How Pressure is Related to Force and Area

What Do You Mean By Thrust And Pressure

Thrust

• The force acting normally on surface is called ‘thrust’.
• This is a vector quantity.
• It is measured in newton (N).

Pressure

• The thrust on an unit area of a surface is called ‘pressure’.
  
• \(\text{Pressure}=\frac{\text{Thrust}}{\text{Area}}\text{   or   P}=\frac{F}{A}\)
• Unit: The SI unit of pressure is newton per meter square or N/m², other units of pressure are pascal and bar.
• One Pascal: One pascal is defined as the pressure exerted on a surface area of 1m² by a thrust of 1 newton.
  i.e. 1 Pascal = 1 N/m²

Some very important and useful devices like syringes, dropper, and drinking straw, work on the principle of pressure.

People also ask
Applications of Pressure in Daily Life

Some examples based on pressure

1. Inserting a pointed nail in a wooden block is an easier task than to insert a rod inside a wooden block with the same force because the nail has a smaller area and thus it will experience more pressure even with the same force.
2. A sharp knife cuts better than a blunt knife.
3. While walking, a man exerts more pressure on the ground in comparison to when he is standing.
4. Figure (a) shows a boy named Tarkan lying on a mattress. When he stands on the mattress as in Figure (b), he notices the mattress sinks deeper. The reason is that the pressure acting on the mattress when he is standing is greater than that when he is lying.
   

Activity

Aim: To observe the effect of pressure.
Materials needed: A sheaf (bundle) of paper and a sharpened pencil.
Method: Press the papers very hard with the butt end of the pencil. Now turn the pencil around and press very hard on the paper with the sharp end of the pencil.
Observation: You will find that if you press very hard, you may be able to make an impression on the paper with the pencil butt. However, with much less effort you could even make a hole in the paper with the sharp end.
Conclusion: The surface area of the pencil butt is larger than the surface area of the sharp end. Therefore, with a much smaller force a greater pressure is produced with the sharp end of the pencil.

Variation of Pressure with Area
Increasing the area over which a particular force acts decreases the pressure produced. The converse is also true decreasing the area over which a particular force acts increases the pressure produced. For example, the pointed end of a high-heeled shoe exerts a greater pressure than the flat end, as the force is acting over a smaller area at the pointed end.

Thrust and Pressure Example Problems with Solutions

Example 1. A force of 150 N is applied on an area of 1.5 m². Calculate the pressure exerted.
Solution:    Force, F = 150 N; area, A = 1.5 m²
\( \text{Pressure}=\frac{\text{Force}\,}{\text{Area}} \)
\( \text{P}=\frac{\text{F}\,}{\text{A}}=\frac{\text{150N}\,}{\text{1}\text{.5}{{\text{m}}^{\text{2}}}}=100\text{ N/}{{\text{m}}^{\text{2}}} \)

Example 2. A force of 500 dynes is applied on an area of 20 cm². Calculate the pressure exerted.
Solution:    Force, F = 500 dynes = 500 × 10^-5 newton
Area, A = 20 cm² = 20 × 10^-4 m²
\( \text{Pressure},\text{ P}=\frac{\text{F}\,}{\text{A}}=\frac{\text{500 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-5}}}\text{N}}{\text{20 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}{{\text{m}}^{\text{2}}}}=2.5\text{ N/}{{\text{m}}^{\text{2}}} \)

Example 3. If a force of 2 N is applied over an area of 2 cm², calculate the pressure produced.
Solution:    To get the pressure in Pa, we have to make sure that the force is in newton and the area in m². Here, the area is in cm². To convert this into m², we have to divide the given area by 10,000.

Example 4. Calculate the pressure if a force of 2 N is applied on an area of 2 mm².
Solution:    Here, again the area is not in m². To change it into m², we divide the area by 1,000,000.

In these examples, we took the same force and calculated the pressure over two different areas. The same force acting on a smaller area produces a greater pressure.

Example 5. Refer to Figure. The weight of Tarkan is 360 N. Calculate the pressure exerted by Tarkan on the mattress when
(a) he is lying down as in Figure (a) and the area of contact between Tarkan and the mattress is 0.24 m².
(b) he is standing as in Figure (b) and the area of contact between his soles and the mattress is 0.024 m².
Solution:

Example 6. Figure shows a fireman standing on a piece of plywood placed on the surface of a muddy ground. The muddy ground can withstand a maximum pressure of 1050 Pa without sinking.

If the fireman has a mass of 78 kg and by considering the mass of the plywood as negligible, calculate the minimum area of the plywood that can be used. [g = 9.8 N kg^-1]
Solution:

Example 7. Tarkan is digging a hole with a spade.

Explain why it is important that the edge of the spade must be sharp.
Solution:
When the edge of the spade is Figure. sharp, its surface area of contact with the ground is small. When a force is applied, a big pressure is resulted. This makes the digging easier.

Example 8. Tarkan’s sister, Daryah weighs 436 N. She has three pairs of shoes X, Y and Z.

(a) By referring to Figure, calculate the pressure, P exerted on the floor by Daryah for each pair of the shoes.
(b) Which pair of shoes is most suitable to be worn by Daryah if she intends to go to the beach? Explain your answer.
Solution:

Example 9. Figure shows the webbed feet of a duck.

Explain why besides helping in the paddling of water, the webbed feet of a duck also allow it to move around more easily on the muddy ground.
Solution:
The webbed feet provide a big surface area of contact between the feet of the duck and the ground. This reduces the pressure exerted on the ground. The legs will not sink too deeply into the muddy ground.