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Forces & pressure: 6.2 Pressure created by standing objects, P = F/A formula calculations including when pressure is increased or decreased when applied to an object

Doc Brown's Physics exam study revision notes on: explaining pressure situations like camel's feet, syringe needle, skis, drawing pin, scissors where a large of small surface area of contact pressure is very important. 

Index for physics notes on 6. Forces & pressure in fluids and calculations

This page contains online questions only. Jot down your answers and check them against the worked out answers at the end of the page

6.2 Pressure created by standing objects, calculations, P = F/A formula including where pressure is deliberately increased or decreased when applied to an object

Pressure is defined as force per unit area and is calculated from the simple formula

pressure = force normal to the surface ÷ area of that surface,

P = F / A,  F = P x A, A = F / P

P, pressure in pascals (Pa);   F, contact force in newtons (N);   A, area on which force acts in square metres (m2)

A force of 1 N acting on 1 m2 creates a pressure of 1 Pa

A variety of situations to increase or decrease pressure in various situations

Often by changing the surface area of contact between an object and other material

camel.gif drawingpin.gif snowshoes.gif scissors.gif syringe.gif F = weight on applying the P = F/A equation

Camels have feet of large surface area, this reduces the F/A ratio (reducing pressure), so their feet do not sink to deeply into sand.

Similarly, skis or snow shoes have a relatively large area to reduce the F/A ratio, hence decreasing the impact pressure on snow, so the wearer does not sink to deeply into the snow.

Scissors have a sharp edge to create high F/A ratio to create a high pressure to cut cleanly through materials.

Drawing pins and hypodermic needles have very sharp end points to create a very high F/A ratio, so the high 'impact' pressure enables them to easily pass into materials when pushed.

Similar arguments apply to ...

Vehicles with large wide tyres or wide caterpillar tracks to minimise sinking in soft ground.

Crampons are sharp to penetrate ice or snow to get a good grip, but the rest of the broad surface area of the boot prevents the wearer from sinking too deeply into the snow.

Snow shoes the size of tennis racquets stop you sinking into snow by increasing the surface area and reducing the pressure compact the snow - this also reduces the effort you have to put walking across deep snow.
 

Pressures caused by standing objects - some simple calculations, if occasionally painful !

Any solid object standing on a solid surface will, due to the force gravity, create a pressure on the surface due to its weight.

This is a normal contact force, balanced by the compressed atoms of the solid surface pushing back up.

(This complies with Newton's 1st Law of Motion)

Ignoring the different weights of people (the weight 'force'), you should realise from the formula why it is better to be trodden on by a broad shoe sole than a stiletto heel !!!! (CLUE !!! P = F / A, no exam pressure here !!!)

 

In moving around the particles of a fluid collide with each other and with any surface they are in contact with.

Although the mass of an individual particle is minute and each collision involves the transfer of an equally minute amount of kinetic energy, collectively the trillions of collisions cause a pressure to be exerted in both gases and liquids.

The combined effects of these particle collisions produces a net resultant force at right angles to the surface of contact with an object or side of a container.

e.g. the pressure of gases in a container or the pressure from the atmosphere of air pressure around you.

It is the same anywhere in a liquid, pressure is exerted against the side of a container wherever the liquid is in contact and it is the same for an object immersed in a liquid.

Remember that the force of the pressure acts in all directions in a fluid.

The maximum pressure exerted in a fluid is considered to be due to the collective force of the particle collisions acting at right angles (normal, 90o, perpendicular) to the surface on which the collisions take place i.e. any surface in contact with the fluid.

 

For specific gas calculations see P-V-T pressure-volume-temperature gas laws and calculations (in my GCSE level chemistry notes).

 

Examples of pressure calculations based on P = F/A

Q1 If a weight of fluid of 200 N acts on a surface of 5 m2, calculate the pressure created.

Worked out ANSWERS to questions

 

Q2 What force must be applied to a surface area of 0.0025 m2, to create a pressure of 200,000 Pa?

Worked out ANSWERS to questions

 

Q3 In a hydraulic lift system, what must the surface area of a piston be in cm2 if a pressure of 300 kPa is used to give a desired upward force of 2000 N?

Worked out ANSWERS to questions

 

Q4 The average standard rectangular building brick has a mass of 3.10 kg and dimensions of 225 mm x 112 mm x 75 mm.

The gravitational field constant g = 9.8 N/kg.

(a) Calculate the pressure the brick creates when standing on its surface of smallest area.

(b) Calculate the pressure the brick creates when standing on its surface of greatest area.

