Force & Pressure (OCR Gateway GCSE Physics)

• A fluid is either a liquid or a gas
• When an object is immersed in a fluid, the fluid exerts a pressure upon the object
  • This pressure is in addition to the pressure already exerted by the atmosphere

• For example, an object at sea level (on the surface of the sea) experiences a pressure of 101 kPa due to the atmosphere
• If this object is now immersed to a depth of 10 metres underwater, it experiences an extra pressure of 100 kPa due to the water
• This means that the object will experience a total pressure of

101 kPa + 100 kPa = 201 kPa

• This pressure arises due to both:
  • The water pressure
  • Atmospheric pressure

When an object is immersed in a fluid, it experiences pressure due to both the fluid and the atmosphere

The Force Exerted by a Fluid

• When an object is immersed in a fluid, the fluid will exert pressure, squeezing the object
  • This pressure is exerted evenly across the whole surface of the fluid and in all directions
  • The pressure exerted on objects in fluids creates forces against surfaces
  • These forces act at 90 degrees (at right angles or 'normal') to the surface

The pressure of a fluid on an object creates a force normal (at right angles) to the surface

Pressure & Depth

• When an object is immersed in a liquid, the liquid will exert a pressure, squeezing the object
• This pressure is exerted evenly across the whole surface of the liquid and in all directions
  • The greater the depth of the liquid, the greater the pressure
  • The greater the density of the liquid, the greater the pressure

• In a liquid, the pressure at a point increases with the height of the column of liquid about that point
  • If there is more liquid above that point, then the pressure is more

• This is because the pressure in a liquid is caused by the weight of the liquid pushing against objects immersed in the liquid
  • As the liquid becomes deeper, the amount of liquid (and hence the weight) increases which causes the pressure to increase

• This is why, for example, the pressure increases with the depth of the ocean
  • The pressure on the seabed is far higher than that on the surface of the ocean

• The weight of the liquid also depends on its density
  • A more dense liquid has a greater weight and therefore will exert a higher pressure

Pressure in a column of water increases with depth, shown by the strong and weak jet of water

• In a column of water, the highest pressure would be at the bottom
  • If a hole is made at the bottom of the column, the water will pour out with a large force
  • If a hole was made at the top of the column, the water will pour out with a small force
  • This is because of the difference in pressure in the column caused by the weight of the water

Atmospheric Pressure

• The Earth's atmosphere is a thin layer (relative to the size of the Earth) of air around it
  • It exerts a pressure of about 101 kPa at sea level

The Earth's atmosphere

• The atmosphere extends more than 100 km into space and becomes less dense with increasing altitude (height above sea level)
  • This means that the pressure becomes less too

• Atmospheric pressure various slightly from day to day, depending on the weather, and fine clear weather is usually associated with high pressure

• The graph below shows how the pressure varies with altitude:

Graph of atmospheric pressure against altitude

• Atmospheric pressure varies with height above a surface, for example, at sea level
• This is due to air molecules colliding with a surface creating atmospheric pressure
  • These molecules create a force per area of the surface which creates the pressure

• The number of air molecules (and so the weight of air) above a surface decreases as the height of the surface above ground level increases
  • This is also known as the density of the air

• Therefore, as height increases, there is always less air above a surface than there is at a lower height and the atmospheric pressure decreases with an increase in height

Atmospheric pressure decreases as the density of the molecules decreases

Pressure in Solids

• Pressure is defined as

The concentration of a force or the force per unit area

• For example, when a drawing pin is pushed downwards:
  • It is pushed into the surface, rather than up towards the finger
  • This is because the sharp point is more concentrated (a small area) creating a larger pressure

When you push a drawing pin, it goes into the surface (rather than your finger)

• Example 1: Tractors
  • Tractors have large tyres
  • This spreads the weight (force) of the tractor over a large area
  • This reduces the pressure which prevents the heavy tractor from sinking into the mud

• Example 2: Nails
  • Nails have sharp pointed ends with a very small area
  • This concentrates the force, creating a large pressure over a small area
  • This allows the nail to be hammered into a wall

Calculating Pressure between Solids

• The pressure between solids can be calculated using the equation:

• Pressure is measured in the units Pascals (Pa)
• The area should always be the cross-sectional area of the object
  • This means the area where the force is at right angles to it

• This equation can be rearranged with the help of a formula triangle:

Force, pressure, area formula triangle

• This equation tells us that:
  • If a force is spread over a large area it will result in a small pressure
  • If it is spread over a small area it will result in a large pressure

High heels produce a higher pressure on the ground because of their smaller area, compared to flat shoes

Step 1: List the known quantities

• • Cross-sectional area = 2.73 × 10^-2 m²
  • Pressure = 5.28 × 10⁵ Pa

Step 2: Write down the relevant equation

Step 3: Rearrange for the force, F

F = p × A

Step 4: Substitute the values into the equation

F = (5.28 × 10⁵) × (2.73 × 10^-2) = 14 414.4

Step 5: Round to the appropriate number of significant figures and quote the correct unit

F = 14 400 N = 14.4 kN (3 s.f)

Calculating Pressure in a Fluid

• The pressure due to a column of liquid can be calculated using the equation

p = h × ρ × g

• Where:
  • p = pressure in pascals (Pa)
  • h = height of the column in metres (m)
  • ρ = density of the liquid in kilograms per metre cubed (kg/m³)
  • g = gravitational field strength on Earth in newtons per kilogram (N/kg)

• The force from the pressure is exerted evenly across the whole surface of an object in a liquid, and in all directions

The force from the pressure of objects in a liquid is exerted evenly across its whole surface

• The pressure is more accurately the difference in pressure at different depths h in a liquid, since the pressure changes with the depth