The Same Push Can Be Gentle or Painful Depending on the Area
Learn to calculate pressure in pascals, explain why straps are broad and knives are sharp, see how liquid pressure grows with depth, and find the evidence that air presses on everything around us.
Why does the same force hurt more through a thin strap than a broad one?
Because pressure depends on the area the force is spread over, not just on the force. The same bag pulling with presses five times harder through a strap one-fifth as wide.
Spread a force out and the pressure falls; concentrate it and the pressure climbs. This page covers everything in the CBSE Class 8 Science chapter's first part: calculating pressure, why area is chosen deliberately, liquid pressure, and air pressure.
Spread a force out and the pressure falls; concentrate it and the pressure climbs. This page covers everything in the CBSE Class 8 Science chapter's first part: calculating pressure, why area is chosen deliberately, liquid pressure, and air pressure.
Formula
How do you calculate pressure?
Pressure is the force acting per unit area, at right angles to a surface:
With force in newtons (N) and area in square metres (m²), pressure comes out in pascals (Pa), where .
Worked examples.
A force of acting over :
A boy of weight standing on both feet, covering :
Now the same boy on one foot, covering :
Half the area doubles the pressure, although his weight never changed.
Running the formula backwards. A pressure of over an area of means a force of
The relationship to hold on to is that pressure is inversely proportional to area for a fixed force. Halve the area and the pressure doubles; double the area and the pressure halves — which is precisely what the next section puts to use.
With force in newtons (N) and area in square metres (m²), pressure comes out in pascals (Pa), where .
Worked examples.
A force of acting over :
A boy of weight standing on both feet, covering :
Now the same boy on one foot, covering :
Half the area doubles the pressure, although his weight never changed.
Running the formula backwards. A pressure of over an area of means a force of
The relationship to hold on to is that pressure is inversely proportional to area for a fixed force. Halve the area and the pressure doubles; double the area and the pressure halves — which is precisely what the next section puts to use.
Why are straps broad while knives and nails are sharp?
Because designers choose the area to get the pressure they want — small pressure where it would hurt or damage, large pressure where something must cut or pierce.
Large area, so low pressure:
- School bag straps are broad, spreading the bag's weight over more of the shoulder, so the pressure is lower and it does not dig in.
- Tractors have wide tyres so the machine's weight spreads over a large area and it does not sink into soft soil.
- A camel's broad feet stop it sinking into loose sand.
- Foundations of buildings are wide, spreading the enormous weight of the walls so the ground is not crushed.
- A sleeping mattress spreads your weight, which is why lying on a plank is uncomfortable.
Small area, so high pressure:
- A knife is sharpened so its force acts over a very small area, giving high enough pressure to cut vegetables.
- Nails and pins are pointed, so a hammer's force concentrates into a tiny tip and pierces wood.
- Needles and drawing pins work the same way.
- The studs on sports shoes press into the ground to grip.
Comparing a blunt knife with a sharp one makes the point: both can be pushed with the same force, but only the sharp one has a small enough area to produce the pressure needed to cut.
So the design question is always which way you want the pressure to go. Reducing pressure means increasing the area; increasing pressure means reducing it — and a blunt knife fails not for lack of force but for having too much area.
Large area, so low pressure:
- School bag straps are broad, spreading the bag's weight over more of the shoulder, so the pressure is lower and it does not dig in.
- Tractors have wide tyres so the machine's weight spreads over a large area and it does not sink into soft soil.
- A camel's broad feet stop it sinking into loose sand.
- Foundations of buildings are wide, spreading the enormous weight of the walls so the ground is not crushed.
- A sleeping mattress spreads your weight, which is why lying on a plank is uncomfortable.
Small area, so high pressure:
- A knife is sharpened so its force acts over a very small area, giving high enough pressure to cut vegetables.
- Nails and pins are pointed, so a hammer's force concentrates into a tiny tip and pierces wood.
- Needles and drawing pins work the same way.
- The studs on sports shoes press into the ground to grip.
