Introduction to Pressure and Upthrust
Have you ever wondered why your ears "pop" when you go up a mountain, or why a massive steel ship can float on the ocean while a tiny pebble sinks? This chapter explores the invisible forces at work in liquids and gases (which we call fluids). We will look at how pressure changes as we move through air or water and how these forces create upthrust.
What is Pressure?
Pressure is a measure of how much force is spread over a certain area. If you apply the same force over a smaller area, the pressure is much higher.
The Formula
To calculate pressure, we use this formula:
\[P = \frac{F}{A}\]
Where:
\(P\) = Pressure (measured in Pascals, \(Pa\) or Newtons per square metre, \(N/m^2\))
\(F\) = Force normal to the surface (measured in Newtons, \(N\))
\(A\) = Area of the surface (measured in metres squared, \(m^2\))
Analogy: Think about walking on snow. If you wear normal shoes, your weight (force) is concentrated on a small area, and you sink. If you wear wide snowshoes, the same weight is spread over a much larger area, so the pressure is lower and you stay on top!
Quick Review: Key Units
In Physics (1PH0), always ensure your units are correct before calculating:
1. Force must be in Newtons (\(N\)).
2. Area must be in \(m^2\). If you are given \(cm^2\), you must convert it!
3. 1 Pascal (\(Pa\)) is exactly the same as \(1 N/m^2\).
Key Takeaway: Pressure is directly proportional to force but inversely proportional to area. Small area = Big pressure!
Atmospheric Pressure
We live at the bottom of a deep "ocean" of air called the atmosphere. This air has weight, and it presses down on everything.
Pressure and Height (15.7P)
As you go higher up (increasing altitude), the atmospheric pressure decreases. There are two main reasons for this:
1. The "Weight" of Air: When you are at sea level, there is a tall column of air above you pressing down. When you are on a mountain, there is less air above you, so there is less weight pressing down.
2. Density: The air is less dense higher up. There are fewer air molecules in a certain volume, meaning fewer collisions and less pressure.
Did you know? Your ears pop because the air pressure inside your ear is trying to balance out with the changing air pressure outside as you change altitude!
Pressure in Liquids (Fluids)
Just like air, liquids exert pressure. However, because liquids are much denser than air, the pressure changes much more quickly.
How Pressure Acts
In a fluid, pressure acts equally in all directions. If you submerge a ball in water, the water presses on the top, bottom, and sides simultaneously.
Depth and Density (15.12P - 15.13P)
Two things determine the pressure at a point in a liquid:
1. Depth: As you go deeper, the weight of the liquid above you increases. This increases the pressure.
2. Density: A denser liquid (like salt water compared to fresh water) is heavier for the same volume. This exerts more pressure at the same depth.
Calculating Liquid Pressure (Higher Tier Only - 15.14P)
For Higher Tier students, you need to calculate the pressure due to a column of liquid using this formula from the equation sheet:
\[P = h \times \rho \times g\]
Where:
\(P\) = Pressure (\(Pa\))
\(h\) = Height (depth) of the column (\(m\))
\(\rho\) = Density of the liquid (\(kg/m^3\)) (Note: \(\rho\) is the Greek letter 'rho')
\(g\) = Gravitational field strength (\(N/kg\)), which is usually \(10 N/kg\) on Earth.
Key Takeaway: Pressure in a liquid increases if the depth increases or the density of the liquid increases.
Upthrust, Floating, and Sinking
Have you ever noticed that you feel "lighter" when you hop into a swimming pool? This is due to a force called upthrust.
What causes Upthrust? (15.15P)
When an object is submerged in a fluid, the bottom of the object is at a greater depth than the top. As we learned earlier, greater depth means greater pressure.
This means the upward force on the bottom of the object is larger than the downward force on the top. This creates a resultant force upwards. This resultant force is Upthrust.
Floating and Sinking (15.16P - 15.17P)
Whether an object floats or sinks depends on the balance between its weight and the upthrust acting on it.
1. To Sink: If the object's weight is greater than the maximum upthrust it can experience, it will sink. This happens if the object is denser than the fluid it is in.
2. To Float: If an object is less dense than the fluid, it will float. As it sinks into the fluid, it displaces (pushes aside) the fluid. It will stay floating when it has displaced enough fluid so that the upthrust equals the weight of the object.
Example: A wooden block is less dense than water. It floats because it only needs to displace a small amount of water for the upthrust to equal its weight. A steel marble is much denser than water; even when fully submerged, the upthrust is smaller than its weight, so it sinks.
Summary Table: Floating vs Sinking
Object Density > Fluid Density \(\implies\) Weight > Upthrust \(\implies\) Sinks
Object Density < Fluid Density \(\implies\) Weight = Upthrust (when partially submerged) \(\implies\) Floats
Common Mistakes to Avoid
1. Confusing Mass and Weight: In pressure and upthrust questions, remember that weight is a force (\(W = m \times g\)). Always use Newtons, not kilograms, in the pressure formula.
2. Forgetting Units: Depth (\(h\)) must be in metres. If a question gives you "20 cm deep", you must use \(0.2 m\).
3. Atmospheric Pressure: Don't forget that atmospheric pressure is always there! If you are calculating the total pressure at the bottom of a pool, you have to add the water pressure to the air pressure above the surface.
Quick Review: Upthrust is an upward force caused by the difference in pressure between the top and bottom of an object. If Upthrust equals Weight, the object floats!