Pressure in solids
Pressure in solids
- Unit 1: Particles & Pressure
- Unit 2: Forces & Motion
- Unit 3: Energy & Heat
- Unit 4: Electricity
- Unit 5: Magnetism & Electromagnetism
- Unit 6: Waves: Sound & Light
- Unit 7: Scientific Investigations
In this topic you will:
- recognise that forces can cause pressure on an area
- understand what affects pressure
- be able to calculate the pressure caused by a force on an area
Key words
- newtons per metre squared
- point
- pressure
- sharp
- surface area
The pushing effect of a force
The picture shows a knife being used to cut modelling clay.
The knife works because the force used to push down on the clay causes pressure on the clay.
You can think of pressure as the pushing effect of a force.
Suppose the clay is difficult to cut. How could you increase the pushing effect of the force?
You could:
- increase the force on the knife; as the force increases, the pressure increases
- use a sharper knife (a sharp knife has less surface area in contact with the clay); as the area decreases, the pressure increases.
The equation linking pressure, force and area is:
pressure = forcearea
Pressure is force divided by area. The unit of force is the newton. The unit of area is the metre squared. That means the unit of pressure is newtons per metre squared, or N/m2.
Sometimes you can use smaller areas, measured in cm2. If the area is in cm2 then the unit of pressure will be N/cm2.
If the area was in mm2, the unit of pressure would be N/mm2.
Some things have large areas to decrease pressure; others have small areas to increase pressure.
Important Concept: Pressure
Pressure is the amount of force applied to a particular area. The same force will create more pressure if it is applied over a smaller area.
Common Mistake
Some learners think pressure is only related to how heavy something is. In reality, both the force and the area are important — reducing the area increases the pressure even if the force stays the same.
Check your understanding
Show Answer
The pressure increases. A smaller contact area with the same force means more pressure is applied.
The camel has large feet. This means the force from the weight of the camel is applied over a large area. The pressure on the sand is decreased, so the camel will not sink in the sand.
The woman in the picture is lying on a bed of nails. Each nail has a sharp point on the end. The weight of the woman acts on many hundreds of nails, so the pressure from each nail is very small.
One end of this pin has a sharp point. The sharp point has a small area to increase pressure. The increased pressure means the pin will easily go into wood or card.
The other end has a larger surface area to decrease pressure. The decreased pressure means this part of the pin will not go into your finger.
Scissors have sharp blades. The area along the cutting edge of each blade is small. This increases the pressure, making things easier to cut.
Important Concept: Surface Area
Surface area is the total area of contact between an object and the surface it touches. A smaller surface area increases pressure when force is applied; a larger surface area decreases it.
Worked Example: Calculating Pressure
Question: An elephant stands on four feet.
The weight of the elephant is 50 000 N.
The total area of all four feet is 0.4 m².
What is the total pressure that the elephant exerts on the ground?
Answer:
pressure = force ÷ area
pressure = 50 000 ÷ 0.4
pressure = 125 000 N/m²
The unit of pressure here is N/m² because the area is given in m².
Question: The total weight of a bicycle and rider is 1000 N.
The bicycle has two tyres in contact with the ground. The weight is supported equally on both tyres.
The area of each tyre in contact with the ground is 5 cm².
What is the pressure that each tyre exerts on the ground?
Answer:
weight on each tyre = 1000 ÷ 2 = 500 N
pressure = force ÷ area
pressure = 500 ÷ 5 = 100 N/cm²
The unit of pressure here is N/cm² because the area of the tyres is given in cm².
Worked Example: Calculating Force
Question:
A hammer is used to push a nail into wood.
The area of the point at the end of the nail is 1.5 mm².
The pressure needed for the nail to go into the wood is 50 N/mm².
Calculate the force needed from the hammer.
Answer:
pressure = force ÷ area
so, force = pressure × area
force = 50 × 1.5
force = 75 N
Questions
Show Answer
pressure = force ÷ area
- a nail that goes into wood has a sharp point
Show Answer
A sharp point has a small area. Since pressure = force ÷ area, a smaller area means greater pressure, allowing the nail to go in easily.
- shoes for walking on snow are wide and flat
Show Answer
Wide, flat shoes have a large area, which reduces the pressure on snow, helping prevent sinking.
- m²
Show Answer
N/m²
- cm²
- mm²
Show Answer
cm²: N/cm²
mm²: N/mm²
Calculate the pressure that the box exerts on the ground.
Show your working and give your answer in N/m².
Show Answer
pressure = 60 ÷ 0.5 = 120 N/m²
The area of one tyre in contact with the ground is 150 cm².
Calculate the pressure that one tyre exerts on the ground.
Show your working and give your answer in N/cm².
Show Answer
Each tyre carries 8000 ÷ 4 = 2000 N
pressure = 2000 ÷ 150 = 13.33 N/cm²
Pressure needed is 40 N/mm².
Calculate the force needed to push it into the wall.
Show your working and give the unit with your answer.
Show Answer
force = pressure × area = 40 × 0.5 = 20 N
Think Like a Scientist
You will investigate how the pressure that a person exerts on the floor varies. This is now an individual activity.
• A person willing to be weighed (you)
• A bathroom scale (if body mass is not known)
• Sheets of squared paper
• Pencil
Step 2. Convert your mass to weight using:
weight in N = mass in kg × strength of gravity in N/kg
(Use gravity = 10 N/kg)
Step 3. Stand with one foot on a piece of squared paper while wearing shoes.
Step 4. Use a pencil to draw around your foot.
Step 6. Repeat with both feet to get the total area.
Step 7. Calculate the pressure when:
- a. Standing equally on both feet
- b. Standing only on one foot
Step 10. Measure the area of contact and calculate the pressure again.
a. How could you calculate the contact area with the ground?
b. Predict how pressure changes when lying vs standing, and explain your answer.
- a. How force affects pressure
- b. How area affects pressure
- c. Calculating pressure from force and area
- d. Units of pressure from force and area units
Show Answer
Because the same force is applied over a smaller area, increasing the pressure.
Show Answer
Pressure would decrease because the body weight is spread over a much larger surface area.
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Ballet dancers often balance on the front of one foot or toes during routines.