Pressure, Force, and Area

Pressure, Force, and Area

Pneumatic and Hydraulics

​Lesson Objectives

​To be able to:

• State the mathematical relationship between Pressure, Force, and Area

• Carry out calculations for pressure, force, and area

Pressure is the amount of force applied to a surface divided by the area over which the force is spread.

As such, the triangle shown adjacent can be used to describe the mathematical relationship between Pressure, Force, and Area.

​

​What is Pressure?

Pressure: Measured in Pascals (Pa) which is 1 Newton per square metre (N/m²)

Force: Measured in Newtons (N)

Area: Measured in square-metres (m²)

​Formulas for Pressure, Force, and Area

• Pressure is proportional to force, meaning pressure will increase when force increases

• Pressure is inversely proportional to area, meaning pressure will decrease when area increases

​Proportionality

Since:

Practice Questions

Use the mathematical relationship between Pressure, Force, and Area to solve the following problems:

Multiple Choice

A force of 500 N is exerted over an area of 0.125 m². Calculate the pressure produced.

• 3000 Pa

• 3500 Pa

• 4000 Pa

• 4500 Pa

Multiple Choice

A force of 15 kN is exerted over an area of 5 m². Calculate the pressure produced.

• 3 Pa

• 3 kPa

• 3 MPa

• 3 GPa

Multiple Choice

What is the force exerted if a pressure of 50 Pa is applied over an area of 2 m²?

• 25 N

• 50 N

• 75 N

• 100 N

Multiple Choice

What is the force exerted if a pressure of 1 kPa is applied over an area of 0.5 m²?

• 300 N

• 400 N

• 500 N

• 600 N

Multiple Choice

A force of 250 N is exerted to produce a pressure of 1,750 Pa. Calculate the area over which the force is applied.

• 5 m²

• 6 m²

• 7 m²

• 8 m²

Multiple Choice

A force of 1.3 kN is exerted to produce a pressure of 1.04 kPa. Calculate the area over which the force is applied.

• 0.75 m²

• 1.25 m²

• 1.75 m²

• 2.25 m²

Math Response

A force of 1500 N is exerted over an area of 1.2 m². Calculate the pressure produced.

Your answer will be in Pa (so not kPa or MPa or GPa).

Type answer here

Correct Answer: 1250

Deg^°

Rad

Math Response

A force of 2.5 kN is exerted over an area of 0.4 m². Calculate the pressure produced.

Your answer will be in Pa (so not kPa or MPa or GPa).

Type answer here

Correct Answer: 6250

Deg^°

Rad

Math Response

A force of 12 kN produces a pressure of 15 kPa. Calculate the area over which this force is applied.

Your answer will be in m².

Type answer here

Correct Answer: 0.8

Deg^°

Rad

Math Response

An object weighing 1,600 N is placed on a surface. If the pressure exerted on the surface is 12,500 Pa, what is the area of contact?

State your answer to 2 decimal places.

Your answer will be in m².

Type answer here

Correct Answer: 0.13

Deg^°

Rad

Math Response

A force is applied over an area of 0.15 m² producing a stress of 1.6 kPa. Calculate the force applied.

Your answer will be in Newtons.

Type answer here

Correct Answer: 240

Deg^°

Rad

Math Response

A car tyre is inflated to a pressure of 250 kPa. If the area of contact with the ground is 0.038 m², what is the force exerted by the tyre on the ground?

Your answer will be in Newtons.

Type answer here

Correct Answer: 9500

Deg^°

Rad

Multiple Choice

Difficulty level: Hard!

A 32,000 N force is applied over a circular plate with a radius of 0.5 m. Calculate the pressure acting on the plate.

State your answer to 2 decimal places.

Tip: Work out the area of the circular plate first using the information given in the question.

• 40,743.67 Pa

• 38,875.74 Pa

• 36,589.43 Pa

• 33,872.92 Pa

Math Response

Difficulty level: Hard!

A 36 kN force is applied over a square plate with edges of 0.75 m. Calculate the pressure acting on the plate.

Your answer will be in Pascals (so not in kPa, MPa or GPa).

Tip: Work out the area of the square plate using the information given in the question.

Type answer here

Correct Answer: 64000

Deg^°

Rad

Math Response

Difficulty level: Hard!

A piston with a diameter of 0.052 m exerts a pressure of 105,640 Pa. What force is exerted by the piston?

State your answer to 2 decimal places.

Your answer will be in Pascals (so not in kPa, MPa or GPa).

Tip: Work out the cross sectional area of the piston using the information given in the question.

Type answer here

Correct Answer: 224.35

Deg^°

Rad

​Lesson Objectives - Recap

​You should now be able to:

• State the mathematical relationship between Pressure, Force, and Area

• Carry out calculations for pressure, force, and area