Comparing a blunt knife with a sharp one makes the point: both can be pushed with the same force, but only the sharp one has a small enough area to produce the pressure needed to cut.
So the design question is always which way you want the pressure to go. Reducing pressure means increasing the area; increasing pressure means reducing it — and a blunt knife fails not for lack of force but for having too much area.
How do you show that liquids exert pressure, and that it grows with depth?
A liquid presses on the base and the walls of its container, and the pressure increases with depth. Two activities show it.
Pressure on the walls. Take a tall plastic bottle and make three small holes in a vertical line — one near the top, one in the middle, one near the bottom. Fill it with water. Water spurts out of all three holes, proving the liquid pushes sideways on the walls, not just downward.
And the jet from the lowest hole travels furthest, while the top one dribbles out. The deeper the hole, the greater the pressure behind the water.
Pressure in all directions. Tie a thin rubber sheet over the mouth of a short tube and lower it into water. The sheet bulges inward, and it bulges more the deeper you push it — whichever way the tube is turned.
So liquid pressure:
- Acts on the base and on the walls
- Acts in all directions at a point
- Increases with depth
- Increases with the density of the liquid
A dam is built thicker at the bottom than the top for exactly this reason, and a water tank placed high on a roof gives a stronger flow at the tap below.
Notice what the pressure does not depend on: the shape or width of the container. Water in a narrow pipe and in a wide tank, at the same depth, exerts the same pressure — which is why a tall thin overhead tank supplies just as much pressure as a broad one at the same height.
Pressure on the walls. Take a tall plastic bottle and make three small holes in a vertical line — one near the top, one in the middle, one near the bottom. Fill it with water. Water spurts out of all three holes, proving the liquid pushes sideways on the walls, not just downward.
And the jet from the lowest hole travels furthest, while the top one dribbles out. The deeper the hole, the greater the pressure behind the water.
Pressure in all directions. Tie a thin rubber sheet over the mouth of a short tube and lower it into water. The sheet bulges inward, and it bulges more the deeper you push it — whichever way the tube is turned.
So liquid pressure:
- Acts on the base and on the walls
- Acts in all directions at a point
- Increases with depth
- Increases with the density of the liquid
A dam is built thicker at the bottom than the top for exactly this reason, and a water tank placed high on a roof gives a stronger flow at the tap below.
Notice what the pressure does not depend on: the shape or width of the container. Water in a narrow pipe and in a wide tank, at the same depth, exerts the same pressure — which is why a tall thin overhead tank supplies just as much pressure as a broad one at the same height.
What is the evidence that air exerts pressure?
Air has weight, and the whole column of air above us presses down and sideways on everything. Its value at sea level is about ****, which is roughly pascals.
That is a large figure, and several simple demonstrations reveal it.
Rubber sucker. Press a rubber sucker onto a smooth wall or tile. Squeezing it pushes the air out, so there is very little air left inside. The atmospheric pressure outside then holds it firmly against the surface, and a real pull is needed to remove it. Soap or water improves the seal by keeping air from leaking back in.
Collapsing bottle or tin. Take a plastic bottle, fill it partly with hot water, empty it and cap it tightly. As the vapour inside cools, the pressure inside falls, and the atmospheric pressure outside crushes the bottle inward with no one touching it.
Straw and glass. Sucking on a straw removes air from inside it, lowering the pressure there, so atmospheric pressure on the drink's surface pushes the liquid up the straw. Strictly, you do not pull the drink up; the air pushes it.
Paper over a glass. Fill a glass with water, cover it with a card, and invert it. The water stays in, held up by atmospheric pressure on the card.
We are not crushed by this pressure because the pressure inside our bodies balances it — which is also why ears feel blocked on a hill road or in an aircraft, as the outside pressure changes and the two sides take a moment to equalise.
That is a large figure, and several simple demonstrations reveal it.
Rubber sucker. Press a rubber sucker onto a smooth wall or tile. Squeezing it pushes the air out, so there is very little air left inside. The atmospheric pressure outside then holds it firmly against the surface, and a real pull is needed to remove it. Soap or water improves the seal by keeping air from leaking back in.
