Pressure

When you push on a car, the whole car moves. This is because all of the parts connected to the car contribute to the cars mass. Like a person sitting in the car.

When you push the car, you also push the person who is sitting in the car. However, that force you are generating to move the car is much greater than the force the person in it will feel. This is because, they will feel the net force. The net forward force is the force you are applying to the car, minus the frictional forces opposing movement.

However, your hands will feel all of that force, the whole forward force you are applying to the car. Because of this concentration of force, if you place your hands on a softer part of the boot, you may dent the car. You want to be pushing on a strong boot, as it will transfer the force from your hands, to the hinges and latching of the boot, then to the body and eventually the chassis of the car. The whole car needs to receive this forward thrust force. Any part of it that does not, will remain behind - for instance, if you had a plank or wood resting against the car door, then it will slide along the car and fall behind it, as it did not receive the forward force.

For the person sitting in the car, this forward force is directed against their inertia - their body wanting to stay still. So, the chair will push against their body, causing their body to move forward. However, as this force is spread out, they won't notice it as they would if you were to simply push them on their back with a force equivalent to the net force being exerted when in the seat. The difference is the area over which that force is distributed.

If you then decide to push the car using the handle of a broom, you will dent the car - because all of your thrust force is being applied to a very small area, and the metal will accelerate inwards until the two forces are balanced

In these videos there are several examples of pressure

If a person is to stand on an egg, it will crack.

However, if a person stands on a carton of eggs they can take the weight, because the persons weight is distributed across all of the eggs. Likewise, if there are enough eggs, they can hold the weight of a car

Likewise, with the bed of nails. When a person lays on a bed of nails, or the car drives over the bed of nails, the weight of the person or car is distributed across all of the nails. So, the force required to puncture the skin or the tire is not met. However, if you start removing nails, then the force on each nail increases, until they eventually puncture the skin or tire.

Pressure = Force / Area

Mr Cowley Pressure Lecture - What is Pressure

Mr Cowley Lecture - Calculating Area

Mr Cowley Lecture - Pressure, Force and Area

Pressure, or the force over an area, is a product of the magnitude of the force and the size of the area.

This means:

The larger the force, for a fixed area, the larger the pressure.
The larger the area, for a fixed force, the smaller the pressure.
The smaller the area, for a fixed force, the larger the pressure.

1kPa = 1 Richie McCaw on a Carpet Square

Blaise Pascal experimented with Pressure. Because of his work, the unit for pressure is named after him - the Pascal

1 Pascal is equal to the force of 1 Newton spread over an area of 1 meter squared.

1Pa = 1 N/m²

So how heavy is that?

Well its about 100g of mass, in earths gravity sitting on a mat that is 1 square meter.
100 grams is 10 $2 coins (a NZ $2 coin is 10grams)
1 square meter is the outline around the dog above - or the space taken up buy 9 unopened Domino Pizza boxes. Or.... It is the size of a large carpet tile as seen at Bunnings Warehouse: https://www.bunnings.co.nz/standard-carpet-1-x-1m-dark-grey-millenium-polypropylene-carpet-tile_p6620830
For the maths of it:
- The total mass of 10 $2 coins is: 10 x 0.01kg = 0.1kg
- The weight of 10 $2 coins is: w=mg, w = 0.1 x 10ms^-2, w = 1Newton
- 1 N over 1m² is 1Pa

1 Pascal = 10 $2 coins on a large 1m² carpet square

So the increase in pressure that a rigid carpet square would exert on the floor when 10 $2 coins are placed evenly on it is equal to 1Pa

This 1 Pa isn't very heavy

The kiloPascal is more commonly used, as this is 1000 Pa.

A kiloPascal is equivilent to a 100kg 1m² carpet square, Or 10,000 $2 coins on a carpet square.

10,000 $2 coins on a carpet square is hard to visualise.

What if instead we stack up our carpet squares.

The average 1m² carpet squares has a mass of 4kg, so if we stack 25 of them on top of each other, then we will have 100kg of mass, and this is pulled down by gravity at approximately 10N/kg, so this will give us 100kg x 10 = 1000 Newtons, which when spread across the 1m² gives us 1000N/m which is 1000Pa or 1kPa

But still, this is hard to remember

So finally we have Richie McCaw!

We can use Richie McCaw to figure out the kiloPascal as he's about 100kg in mass. So, his weight is 100kg x 9.81N/kg is 981N, then rounded to the nearest 1000, his weight is 1000N. There is also air on the carpet square, so we'll place them in a vacuum chamber. So then, the pressure that a rigid carpet square would exert on the floor would be 1kPa

1kPa would be the same as the pressure under a rigid 1m² carpet square with 1 Richie McCaw sitting on it

Mr Cowley Lecture - Pascal, KiloPascal, Richie McCaw

Pressure = Force over Area

Pressure

The dumbell, the big wood, the little wood and the flutter board.

Mr Cowley Pressure Lecture 1 - Pressure, Force and Area

In the video clip above, I rest a 20kg dumbell on two different sized pieces of wood. These themselves rest on a foam flutterboard, then on my picnic table.

Gravity pulls down the wood, and the wood sinks into the foam until the Force (reactive force) resisting further compression of the foam, is equal to the downward force of gravity.

As you walk across a field or sand, you compresse sand, the more pressure you exert downwards on the field, the more compression will occur until the reactive force is equal to the downward force of gravity. So, the adage that when you jump the earth moves is wrong, when you jump the earth is compressed.

Anyway, back on point. The mass stays the same, 20kg, however the compression of the foam is much greater with the smaller piece of wood than the larger one. Why?

