Why does a sharp knife cut, when a blunt one only squashes?
Your guess
Pick one before you read on. It is fine to be wrong.
By the end you can
Calculate pressure as force divided by area
Explain why sharp knives cut and wide feet stop camels sinking in sand
Press the flat end of a pencil gently into your palm. Then press the sharp tip with the same push. The tip hurts more. The push is the same, but the feeling is not.
The area is how much surface the force touches. We measure it in square centimetres, cm². A tip touches a tiny area. A flat end touches a bigger one.
Pressure tells you how much force pushes on each square centimetre. Look at 10 N pushing down on a flat patch.
The same 10 N. On 5 squares each square takes 2 N. On 1 square it takes all 10 N.
Share the force out over the squares. 10 N over 5 squares is 2 N on each. So pressure = force ÷ area. We read N/cm² as "newtons for each square centimetre".
Draw it first
Draw one block on a big face and a small face
1 Draw a light block lying flat. Press down on it with 24 N. The push is on 12 cm². Pressure = 24 ÷ 12 = 2 N/cm².
2 Stand the same block on its end and press down with the same 24 N. Now the push is on only 3 cm².
3 Pressure = 24 ÷ 3 = 8 N/cm². The same force on a smaller area gives more pressure.
Scientists often give pressure in N/m², which is called the pascal, Pa. We stay with N/cm² here, because the sums are smaller.
See it three ways
As a picture
In words
The force stays the same. The area gets smaller, so the pressure gets bigger. A small area means a big pressure.
The start of the next example. Joseph stands on two feet, then on one.
Worked example
Joseph has a mass of 40 kg. Each of his soles touches the ground over 100 cm². What pressure does he put on the ground on two feet, and on one foot?
Pressure = force ÷ area. His weight is the force.
Weight = 40 × 10 = 400 N.
Both soles: 2 × 100 = 200 cm².
Pressure on two feet = 400 ÷ 200 = 2 N/cm².
On one foot the area is only 100 cm².
Pressure on one foot = 400 ÷ 100 = 4 N/cm².
The pressure doubles when the area halves.
Answer: 2 N/cm² on two feet, 4 N/cm² on one foot
Now the camel. A camel weighs about 6000 N. Its four wide feet touch the sand over about 2000 cm². The pressure is 6000 ÷ 2000 = 3 N/cm². That is small, so the camel does not sink far.
The same camel on wide feet puts 3 N/cm² on the sand. On small hooves of 400 cm² in all it would put 15 N/cm², and it would sink.
A knife works the other way. Push a knife with 20 N. A blunt edge touches 4 cm², so the pressure is 5 N/cm². A sharp edge may touch only 0.2 cm², so the pressure is 100 N/cm². That is much bigger, and it cuts.
The same 20 N push on a sharp edge gives 20 times the pressure.
Try it
Make a box press into sand
You need: a tray or a wide bowl of dry sand or fine soil, a shoe box with the lid taped shut and stones inside to make it heavy, a ruler or a stick, and paper.
Be safe: The box is heavy. Lower it slowly and keep it off your feet. Keep sand away from your eyes and mouth.
Smooth the sand flat with your hand. Lay the box on its widest face. Count five seconds.
Lift the box straight up. Measure how deep the dent is with the ruler.
Smooth the sand flat again.
Stand the box on its narrowest end. Count five seconds, then lift it.
Measure the new dent. Compare the two. The box is the same, so its weight is the same.
What you will see: The dent is deeper when the box stands on its narrow end. The weight is the same. The area is smaller, so the pressure is bigger. Our dents were 2 mm and 8 mm. Yours will differ.
If you cannot try it, this is what happens.
A wrong idea many people have
A bigger force always means a bigger pressure.
Why it feels right: In daily talk, people use "pressure" and "push" to mean the same thing.
The test that breaks it: Joseph on one foot puts 4 N/cm² on the ground. The camel puts 3 N/cm². The camel's force is 15 times bigger, but its pressure is smaller.
What is true: Pressure is force divided by area. A big force spread over a big area can give a small pressure.
