Pressure

(Triple Only)

Pressure on a surface is the force acting at a right angle to the surface per unit area -> it is a measure of the size of the force over a given area.

Formula:

Pressure is directly proportional to the force applied to a surface, . As the force increases, pressure increases. However, pressure is also inversely proportional to the area. As the area increases, the pressure decreases.

For example, if you press your finger onto a table, you're applying a force over the area of your fingertip. But if you press a sharp pencil onto the table, as the same force is concentrated on a tiny area, the pencil dents the table as the pressure is much higher.

-> If the area of your fingertip is , and the force applied is , the pressure would be:

-> If the area of a sharp pencil is , and the force applied is , the pressure would be:

We can clearly see from the maths that if the same force is applied to a smaller area, the force significantly increases.

A fluid is any substance that can flow, including liquids and gases.

Gas particles exert pressure on the walls of their container. For example, in a balloon, the gas particles move randomly and collide with the balloon's surface, thus exerting a force on the balloon at right angles to its surface. This force per unit area is pressure and keeps the balloon inflated.

Liquid particles exert pressure on the surfaces of substances. For example, imagine a ball submerged in a large beaker of water, as shown in the image below. The water particles collide with the surface of the ball, thus exerting a force on the ball at right angle to its surface, shown by the blue arrows. These collisions exert a force over a certain area of the ball, thus creating pressure.

We can see in the image above that the force arrows on the ball at the bottom are larger than at the top, indicating that the force per unit area on the ball is greater at the bottom than at the top. This is because pressure in a liquid increases with depth, as shown by the equation below:

Formula:

The pressure is directly proportional to height/depth in the water. At greater depths, there are more water particles above, all pushing down -> at greater depths, the weight of the water above, acting down, is greater, so the pressure is greater.

This difference in pressure between the top and bottom of the ball is known as upthrust. The larger pressure at the bottom of the ball, and thus the larger force per unit area on the bottom of the ball (shown by the larger blue arrows), creates a resultant force on the ball upwards. This is upthrust.

To prove with maths that there is a resultant force upwards on the ball, known as upthrust:

The top of the ball in the image above is below the surface. The density of water is . The pressure at teh top of the ball is,

The bottom of the ball is below the surface,

The pressure at the bottom is much larger than at the top. Therefore, the force acting on the ball at the bottom is much larger than at the top -> if we look at an area of of the ball, as , the force on the top of the ball is whereas, the force on the bottom is . This is a resultant force of, upwards, on the ball. This upward resultant force is called upthrust.

We can also see from the equation above that the denser the liquid is, the greater the pressure.

Factors That Influence Floating and Sinking

Whether an object floats or sinks depends on two forces: the weight of the object (acting downwards) and the upthrust from the fluid (acting upwards).

• If upthrust weight: The object floats (or rises up through the fluid).

• If upthrust weight: The object stays where it is (neutral buoyancy - like a submarine hovering)

• If upthrust weight: The object sinks

The atmosphere is a thin layer of air surrounding the Earth, about in depth. The atmosphere gets less dense as you go higher up, as there are fewer air particles in a given volume. This is why people who hike to high altitudes, like the top of Mount Everest, need to carry oxygen tanks.

Atmospheric pressure is created by air molecules colliding with surfaces. Every time an air molecule bounces off your skin, it exerts a tiny force. When you add up all the billions and billions of collisions happening every second, you get atmospheric pressure.

At sea level, there's a lot of air above you - the entire atmosphere is pressing down on you. But as you climb a mountain or go up in a plane, there's less and less air above you. Less air above -> less weight acting down -> less force per unit area -> lower pressure.

Think of it like being at the bottom of a swimming pool versus being near the surface. At the bottom, you have the whole depth of water above you creating pressure. Near the surface, there's hardly any water above you, so less pressure. The same principle applies to the atmosphere.

As you go higher:

• The number of air molecules above you decreases -> becomes less dense

• The weight of air above you decreases

• Therefore, the atmospheric pressure decreases

At sea level, atmospheric pressure is about (or ). It's equivalent to having a weight of about pressing on every square centimetre of your body. You don't notice it because the pressure inside your body balances it out.