Well, first lets calculate the downward force due to the mass x gravity

The 20kg masses weight is = 20kg x 10 N/kg = 200Newtons

Then lets look at area - the big block is a square with sides that are 90mm and the little one is a square with sides that are 18mm

Big wood area - Length x width = 90 x 90 = 8100mm

Little Wood area - Length x width = 18 x 18 = 324mm

The equation only works with area as squared meters.

So, there are 1000mm x 1000mm = 1,000,000mm (1 million) square millimeters in a square meter.

So each of our areas need to be divided by 1 million

Big wood = 8100/1000000 = 0.0081m²

Little wood = 0.000324m²

Pressure exerted by the big wood

P = F/a

P = 200N / 0.0081m²

P = 24691Pa

P = 25 kPa

Pressure exerted by the small wood

P = F/a

P = 200N / 0.000324m²

P = 617284Pa

P = 617 kPa

By reducing the area, the force applied to the smaller area is 25 times greater than the force applied to the larger area - even though the force itself stays the same

The Girl in the Stilettos

The parents were away, and a party was arranged.

All were in attendance, shoes off at the door? 'No no, no need, for the parents are away'.

The music was funky, the dancing was funny. Everyone had fun, and then they tired.

Some slept on the sofa, and some on the floor, others went home, and a good night was done.

In the morning the clean up begun, the parents were driving, all evidence in hiding.

Everything was washed, everyone was gone, every scrap of rubbish removed, but something was wrong.

On the floor there were marks, they weren't there before.

The scrubbing was vigorous, the sweat it poured, for the panic was real, for the parents were coming and the marks, they were staying.

A finger struck over a mark. To the greatest of horror, the realization sunk in, as the finger applied, sunk into the mark.

These were not mere marks, no, no sole scuffs neither.

For these were indentations. Indentations in the varnish and dents in the wood.

Dents in the Dining room, Kitchen and Lounge.

These dents were not there before, the parents were coming, these dents would never leave, the car was approaching.

The chatter of two speakers outside grew louder and louder, as the clip-clap taps of their shoes on the pavement grew closer and closer.

The sound resembled a sound from the night before.

That sound sequestered from the memory surrounded the mind.

The memory of the muffled sounds of chatter so fresh. And there amongst the sounds of an evening so sordid, was the tap of a shoe on the wooden floor.

The mind muffled the sounds of the soiree, till the only sound heard was the tap.

The tapping became a pounding, a hammering, a slamming of stilettos on a wooden floor.

Then a tapping on the door.

Mr Cowley Lecture - The Girl in the Stilettos

The girl in the Stiletto is a true story that happened at a mates party. I have exercised my literary flare with the retelling of it.

But what happened, why did the Stiletto do so much damage. The girl was only around 55kg in mass but the wooden floors were permanently damaged. Below is two videos of my sister walking across a piece of polystyrene. Firstly with flats on, and then with stilettos.

Pressure on the polystrene with converse flats

P = F/A

Mass is 65kg and area of Converse sole is 27cm x 7cm

Force is weight force, so w = m*g

weight = 65kg x 9.81ms^-2

weight = 637.65 Newtons

Area of Converse is 0.27m*0.07m = 0.0189m²

P = F/ A

P = 637.65N / 0.0189m²

P = 33,738N/m²

P = 33.7kPa

Mr Cowley Lecture - Stiletto Pressure Calculations

Pressure on the polystrene with stilettos

P = F/A

Mass is 65kg and area of Stiletto heel is 1cm x 1cm

Force is weight force, so w = m*g

weight = 65kg x 9.81ms^-2

weight = 637.65 Newtons

Area of Stiletto heel is 0.01m*0.01m = 0.0001m²

P = F/ A

P = 637.65N / 0.0001m²

P = 6,376,500N/m²

P = 6,376.5kPa

So by apply the formula pressure = force / area to the situation of the stilettos we can see that the stilettos apply 189 times more pressure to the floor than the flats do!!

Using these calculations, the pressure on the floor when wearing converse is the same as 33 Richie McCaws on a carpet square. Where as the stiletto is equivalent to over 6 thousand Richie McCaws on the carpet square. And thus the stilettos until the compression of the wooden floor is balanced with this huge downward force, thus leaving indentations, or dents on the wooden floor.

If P = F/A then F = PA

Hydraulics!

You can rearrange the equation, so that by applying a force to a smaller area, in other words pressure, then the resulting force is much greater.

In the video to the right, a small force of say 20N is applied to the small syringe that has an area of 1cm2

So to calculate the small syringe area as a m2, we need to find out how many cm2 there are in a m2 = 100cm in a meter x 100cm =10,000

So now, 1/10000 = 0.0001m2

The large syringe has a surface area of 4cm so 0.0004m2

Now p = F/A

So the pressure in the small syringe is 20N/0.0001m2 = 200,000 Pa

Now that will generate a force at the surface of the large syringe that will equal what?

F = pA

F = 200,000Pa x 0.0004m2

F = 80N

So, you can push down on the small syringe with a force of 20N, and it will cause the big syringe to push up with a force of 80N

And that is how hydraulics work!

Mr Cowley Lecture - Hydraulics

SciPad

Pages 46, 47, 48

Answers

ABA

The following pages from the ABA Mechanics book explain Pressure very thoroughly and make for very good revision and practice

Mr Cowley Lecture - ABA Answers 1 - 9

Mr Cowley Lecture - ABA Answers 10 & 11

Pressure in 3 Dimensions

Pressure in 3 dimensions is not covered in NCEA Level 1 - so these videos are just here so that you can see the implications of 3 dimensional pressure - which occurs when objects are in liquids or in gases - so anywhere and everywhere on Earth.

Buoyancy and Lift

3 dimensional pressure results in buoyancy. Again, this is not covered in NCEA level 1 - so these videos are just here out of interest