Key words
area
how much surface a force touches. We measure it in cm².
pressure
the force on each unit of area, such as each square centimetre: force ÷ area.
pascal
the unit of pressure in N/m². We write Pa.
Back to your guess
The answer is C: The sharp edge is so thin that the same push is on a much smaller area.
The push can be the same. A sharp edge touches a tiny area, so the force is squeezed into a very small space. That makes a very big pressure.
Check yourself
Try each one before you look. A wrong answer tells you where to go next.
A force of 60 N pushes on an area of 20 cm². What is the pressure?
See the answer
3 N/cm²
Pressure = force ÷ area = 60 ÷ 20 = 3 N/cm².
A knife is pushed with 20 N. Its edge touches the food over 0.5 cm². What is the pressure?
See the answer
40 N/cm²
Pressure = force ÷ area = 20 ÷ 0.5 = 40 N/cm². A small area gives a big pressure.
If you chose B: You multiplied the force by the area. Pressure is the force shared out over the area, so divide. Go to S3.7.7.
If you chose C: You divided the area by the force, upside down. Put the force first: force ÷ area. Go to S3.7.7.
Ravi has a mass of 50 kg. He stands on two feet that touch the ground over 250 cm² in all. What pressure does he put on the ground?
See the answer
2 N/cm²
His weight is 50 × 10 = 500 N. Pressure = 500 ÷ 250 = 2 N/cm².
If you chose A: You divided the mass in kilograms. Pressure needs a force in newtons, so find the weight first: kilograms × 10. Go to S3.7.4.
If you chose C: That is his weight in newtons. You still have to divide it by the area to get the pressure. Go to S3.7.7.
Two knives are pushed with the same force. One is sharp and one is blunt. Why does the sharp knife cut better?
See the answer
The sharp edge touches a much smaller area, so the pressure is much bigger.
Pressure = force ÷ area. The same force on a smaller area gives a bigger pressure.
If you chose A: The force is the same here. What differs is the area the edge touches. Go to S3.7.7.
If you chose B: The weight is not the reason. A thin edge puts the same force on a tiny area. Go to S3.7.4.
A camel walks on soft sand and does not sink far. Why?
See the answer
Its wide feet spread its weight over a big area, so the pressure is small.
Pressure = force ÷ area. The camel is heavy. Its wide feet give a big area, so the pressure on the sand is small.
If you chose B: Small feet would put the weight on a small area and sink deep. A camel has wide feet. Go to S3.7.7.
If you chose C: A camel is heavy. It is the wide feet that matter: the same weight on a bigger area gives a smaller pressure. Go to S3.7.7.
Amina has a mass of 60 kg. Her feet touch the ground over 300 cm² in all. Kofi has a mass of 30 kg. His feet touch the ground over 60 cm² in all. Who puts the bigger pressure on the ground?
See the answer
Kofi. He puts 5 N/cm² on the ground, and Amina puts 2 N/cm².
Kofi weighs 30 × 10 = 300 N, so his pressure is 300 ÷ 60 = 5 N/cm². Amina weighs 600 N, so her pressure is 600 ÷ 300 = 2 N/cm².
If you chose A: A bigger force does not always mean a bigger pressure. You must divide the weight by the area of the feet. Go to S3.7.7.
If you chose C: Wider feet spread the weight over more area, which makes the pressure smaller, not bigger. Go to S3.7.7.
From an earlier chapter
Review: a skater glides 30 m in 6 s. What is her speed?
See the answer
5 m/s
Speed = distance ÷ time = 30 ÷ 6 = 5 m/s.
If you chose A: You added the two numbers. Speed is distance divided by time. Go to S3.7.1.
If you chose B: You divided time by distance. Speed is distance divided by time. Go to S3.7.1.
Keep it
Copy this into your exercise book.
Pressure = force ÷ area, in N/cm². The same force on a smaller area gives a bigger pressure. Sharp edges cut. Wide feet spread weight out.
Draw: A block with 24 N on 12 cm², and the same block on 3 cm². Write 2 N/cm² and 8 N/cm².