Worked out ANSWERS to questions

 

Q5 A stiletto heel has a surface area of approximately 2.5 cm x 2.0 cm.

Worked out ANSWERS to questions

 

Q6 A person is standing on both feet, with flat trainers, each of which has an ground contact area of 0.025 m2.

If the person weighs 800 N, what pressure is created on the ground by each foot when the person is standing still?

Worked out ANSWERS to questions

 

Q7 An elephant is standing on all of its feet, each of which has an ground contact area of 0.08 m2. If the elephant weighs 50000 N, what pressure is created on the ground?

Worked out ANSWERS to questions

 

Q8 A ski design team has to take into account the pressure created by the skier on the surface of deep snow.

They need to the calculate the effects of the variables which are (i) area of one ski, (ii) weight of skier, (iii) pressure created by the skier on the snow and (iv) the pressure the snow can take without the skier sinking in too much!

If the maximum acceptable snow pressure is 5000 N/m2, for a single ski surface area of 0.15 m2, what is the maximum weight the skier can be?

Worked out ANSWERS to questions

 

Q9 A ski design team has to take into account the pressure created by the skier on the surface of deep snow.

They need to the calculate the effects of the variables which are (i) area of one ski, (ii) weight of skier, (iii) pressure created by the skier on the snow and (iv) the pressure the snow can take without the skier sinking in too much!

If the maximum acceptable snow pressure is 4000 N/m2, what is the minimum single ski surface area acceptable, for a skier of weight 800 N?

Worked out ANSWERS to questions

 

Q10 A bag of sugar has a base of 6 cm x 10 cm. If it weighs 18 N, what pressure does it create standing on a shelf?

Worked out ANSWERS to questions

 

Q11 A stiletto heal has a base area of 3 cm2.

If the woman weighs 750 N, what pressure does she create on the floor when standing on one heel?

Worked out ANSWERS to questions

 

Q12 A waste skip a base of 2m x 4m. If it weighs 10000 N when full, what pressure does it create when standing on the road?

Worked out ANSWERS to questions

 

Q13 A brick has a base of 10 cm x 25 cm and weighs 30 N. what pressure does a stack of ten bricks create simulating the pressure created by a low wall?

Worked out ANSWERS to questions

See also Part 6.3

Pressure in a liquid - density, depth factors and calculations

 

For specific gas pressure calculations see P-V-T pressure-volume-temperature gas laws and calculations (in my GCSE level chemistry notes).

Index physics Forces notes 6. Forces & pressure in fluids, calculations

Keywords, phrases and learning objectives for forces involving pressure situations

Be able to explain in terms of forces the pressure created by standing objects.

Be able to solve problems and do calculations using the formula pressure = force/area with the appropriate units.

Be able to describe and explain situations where pressure is deliberately increased or decreased by changing surface area when applied to an object or context e.g. camel's feet, snow shoes, syringe needle, skis, drawing pin and scissors.

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Index physics Forces notes 6. Forces & pressure in fluids, calculations
Worked out ANSWERS to the force and pressure calculations

Examples of pressure calculations based on P = F/A

Q1 If a weight of fluid of 200 N acts on a surface of 5 m2, calculate the pressure created.

pressure = force ÷ area,    P = F / A = 200 / 5 = 40 Pa

 

Q2 What force must be applied to a surface area of 0.0025 m2, to create a pressure of 200,000 Pa?

P = F / A, rearranging gives: F = P x A = 200000 x 0.0025 = 500 N

 

Q3 In a hydraulic lift system, what must the surface area of a piston be in cm2 if a pressure of 300 kPa is used to give a desired upward force of 2000 N?

P = F / A, rearranging gives: A = F / P = 2000 / 300000 = 0.00667 m2

What is the piston surface area in cm2?

1 m2 = 100 cm x 100 cm = 10 000 cm2, so the area of the piston = 10 000 x 0.00667 = 66.7 cm2

 

Q4 The average standard rectangular building brick has a mass of 3.10 kg and dimensions of 225 mm x 112 mm x 75 mm.

The gravitational field constant g = 9.8 N/kg.