Collapsing bottle or tin. Take a plastic bottle, fill it partly with hot water, empty it and cap it tightly. As the vapour inside cools, the pressure inside falls, and the atmospheric pressure outside crushes the bottle inward with no one touching it.
Straw and glass. Sucking on a straw removes air from inside it, lowering the pressure there, so atmospheric pressure on the drink's surface pushes the liquid up the straw. Strictly, you do not pull the drink up; the air pushes it.
Paper over a glass. Fill a glass with water, cover it with a card, and invert it. The water stays in, held up by atmospheric pressure on the card.
We are not crushed by this pressure because the pressure inside our bodies balances it — which is also why ears feel blocked on a hill road or in an aircraft, as the outside pressure changes and the two sides take a moment to equalise.
Exam tip
Exam tip: converting area to square metres first
Pressure numericals are short, and nearly all lost marks are units.
Write the formula first, , then substitute. That line is marked on its own.
Convert the area to square metres before dividing. Remember , so — squaring the conversion factor is the step that gets skipped.
Give force in N, area in m² and pressure in Pa, and label the answer.
For an explanation question, name the direction of the change: broad straps increase the area, so the pressure decreases. Both halves are needed.
And for liquid pressure, say it increases with depth and density but not with the container's shape or width — that last point is a favourite one-mark question.
Write the formula first, , then substitute. That line is marked on its own.
Convert the area to square metres before dividing. Remember , so — squaring the conversion factor is the step that gets skipped.
Give force in N, area in m² and pressure in Pa, and label the answer.
For an explanation question, name the direction of the change: broad straps increase the area, so the pressure decreases. Both halves are needed.
And for liquid pressure, say it increases with depth and density but not with the container's shape or width — that last point is a favourite one-mark question.
Did you know
Why does the water jet from the lowest hole travel the furthest?
Because there is more water above it pressing down.
The pressure at any point in a liquid comes from the weight of everything above that point. Near the top of the bottle only a little water sits above the hole, so the pressure is small and the water dribbles out. At the bottom, the whole column presses down, so the water is forced out hard and shoots further.
This is why a dam is built much thicker at its base than at its top, and why divers must equalise their ears as they descend — the pressure keeps climbing with every metre of depth.
The pressure at any point in a liquid comes from the weight of everything above that point. Near the top of the bottle only a little water sits above the hole, so the pressure is small and the water dribbles out. At the bottom, the whole column presses down, so the water is forced out hard and shoots further.
This is why a dam is built much thicker at its base than at its top, and why divers must equalise their ears as they descend — the pressure keeps climbing with every metre of depth.
Key takeaways
Pressure: quick revision
- , with force in N, area in m² and pressure in pascals (Pa), where .
- Pressure is inversely proportional to area for a fixed force — on gives , but on gives .
- Broad straps, wide tyres and wide foundations spread force to lower pressure; sharp knives, pointed nails and studs concentrate it to raise pressure.
- Liquids press on the base and walls, in all directions, and the pressure increases with depth and density — but not with the container's shape or width.
- Three holes in a bottle show all of this, with the lowest jet travelling furthest; dams are built thicker at the base for the same reason.
- Atmospheric pressure is about **** at sea level, shown by rubber suckers, collapsing bottles and drinking straws, and we are not crushed because internal pressure balances it.
You will remember all of this far better after answering five questions on it than after reading it twice.
- Pressure is inversely proportional to area for a fixed force — on gives , but on gives .
- Broad straps, wide tyres and wide foundations spread force to lower pressure; sharp knives, pointed nails and studs concentrate it to raise pressure.
- Liquids press on the base and walls, in all directions, and the pressure increases with depth and density — but not with the container's shape or width.
- Three holes in a bottle show all of this, with the lowest jet travelling furthest; dams are built thicker at the base for the same reason.
- Atmospheric pressure is about **** at sea level, shown by rubber suckers, collapsing bottles and drinking straws, and we are not crushed because internal pressure balances it.
You will remember all of this far better after answering five questions on it than after reading it twice.