(d) The lorry has 6 tyres.
State the relationship between pressure, force and area.
Youce is Puspoor ruil
area is around the object
Pressure is puce the door
m The pressure in each tyre is 240 kPa.
The weight of the lorry is 180 KN.
Calculate the area of each tyre that is in contact with the road.
Answers
Answer:
Pressure Force Area
Pressure is a measure of how much force is applied over a given area of an object, so it is calculated by dividing the amount of force being applied by the area over which it is being applied.
Make sure you are happy with the following topics before continuing.
Rearranging formulae
Units and conversions
Level 4-5
Pressure Force Area – Formula
Pressure, force and area are all related by the formula:
p = \dfrac{F}{A}p=
A
F
where pp is the pressure, FF is force, and AA is area. You can rearrange this formula to find the other two, for example, if we multiply both sides of the equation by AA, then swap the left-hand side and right-hand side, we get.
F = p \times AF=p×A
So, we we can calculate the force by multiplying the pressure by the area.
Since area is measured in square metres (m^2
2
), and force is measured in Newtons (N), the standard units for pressure are Newtons per square metre (N/m^2
2
). These are compound units (for more information, see Conversions revision).
Level 4-5
Pressure Force Area – Formula Triangle
A quick way of remembering how to calculate one of either pressure, force or area using the other two is to use the triangles below.
The horizontal line means divide and the \times× symbol means multiply. We then:
We then cover up the one we want to find (represented by a red circle) and substitute values into the formula for the two remaining quantities in the triangle.
Pressure Force Area Formula Pyramid
p = \dfrac{F}{A} \,\,\,\,\,\,\,p=
A
F
\,\,\,\,\,\,\,\,\,\, F = p\times A\,\,\,\,\,\,\,\,\,F=p×A \,\,\,\,\,\,\,\,\, A = \dfrac{F}{p}A=
p
F
Level 4-5
Example 1: Calculating Pressure
A force of 150150 N is being applied over an area measuring 0.50.5 m^2
2
. Calculate the pressure on the object ensuring you give the correct units.
[2 marks]
Pressure Force Area Formula Pyramid
We’re looking for pressure, so constructing the triangle and covering up the pp, we must divide the force by the area. So
\text{Pressure } = 150 \div 0.5 = 300Pressure =150÷0.5=300 N/m^2
2
Level 4-5
Example 2: Calculating Force
A woman is applying 300300 N/m^2
2
of pressure onto a door with her hand. Her hand has area 0.020.02 m^2
2
. Work out the force being applied.
[2 marks]
Pressure Force Area Formula Pyramid
We’re looking for force, so constructing the triangle and covering up the FF, we must multiply the pressure by the area. So
\text{Force } = 300 \times 0.02 = 6Force =300×0.02=6 N
Level 4-5
Example 3: Calculating Area
Pressure of 150150 N/m^2
2
is experienced when a force of 22 kN is applied. Calculate the area over which the force is applied to obtain the pressure stated.
[2 marks]
Pressure Force Area Formula Pyramid
Now, before we do any calculations, we need to make sure our units are in the same form. In this example we need to convert kilo-newtons into newtons by multiplying by 10001000. This gives us 20002000 N.
We’re looking for area, so constructing the triangle and covering up the AA, we must divide the force by the pressure. So
\text{Area } = 2000 \div 150 = 13.3Area =2000÷150=13.3 m^2
2
Level 4-5
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Example Questions
Question 1: A force of 185.6185.6 N is applied to a square of side length 33 m. Work out the pressure on the square to 33 significant figures.
[2 marks]
Level 4-5
Question 2: A man with a weight of 740740 N is standing on one leg. His foot is exerting 2312.52312.5 N/m^2
2
of pressure onto the ground. What is the surface area of the bottom of his foot?
[2 marks]
Level 4-5
Question 3: A shipping container is removed from a ship and placed on the ground. The area of the container in contact with the ground is 1616 m^2
2
. The pressure exerted on the floor is 24802480 N/m^2
2
.
What force is being exerted by the shipping container on the ground?
[2 marks]
Level 4-5
Question 4: A cylinder is resting on one of its circular faces on the ground. The weight of the cylinder is 48724872 N and the cylinder exerts a pressure of 812812 N/m^2
2
on the ground.
To 22 decimal places, what is the diameter of the cylinder?
[4 marks]
Level 4-5
Question 5: A cube and a square-based pyramid exert the same pressure on the ground.
The square of the pyramid’s base has a side length of 88 metres and has a weight of 440440 N. The cube has a weight of 110110 N. What is the side length of the cube?
[4 marks]
Level 4-5
GCSE Maths Revision Cards
Worksheets and Exam Questions
(NEW) Pressure Force Area Exam Style Questions - MME
Level 4-5 New Official MME
Exam Questions
Mark Scheme
Drill Questions
Density and Pressure - Drill Questions
Worksheet
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