6.3 Forces, Friction, Pressure & Hydraulics

Forces and Friction

A force is a push or a pull acting upon an object as a result of its interaction with another object. Forces are vector quantities, meaning they have both a magnitude (size) and a direction. When multiple forces act on an object, they combine to form a net force. If two forces pull in opposite directions, the net force is the difference between them, in the direction of the larger force.

Friction

Friction is a resistive force that opposes the relative motion or tendency of such motion of two surfaces in contact. There are two primary types of friction to understand:

• Static Friction: The friction that exists between a stationary object and the surface on which it's resting. Static friction must be overcome to start moving an object.
• Kinetic (Dynamic) Friction: The friction that acts between moving surfaces.

Crucially, static friction is almost always greater than kinetic friction. This is why it takes a massive shove to get a heavy piece of furniture moving across a carpet, but once it is sliding, it requires much less force to keep it moving. Factors affecting friction include the roughness of the surfaces and the normal force (the weight of the object pressing down).

Pressure

In mechanical comprehension, it is essential to differentiate between force and pressure. While force is a total push or pull, pressure is a measure of how that force is distributed over a specific area.

The formula is: Pressure = Force / Area (P = F / A)

Where:

• Pressure (P) is measured in Pascals (Pa), where 1 Pascal = 1 Newton per square meter (N/m²), or in pounds per square inch (psi).
• Force (F) is measured in Newtons (N).
• Area (A) is measured in square meters (m²).

The Area Effect: From the formula, we can see that for a constant force, decreasing the area increases the pressure. This explains why a sharp knife cuts better than a dull one—the force of your hand is concentrated onto the incredibly small area of the sharp blade edge, generating immense pressure. Conversely, snowshoes prevent you from sinking into deep snow by spreading your body weight over a large area, thereby reducing the pressure applied to the snow.

Hydraulics and Pascal's Principle

Hydraulic systems use confined liquids (like oil or water) to transmit power. Liquids are practically incompressible, making them excellent mediums for transferring force. The foundation of fluid power is Pascal's Principle, which states that a change in pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of its container.

Force Multiplication in Hydraulics

Hydraulic systems can act as a "liquid lever," multiplying force based on differences in piston area.

Imagine a system with a small input piston (Piston 1) connected by a fluid-filled tube to a much larger output piston (Piston 2).

• The pressure generated at Piston 1 is: P1 = F1 / A1
• According to Pascal, this same pressure reaches Piston 2: P2 = P1
• The force exerted by Piston 2 is: F2 = P2 × A2

If the area of Piston 2 is 10 times larger than the area of Piston 1, the output force (F2) will be 10 times greater than the input force (F1).

Worked Example: An input piston has an area of 2 m² and an input force of 50 N is applied.

1. Calculate Pressure: P = 50 N / 2 m² = 25 Pascals.
2. The fluid transmits 25 Pascals of pressure to the output piston.
3. The output piston has an area of 10 m².
4. Calculate Output Force: F = Pressure × Area = 25 Pa × 10 m² = 250 N. The force has been multiplied by 5 (because the area increased by a factor of 5).

Like mechanical levers, there is a trade-off: to move the large piston up by 1 meter, the small piston must be pushed down 5 meters. Energy is conserved.

Fluid Mechanics Basics

Liquid Levels

A common mechanical principle is that "water finds its own level." If you have a series of connected containers of various shapes and sizes, all open to the atmosphere and filled with a liquid, the surface of the liquid will reach the exact same height in all of the containers, regardless of their shape or volume. This happens because the atmospheric pressure and gravity act uniformly across the system.

Buoyancy and Archimedes' Principle

When an object is submerged in a fluid, the fluid exerts an upward force on it. This upward force is called buoyancy. Archimedes' Principle states that the buoyant force on an object is equal to the weight of the fluid displaced by the object.

• If the object is denser than the fluid, it displaces a volume of fluid that weighs less than the object itself. The buoyant force is insufficient, and the object sinks (e.g., a rock in water).
• If the object is less dense than the fluid, it will displace a volume of fluid equal to its own weight before becoming fully submerged. The upward buoyant force matches the downward force of gravity, and the object floats (e.g., a wooden block in water).

This explains how massive steel ships can float: the hull is hollow and filled with air, so the average density of the entire ship is less than that of the water it displaces.