} = \text{force} \div \text{area}\). More force or less area gives more pressure. The unit is \(\text{N/m}^2\), called the pascal (Pa).
2. Pressure in Daily Life
When we want a LARGE pressure (make the area small)
Sharp knife – The edge of a sharp knife is very thin, so its area is tiny. Your push becomes a large pressure that cuts food easily. A blunt knife has a wider edge, so you must push much harder.
Drawing pin – The pointed tip has a tiny area, so the pressure is large enough to go into a notice board. The head is wide and flat, so the pressure on your thumb is small. The force is about the same at both ends; only the area is different!
When we want a SMALL pressure (make the area large)
High heels vs flat shoes – A thin high heel has a very small area, so the pressure under it is large and it can sink into grass. Flat shoes spread the same weight over a much larger area, so the pressure is smaller.
Snowshoes – Snowshoes are wide and flat. They spread a person's weight over a large area, so the pressure on the snow is small and the person does not sink in.
Wide straps – A school bag with wide straps is more comfortable than one with thin straps. Wide straps press on a bigger area of your shoulders, so the pressure is smaller.
Tractor tyres – Tractors are heavy, but their very wide tyres give a large area and a smaller pressure on soft, muddy farmland, so they do not sink.
Key takeaway: To increase pressure, make the area smaller (knives, pins). To reduce pressure, make the area larger (snowshoes, wide straps, tractor tyres).
3. Atmospheric Pressure: The Weight of the Air Above You
Air has weight
The Earth is wrapped in a thick layer of air called the atmosphere. Air has mass, and gravity pulls it towards the Earth, so air has weight.
Atmospheric pressure is the weight of the air above pressing on each unit area of a surface. We live at the bottom of an "ocean of air"! At sea level, atmospheric pressure is about 100 000 Pa, like the weight of about ten small cars on every square metre.
Why are we not crushed? Air pushes on us from all directions, and the fluids inside our bodies push outwards just as hard, so we hardly notice it. (How gas particles create this push is explained in the chapter "Gas pressure".)
Did you know? Weather reports give air pressure in hectopascals (hPa), where \(1\ \text{hPa} = 100\ \text{Pa}\). In Hong Kong it is usually between about 1 000 and 1 020 hPa. The centre of a typhoon has a much lower pressure.
Atmospheric pressure falls as you go higher
The higher you go, the less air there is above you. Less air above means less weight pressing down, so atmospheric pressure is lower at higher altitude. Near the ground, it drops by about 1 hPa for every 8 to 10 metres you climb.
On top of Tai Mo Shan, Hong Kong's highest mountain, the pressure is roughly one-tenth lower than at sea level. At the top of Mount Everest, it is only about one-third.
Key practical task: measuring pressure with a mobile phone
Many smartphones contain a tiny pressure sensor called a barometer. With a sensor app, you can collect evidence that atmospheric pressure changes with height.
1. Record the reading on the ground floor of a tall building.
2. Go up and record the reading at different floors (for example, every 5 floors). Let the reading settle each time.
3. Repeat the trip and average the readings.
4. Plot a graph of pressure against floor number.
Variables: the independent variable is the height (floor); the dependent variable is the atmospheric pressure; control variables include the same phone, app and building.
Result: the higher the floor, the lower the pressure. Work quickly, because weather changes also change air pressure. If one reading is very different from the rest (an outlier), measure it again.
More evidence from daily life
Ears popping – In a fast lift going up or a plane taking off, the air pressure outside falls quickly. The air behind your eardrum is still at the higher pressure, so it pushes the eardrum outwards and your ears feel blocked. Swallowing or yawning lets some air out through a small tube to the throat, and your ears "pop".
Puffed-up snack bags – A bag of crisps sealed near sea level swells up on a high mountain or a plane. The pressure outside is now lower than that of the air sealed inside, so the air inside pushes the bag outwards.
Key takeaway: Atmospheric pressure is the weight of the air above pressing on each unit area. It decreases as altitude increases, because there is less air above.
4. Water Pressure: Deeper Means Stronger
What causes water pressure?
Water pressure is the weight of the water above pressing on the surface of a submerged object. The deeper you go, the more water there is above you, so the water pressure is greater.
Water pressure acts in all directions: on the bottom and sides of a container, and on every side of a diver. Water is much heavier than air, so going about 10 m down adds roughly the same pressure as the whole atmosphere!
Evidence: water jets at different depths
Make three small holes, one above another, in a tall plastic bottle. Cover them, fill the bottle with water, then uncover them over a sink. Water from the lowest hole squirts out fastest and most strongly, because the pressure is greatest at the greatest depth.
Tip: Compare how fast each jet leaves its hole. Where a jet lands also depends on how high the hole is, so do not judge by landing spot alone.
Water pressure in daily life
Dam walls – Water pressure is greatest at the bottom of a reservoir, so dam walls are built much thicker at the bottom than at the top.
Divers – The deeper a diver goes, the greater the water pressure on the body, and they often feel it on their ears first. Deep-sea submarines need very thick, strong walls so they are not crushed.
Did you know? China's deep-sea submersible Fendouzhe (Striver) has dived more than 10 000 m deep in the Mariana Trench, where the water pressure is about 1 000 times the atmospheric pressure at sea level!
Key takeaway: Water pressure comes from the weight of the water above. It increases with depth and acts in all directions.
5. Air Pressure at Work: Suction Cups, Straws and Syringes
These objects use the same trick: we remove some air from one side, so the pressure there becomes lower. The greater atmospheric pressure on the other side then pushes. Air pushes; it does not "suck".
Suction cups
Pressing a suction cup onto a smooth tile squeezes out most of the air underneath, so the pressure under the cup is low. The greater atmospheric pressure outside pushes the cup firmly against the wall. On a rough surface, air leaks in and the cup falls off.
Drinking straws
When you drink lemon tea through a straw, you take air out of the straw, lowering the pressure inside it. The atmospheric pressure on the surface of the drink is now greater, so it pushes the drink up the straw into your mouth.
Syringes
Put the tip of a syringe into a liquid and pull the plunger back. The space inside gets bigger, so the pressure inside becomes lower. The atmospheric pressure on the liquid surface pushes the liquid up into the syringe. Nurses use this to draw up medicine.
Key takeaway: Suction cups, straws and syringes work because the pressure on one side is lowered and the greater atmospheric pressure on the other side pushes.
6. Common Mistakes and Quick Review
Common mistakes
Common mistake 1: "Pressure and force are the same thing." No! The same force can give a small or a large pressure, depending on the area.
Common mistake 2: "A bigger area gives a bigger pressure." It is the opposite: for the same force, a bigger area gives a smaller pressure.
Common mistake 3: "Straws and suction cups work by sucking." Really, the outside atmospheric pressure pushes.
Common mistake 4: "Water pressure only pushes downwards." It pushes in all directions.
Quick review
1. \(P = \dfrac{F}{A}\); pressure is measured in \(\text{N/m}^2\) or pascals (Pa).
2. More force or less area gives more pressure. Knives and pins use a small area; snowshoes, wide straps and tractor tyres use a large area.
3. Atmospheric pressure is the weight of the air above on each unit area. It decreases as altitude increases.
4. Water pressure is the weight of the water above on a submerged surface. It increases with depth, so dams are thicker at the bottom.
5. Suction cups, straws and syringes work because atmospheric pressure pushes where the pressure has been lowered.
Well done! Next time you cut an apple, ride a fast lift or sip a drink through a straw, you will know the science behind it. Keep exploring!