Calculating pressure
Pressure is A push or a pull. The unit of force is the newton (N). per unit area. Pressure determines the effect of a force on a surface.
Pressure exerted by different shoes
Different styles of shoe can cause different pressures due to their area.
Flat shoes spread the force over a large area, reducing the pressure. Snow shoes have a much larger area than feet to spread the force over a larger area and reduce the pressure on the snow - this stops people sinking into the snow.
High heeled shoes transfer the force through a much smaller area, causing a much greater pressure. It will hurt more if a person steps on someone’s foot in high heels than if they are wearing flat shoes. This is also why accidentally stepping on a small object barefoot hurts so much - the force acts on a small area and the pressure is increased.
Importance of pressure
Pressure is important in a range of everyday situations.
When using a sharp knife, the small area of the blade creates a large pressure, making cutting easier.
Having caterpillar tracks on vehicles means their weight acts over a large area. This reduces the pressure they exert and are less likely to sink in to wet ground.
Question
A metal box is 60 cm long, 20 cm wide and 50 cm tall.
It has a weight of 300 N. Find the maximum pressure, in N/cm2, which the box can exert on the top of a table.
The maximum pressure will occur when the face with minimum area is in contact with the table.
The face with minimum area has dimensions 20 cm by 50 cm.
Area = 20 cm x 50 cm.
A = 1 000 cm2.
Force on the table = 300 N.
\(p = \frac{\text{F}}{\text{A}}\)
\(p = \frac{\text{300 N}}{\text{1000 cm}^{2}}\)
p = 0.3 N/cm2
The maximum pressure exerted by the box is 0.3 N/cm2.
Question
A girl standing on one foot exerts a pressure of 6 N/cm2 on the ground. If the area of her foot is 75 cm2, calculate the downward force.
F = pA.
p = 6 N/cm²
A = 75 cm²
P = 6 N/cm² × 75 cm²
P = 450 N.
The downward force exerted by the girl is 450 N.
Calculating pressure in fluids
To calculate pressure, use the equation:
\(\text{pressure} = \frac{\text{force}}{\text{area}}\)
\(p = \frac{F}{A}\)
This is when:
- pressure (p) is measured in pascals (Pa)
- force (F) is measured in newtons (N)
- area (A) is measured in metres squared (m2)
One pascal is one newton per square metre. Pressure can also be measured in newtons per square centimetre.
Example
A fluid exerts a force of 50 N over an area of 2 m2. Calculate the pressure on the surface.
\(p = \frac{F}{A}\)
\(p = 50 \div 2\)
\(p = 25 Pa\)
Question
A fluid exerts a force of 150 N over an area of 1.2 m2. Calculate the pressure on the surface.
\(p = \frac{F}{A}\)
\(p = 150 \div 1.2\)
\(p = 125 Pa\)
Calculating pressure in a liquid
Liquids and gases are A substance that can flow, such as a liquid or a gas.. The pressure in fluids causes a force The support force exerted upon an object that is in contact with another stable object. to a surface. A force that is normal to a surface acts at a right angle (90°) to it.
The The amount of force acting on a certain area. Pressure is measured in pascals (Pa) which are the same as newtons per metre squared (N/m²). in a liquid is different at different depths. Pressure increases as the depth increases. The pressure in a liquid is due to the A force that acts on mass due to gravity. Because weight is a force, it is measured in newtons (N). of the column of water above. Since the particles in a liquid are tightly packed, this pressure acts in all directions. For example, the pressure acting on a dam at the bottom of a reservoir is greater than the pressure acting near the top. This is why dam walls are usually wider at the bottom with a wedge-shape.
Extended syllabus content
If you are studying the Extended syllabus, you will also need to be able to recall and use the equation for the change in pressure beneath the surface of a liquid. Click 'show more' for this content:
The pressure caused by a column of liquid can be calculated using the equation:
change in pressure = density of the liquid × gravitational field strength × change in height of column
\(\Delta p = \rho g \Delta h\)
Where:
\((\Delta p)\) is the change in pressure
\((\rho)\) is the density of the liquid
\((g)\) is the gravitational field strength
\((\Delta h)\) is the change in height of the column
Example
The density of water is 1,000 kg/3. Calculate the pressure exerted by the water on the bottom of a 2.0 m deep swimming pool. (Gravitational field strength = 9.8 N/kg).
\(\Delta p = \rho g \Delta h\)
\(p = 2.0 \times 1,000 \times 9.8\)
\(p = 19,600~Pa\)
Quiz
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