(a) Calculate the pressure the brick creates when standing on its surface of smallest area.

smallest surface area = 112 mm x 75 mm

area = (112/1000) x (75/1000) =  0.0084 m2

downward force (weight) = mass x g = 3.1 x 9.8 =  30.38 N

pressure = force / area = 30.38 / 0.0084 = 3620 Pa (3 sf)

(b) Calculate the pressure the brick creates when standing on its surface of greatest area.

largest surface area = 225 mm x 112

area = (225/1000) x (112/1000) =  0.0252 m2

downward force (weight) = mass x g = 3.1 x 9.8 =  30.38 N

pressure = force / area = 30.38 / 0.0252 = 1210 Pa (3 sf)

 

Q5 A stiletto heel has a surface area of approximately 2.5 cm x 2.0 cm.

If a lady puts all of her 60 kg 'weight' on it, what pressure is created on the floor surface.

The gravitational field constant g = 9.80 N/kg.

Stiletto area = (2.5/100 x 2.0/100) =  0.0005 m2

Weight force = m x g = 60 x 9.8 = 588 N

Stiletto pressure = P / A = 588 / 0.0005 =  ~1 176 000 = ~1.2 x 106 Pa

Ad hoc notes!

This is over a million pascals! Painful if you are trodden on!

If trodden on, on the Moon, its not so bad, with its 1/6th the gravity of Earth.

Atmospheric pressure is ~101 000 Pa, so its over 10 x greater than the pressure of the air around you!

Its also the same pressure you experience at depth of 100 m in water!

(See Part 6.3 where in fluids P = hρg = 100 x 1000 x 9.8 = 9.8 x 105 Pa)

 

Q6 A person is standing on both feet, with flat trainers, each of which has an ground contact area of 0.025 m2.

If the person weighs 800 N, what pressure is created on the ground by each foot when the person is standing still?

Answer: P = F/A = pressure = force or weight / area = 800 / (2 x 0.025) = 800 / 0.05 = 32000 N/m2 or Pa (pascals), divide by 2 because of two feet.

 

Q7 An elephant is standing on all of its feet, each of which has an ground contact area of 0.08 m2. If the elephant weighs 50000 N, what pressure is created on the ground?

Answer: P = F/A = pressure = force or weight / area = 50000 / (4 x 0.08) = 50000 / 0.32 = 156250 N/m2 or Pa (pascals)

 

Q8 A ski design team has to take into account the pressure created by the skier on the surface of deep snow.

They need to the calculate the effects of the variables which are (i) area of one ski, (ii) weight of skier, (iii) pressure created by the skier on the snow and (iv) the pressure the snow can take without the skier sinking in too much!

If the maximum acceptable snow pressure is 5000 N/m2, for a single ski surface area of 0.15 m2, what is the maximum weight the skier can be?

P = F/A, so max. weight = F = P x A = pressure x area = 5000 x 015 = 750N

 

Q9 A ski design team has to take into account the pressure created by the skier on the surface of deep snow.

They need to the calculate the effects of the variables which are (i) area of one ski, (ii) weight of skier, (iii) pressure created by the skier on the snow and (iv) the pressure the snow can take without the skier sinking in too much!

If the maximum acceptable snow pressure is 4000 N/m2, what is the minimum single ski surface area acceptable, for a skier of weight 800 N?

P = F/A, so min. area A = F/P = weight/pressure = 800/4000 = 0.2 m2

 

Q10 A bag of sugar has a base of 6 cm x 10 cm. If it weighs 18 N, what pressure does it create standing on a shelf?

P = F/A = pressure = force or weight / total area = 18 / (6 x 10) = 18/60 = 0.3 N/cm2

Conversion: 1 m2 = 104 cm2

so, 0.3 x 104 = 3000 Pa (pascals)

 

Q11 A stiletto heal has a base area of 3 cm2.

If the woman weighs 750 N, what pressure does she create on the floor when standing on one heel?

P = F/A = pressure = force or weight / total area = 750 / 3 = 250 N/cm2

Conversion: 1 m2 = 104 cm2

so, 250 x 104 = 2.5 x 106 N/m2 (Pa)

 

Q12 A waste skip a base of 2m x 4m. If it weighs 10000 N when full, what pressure does it create when standing on the road?

P = F/A = pressure = force or weight / total area = 10000/(2 x 4) = 10000/8 = 1250 N/m2 (Pa)

 

Q13 A brick has a base of 10 cm x 25 cm and weighs 30 N. what pressure does a stack of ten bricks create simulating the pressure created by a low wall?

P = F/A = pressure = force or weight / total area = (30 x 10) / (10 x 25) = 300 / 250 = 1.2 N/cm2

Conversion: 1 m2 = 104 cm2

so, 1.2 x 104 = 1.2 x 104 N/m2 (Pa)

 

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Index physics Forces notes 6. Forces & pressure in fluids, calculations

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